id sid tid token lemma pos work_zpfso6pk3vf5df7625v6vawp2e 1 1 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 1 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 1 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 5 square square NNP work_zpfso6pk3vf5df7625v6vawp2e 1 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 7 root root NN work_zpfso6pk3vf5df7625v6vawp2e 1 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 9 of of IN work_zpfso6pk3vf5df7625v6vawp2e 1 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 11 probability probability NNP work_zpfso6pk3vf5df7625v6vawp2e 1 12     _SP work_zpfso6pk3vf5df7625v6vawp2e 1 13 density density NN work_zpfso6pk3vf5df7625v6vawp2e 1 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 15 function function VBP work_zpfso6pk3vf5df7625v6vawp2e 1 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 17 on on IN work_zpfso6pk3vf5df7625v6vawp2e 1 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 19 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 1 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 21 manifold manifold JJ work_zpfso6pk3vf5df7625v6vawp2e 1 22     _SP work_zpfso6pk3vf5df7625v6vawp2e 1 23 Article Article NNP work_zpfso6pk3vf5df7625v6vawp2e 1 24     _SP work_zpfso6pk3vf5df7625v6vawp2e 1 25 Accepted Accepted NNP work_zpfso6pk3vf5df7625v6vawp2e 1 26   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 27 Version Version NNP work_zpfso6pk3vf5df7625v6vawp2e 1 28     _SP work_zpfso6pk3vf5df7625v6vawp2e 1 29 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 1 30 , , , work_zpfso6pk3vf5df7625v6vawp2e 1 31   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 32 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 1 33   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 34 and and CC work_zpfso6pk3vf5df7625v6vawp2e 1 35   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 36 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 1 37 , , , work_zpfso6pk3vf5df7625v6vawp2e 1 38   _SP work_zpfso6pk3vf5df7625v6vawp2e 1 39 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 2 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 2 2 2018 2018 CD work_zpfso6pk3vf5df7625v6vawp2e 2 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 2 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 5 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 2 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 2 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 9 square square NNP work_zpfso6pk3vf5df7625v6vawp2e 2 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 11 root root NN work_zpfso6pk3vf5df7625v6vawp2e 2 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 13 of of IN work_zpfso6pk3vf5df7625v6vawp2e 2 14     _SP work_zpfso6pk3vf5df7625v6vawp2e 2 15 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 2 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 17 density density NN work_zpfso6pk3vf5df7625v6vawp2e 2 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 19 function function VBP work_zpfso6pk3vf5df7625v6vawp2e 2 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 21 on on IN work_zpfso6pk3vf5df7625v6vawp2e 2 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 23 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 2 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 2 25 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 2 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 3 1 Expert Expert NNP work_zpfso6pk3vf5df7625v6vawp2e 3 2     _SP work_zpfso6pk3vf5df7625v6vawp2e 3 3 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 3 4 : : : work_zpfso6pk3vf5df7625v6vawp2e 3 5   _SP work_zpfso6pk3vf5df7625v6vawp2e 3 6 International International NNP work_zpfso6pk3vf5df7625v6vawp2e 3 7   _SP work_zpfso6pk3vf5df7625v6vawp2e 3 8 Journal Journal NNP work_zpfso6pk3vf5df7625v6vawp2e 3 9   _SP work_zpfso6pk3vf5df7625v6vawp2e 3 10 of of IN work_zpfso6pk3vf5df7625v6vawp2e 3 11   _SP work_zpfso6pk3vf5df7625v6vawp2e 3 12 Knowledge knowledge NN work_zpfso6pk3vf5df7625v6vawp2e 3 13   _SP work_zpfso6pk3vf5df7625v6vawp2e 3 14 Engineering engineering NN work_zpfso6pk3vf5df7625v6vawp2e 3 15 . . . work_zpfso6pk3vf5df7625v6vawp2e 4 1 e12266 e12266 NNP work_zpfso6pk3vf5df7625v6vawp2e 4 2 . . . work_zpfso6pk3vf5df7625v6vawp2e 5 1 ISSN issn NN work_zpfso6pk3vf5df7625v6vawp2e 5 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 3 1468­0394 1468­0394 NNS work_zpfso6pk3vf5df7625v6vawp2e 5 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 5 doi doi XX work_zpfso6pk3vf5df7625v6vawp2e 5 6 : : : work_zpfso6pk3vf5df7625v6vawp2e 5 7     _SP work_zpfso6pk3vf5df7625v6vawp2e 5 8 https://doi.org/10.1111/exsy.12266 https://doi.org/10.1111/exsy.12266 NN work_zpfso6pk3vf5df7625v6vawp2e 5 9   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 10 Available available JJ work_zpfso6pk3vf5df7625v6vawp2e 5 11   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 12 at at IN work_zpfso6pk3vf5df7625v6vawp2e 5 13     _SP work_zpfso6pk3vf5df7625v6vawp2e 5 14 http://centaur.reading.ac.uk/75374/ http://centaur.reading.ac.uk/75374/ ADD work_zpfso6pk3vf5df7625v6vawp2e 5 15     _SP work_zpfso6pk3vf5df7625v6vawp2e 5 16 It -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 5 17   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 18 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 5 19   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 20 advisable advisable JJ work_zpfso6pk3vf5df7625v6vawp2e 5 21   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 22 to to TO work_zpfso6pk3vf5df7625v6vawp2e 5 23   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 24 refer refer VB work_zpfso6pk3vf5df7625v6vawp2e 5 25   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 26 to to IN work_zpfso6pk3vf5df7625v6vawp2e 5 27   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 28 the the DT work_zpfso6pk3vf5df7625v6vawp2e 5 29   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 30 publisher publisher NN work_zpfso6pk3vf5df7625v6vawp2e 5 31 ’s ’s POS work_zpfso6pk3vf5df7625v6vawp2e 5 32   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 33 version version NN work_zpfso6pk3vf5df7625v6vawp2e 5 34   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 35 if if IN work_zpfso6pk3vf5df7625v6vawp2e 5 36   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 37 you -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 5 38   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 39 intend intend VBP work_zpfso6pk3vf5df7625v6vawp2e 5 40   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 41 to to TO work_zpfso6pk3vf5df7625v6vawp2e 5 42   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 43 cite cite VB work_zpfso6pk3vf5df7625v6vawp2e 5 44   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 45 from from IN work_zpfso6pk3vf5df7625v6vawp2e 5 46   _SP work_zpfso6pk3vf5df7625v6vawp2e 5 47 the the DT work_zpfso6pk3vf5df7625v6vawp2e 5 48     _SP work_zpfso6pk3vf5df7625v6vawp2e 5 49 work work NN work_zpfso6pk3vf5df7625v6vawp2e 5 50 . . . work_zpfso6pk3vf5df7625v6vawp2e 6 1 See see VB work_zpfso6pk3vf5df7625v6vawp2e 6 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 6 3 Guidance guidance NN work_zpfso6pk3vf5df7625v6vawp2e 6 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 6 5 on on IN work_zpfso6pk3vf5df7625v6vawp2e 6 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 6 7 citing cite VBG work_zpfso6pk3vf5df7625v6vawp2e 6 8       _SP work_zpfso6pk3vf5df7625v6vawp2e 6 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 7 1 To to TO work_zpfso6pk3vf5df7625v6vawp2e 7 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 3 link link VB work_zpfso6pk3vf5df7625v6vawp2e 7 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 5 to to IN work_zpfso6pk3vf5df7625v6vawp2e 7 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 7 this this DT work_zpfso6pk3vf5df7625v6vawp2e 7 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 9 article article NN work_zpfso6pk3vf5df7625v6vawp2e 7 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 11 DOI DOI NNP work_zpfso6pk3vf5df7625v6vawp2e 7 12 : : : work_zpfso6pk3vf5df7625v6vawp2e 7 13   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 14 http://dx.doi.org/10.1111/exsy.12266 http://dx.doi.org/10.1111/exsy.12266 NNP work_zpfso6pk3vf5df7625v6vawp2e 7 15     _SP work_zpfso6pk3vf5df7625v6vawp2e 7 16 Publisher Publisher NNP work_zpfso6pk3vf5df7625v6vawp2e 7 17 : : : work_zpfso6pk3vf5df7625v6vawp2e 7 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 19 Wiley Wiley NNP work_zpfso6pk3vf5df7625v6vawp2e 7 20     _SP work_zpfso6pk3vf5df7625v6vawp2e 7 21 All all DT work_zpfso6pk3vf5df7625v6vawp2e 7 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 23 outputs output NNS work_zpfso6pk3vf5df7625v6vawp2e 7 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 25 in in IN work_zpfso6pk3vf5df7625v6vawp2e 7 26   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 27 CentAUR centaur NN work_zpfso6pk3vf5df7625v6vawp2e 7 28   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 29 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 7 30   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 31 protected protect VBN work_zpfso6pk3vf5df7625v6vawp2e 7 32   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 33 by by IN work_zpfso6pk3vf5df7625v6vawp2e 7 34   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 35 Intellectual intellectual JJ work_zpfso6pk3vf5df7625v6vawp2e 7 36   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 37 Property property NN work_zpfso6pk3vf5df7625v6vawp2e 7 38   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 39 Rights right NNS work_zpfso6pk3vf5df7625v6vawp2e 7 40   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 41 law law NN work_zpfso6pk3vf5df7625v6vawp2e 7 42 , , , work_zpfso6pk3vf5df7625v6vawp2e 7 43     _SP work_zpfso6pk3vf5df7625v6vawp2e 7 44 including include VBG work_zpfso6pk3vf5df7625v6vawp2e 7 45   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 46 copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 7 47   _SP work_zpfso6pk3vf5df7625v6vawp2e 7 48 law law NN work_zpfso6pk3vf5df7625v6vawp2e 7 49 . . . work_zpfso6pk3vf5df7625v6vawp2e 8 1 Copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 8 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 8 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 5 IPR IPR NNP work_zpfso6pk3vf5df7625v6vawp2e 8 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 7 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 8 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 9 retained retain VBN work_zpfso6pk3vf5df7625v6vawp2e 8 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 11 by by IN work_zpfso6pk3vf5df7625v6vawp2e 8 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 8 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 15 creators creator NNS work_zpfso6pk3vf5df7625v6vawp2e 8 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 17 or or CC work_zpfso6pk3vf5df7625v6vawp2e 8 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 19 other other JJ work_zpfso6pk3vf5df7625v6vawp2e 8 20     _SP work_zpfso6pk3vf5df7625v6vawp2e 8 21 copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 8 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 8 23 holders holder NNS work_zpfso6pk3vf5df7625v6vawp2e 8 24 . . . work_zpfso6pk3vf5df7625v6vawp2e 9 1 Terms term NNS work_zpfso6pk3vf5df7625v6vawp2e 9 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 9 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 5 conditions condition NNS work_zpfso6pk3vf5df7625v6vawp2e 9 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 7 for for IN work_zpfso6pk3vf5df7625v6vawp2e 9 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 9 use use VB work_zpfso6pk3vf5df7625v6vawp2e 9 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 11 of of IN work_zpfso6pk3vf5df7625v6vawp2e 9 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 13 this this DT work_zpfso6pk3vf5df7625v6vawp2e 9 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 15 material material NN work_zpfso6pk3vf5df7625v6vawp2e 9 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 17 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 9 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 19 defined define VBN work_zpfso6pk3vf5df7625v6vawp2e 9 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 21 in in IN work_zpfso6pk3vf5df7625v6vawp2e 9 22     _SP work_zpfso6pk3vf5df7625v6vawp2e 9 23 the the DT work_zpfso6pk3vf5df7625v6vawp2e 9 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 25 End end NN work_zpfso6pk3vf5df7625v6vawp2e 9 26   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 27 User User NNP work_zpfso6pk3vf5df7625v6vawp2e 9 28   _SP work_zpfso6pk3vf5df7625v6vawp2e 9 29 Agreement Agreement NNP work_zpfso6pk3vf5df7625v6vawp2e 9 30       _SP work_zpfso6pk3vf5df7625v6vawp2e 9 31 . . . work_zpfso6pk3vf5df7625v6vawp2e 10 1 www.reading.ac.uk/centaur www.reading.ac.uk/centaur VB work_zpfso6pk3vf5df7625v6vawp2e 10 2         _SP work_zpfso6pk3vf5df7625v6vawp2e 10 3 CentAUR centaur NN work_zpfso6pk3vf5df7625v6vawp2e 10 4     _SP work_zpfso6pk3vf5df7625v6vawp2e 10 5 http://centaur.reading.ac.uk/71187/10/CentAUR%20citing%20guide.pdf http://centaur.reading.ac.uk/71187/10/CentAUR%20citing%20guide.pdf NFP work_zpfso6pk3vf5df7625v6vawp2e 10 6 http://www.reading.ac.uk/centaur http://www.reading.ac.uk/centaur VBP work_zpfso6pk3vf5df7625v6vawp2e 10 7 http://centaur.reading.ac.uk/licence http://centaur.reading.ac.uk/licence NNP work_zpfso6pk3vf5df7625v6vawp2e 10 8 Central Central NNP work_zpfso6pk3vf5df7625v6vawp2e 10 9   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 10 Archive archive JJ work_zpfso6pk3vf5df7625v6vawp2e 10 11   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 12 at at IN work_zpfso6pk3vf5df7625v6vawp2e 10 13   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 10 15   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 16 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 10 17   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 18 of of IN work_zpfso6pk3vf5df7625v6vawp2e 10 19   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 20 Reading read VBG work_zpfso6pk3vf5df7625v6vawp2e 10 21     _SP work_zpfso6pk3vf5df7625v6vawp2e 10 22 Reading Reading NNP work_zpfso6pk3vf5df7625v6vawp2e 10 23 ’s ’s POS work_zpfso6pk3vf5df7625v6vawp2e 10 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 25 research research NN work_zpfso6pk3vf5df7625v6vawp2e 10 26   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 27 outputs output VBZ work_zpfso6pk3vf5df7625v6vawp2e 10 28   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 29 online online RB work_zpfso6pk3vf5df7625v6vawp2e 10 30 Estimating estimating NN work_zpfso6pk3vf5df7625v6vawp2e 10 31   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 32 the the DT work_zpfso6pk3vf5df7625v6vawp2e 10 33   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 34 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 10 35   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 36 Root root NN work_zpfso6pk3vf5df7625v6vawp2e 10 37   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 38 of of IN work_zpfso6pk3vf5df7625v6vawp2e 10 39   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 40 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 10 41     _SP work_zpfso6pk3vf5df7625v6vawp2e 10 42 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 10 43   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 44 Function function NN work_zpfso6pk3vf5df7625v6vawp2e 10 45   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 46 on on IN work_zpfso6pk3vf5df7625v6vawp2e 10 47   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 48 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 10 49   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 50 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 10 51     _SP work_zpfso6pk3vf5df7625v6vawp2e 10 52 Article Article NNP work_zpfso6pk3vf5df7625v6vawp2e 10 53     _SP work_zpfso6pk3vf5df7625v6vawp2e 10 54 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 10 55 , , , work_zpfso6pk3vf5df7625v6vawp2e 10 56   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 57 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 10 58   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 59 and and CC work_zpfso6pk3vf5df7625v6vawp2e 10 60   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 61 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 10 62 , , , work_zpfso6pk3vf5df7625v6vawp2e 10 63   _SP work_zpfso6pk3vf5df7625v6vawp2e 10 64 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 11 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 11 2 2018 2018 CD work_zpfso6pk3vf5df7625v6vawp2e 11 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 11 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 5 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 11 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 11 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 9 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 11 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 11 Root root NN work_zpfso6pk3vf5df7625v6vawp2e 11 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 13 of of IN work_zpfso6pk3vf5df7625v6vawp2e 11 14     _SP work_zpfso6pk3vf5df7625v6vawp2e 11 15 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 11 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 17 Density density NN work_zpfso6pk3vf5df7625v6vawp2e 11 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 19 Function function NN work_zpfso6pk3vf5df7625v6vawp2e 11 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 21 on on IN work_zpfso6pk3vf5df7625v6vawp2e 11 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 23 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 11 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 11 25 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 11 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 12 1 Expert Expert NNP work_zpfso6pk3vf5df7625v6vawp2e 12 2     _SP work_zpfso6pk3vf5df7625v6vawp2e 12 3 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 12 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 13 1 ISSN issn NN work_zpfso6pk3vf5df7625v6vawp2e 13 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 3 1468­0394 1468­0394 VBZ work_zpfso6pk3vf5df7625v6vawp2e 13 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 5 Available available JJ work_zpfso6pk3vf5df7625v6vawp2e 13 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 7 at at IN work_zpfso6pk3vf5df7625v6vawp2e 13 8     _SP work_zpfso6pk3vf5df7625v6vawp2e 13 9 http://centaur.reading.ac.uk/75843/ http://centaur.reading.ac.uk/75843/ CD work_zpfso6pk3vf5df7625v6vawp2e 13 10     _SP work_zpfso6pk3vf5df7625v6vawp2e 13 11 It -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 13 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 13 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 13 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 15 advisable advisable JJ work_zpfso6pk3vf5df7625v6vawp2e 13 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 17 to to TO work_zpfso6pk3vf5df7625v6vawp2e 13 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 19 refer refer VB work_zpfso6pk3vf5df7625v6vawp2e 13 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 21 to to IN work_zpfso6pk3vf5df7625v6vawp2e 13 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 23 the the DT work_zpfso6pk3vf5df7625v6vawp2e 13 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 25 publisher publisher NN work_zpfso6pk3vf5df7625v6vawp2e 13 26 ’s ’s POS work_zpfso6pk3vf5df7625v6vawp2e 13 27   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 28 version version NN work_zpfso6pk3vf5df7625v6vawp2e 13 29   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 30 if if IN work_zpfso6pk3vf5df7625v6vawp2e 13 31   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 32 you -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 13 33   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 34 intend intend VBP work_zpfso6pk3vf5df7625v6vawp2e 13 35   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 36 to to TO work_zpfso6pk3vf5df7625v6vawp2e 13 37   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 38 cite cite VB work_zpfso6pk3vf5df7625v6vawp2e 13 39   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 40 from from IN work_zpfso6pk3vf5df7625v6vawp2e 13 41   _SP work_zpfso6pk3vf5df7625v6vawp2e 13 42 the the DT work_zpfso6pk3vf5df7625v6vawp2e 13 43     _SP work_zpfso6pk3vf5df7625v6vawp2e 13 44 work work NN work_zpfso6pk3vf5df7625v6vawp2e 13 45 . . . work_zpfso6pk3vf5df7625v6vawp2e 14 1 Publisher publisher NN work_zpfso6pk3vf5df7625v6vawp2e 14 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 14 3   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 4 Wiley­Blackwell Wiley­Blackwell NNP work_zpfso6pk3vf5df7625v6vawp2e 14 5     _SP work_zpfso6pk3vf5df7625v6vawp2e 14 6 All All NNP work_zpfso6pk3vf5df7625v6vawp2e 14 7   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 8 outputs output NNS work_zpfso6pk3vf5df7625v6vawp2e 14 9   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 10 in in IN work_zpfso6pk3vf5df7625v6vawp2e 14 11   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 12 CentAUR centaur NN work_zpfso6pk3vf5df7625v6vawp2e 14 13   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 14 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 14 15   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 16 protected protect VBN work_zpfso6pk3vf5df7625v6vawp2e 14 17   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 18 by by IN work_zpfso6pk3vf5df7625v6vawp2e 14 19   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 20 Intellectual intellectual JJ work_zpfso6pk3vf5df7625v6vawp2e 14 21   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 22 Property property NN work_zpfso6pk3vf5df7625v6vawp2e 14 23   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 24 Rights right NNS work_zpfso6pk3vf5df7625v6vawp2e 14 25   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 26 law law NN work_zpfso6pk3vf5df7625v6vawp2e 14 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 14 28     _SP work_zpfso6pk3vf5df7625v6vawp2e 14 29 including include VBG work_zpfso6pk3vf5df7625v6vawp2e 14 30   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 31 copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 14 32   _SP work_zpfso6pk3vf5df7625v6vawp2e 14 33 law law NN work_zpfso6pk3vf5df7625v6vawp2e 14 34 . . . work_zpfso6pk3vf5df7625v6vawp2e 15 1 Copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 15 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 15 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 5 IPR IPR NNP work_zpfso6pk3vf5df7625v6vawp2e 15 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 7 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 15 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 9 retained retain VBN work_zpfso6pk3vf5df7625v6vawp2e 15 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 11 by by IN work_zpfso6pk3vf5df7625v6vawp2e 15 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 15 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 15 creators creator NNS work_zpfso6pk3vf5df7625v6vawp2e 15 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 17 or or CC work_zpfso6pk3vf5df7625v6vawp2e 15 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 19 other other JJ work_zpfso6pk3vf5df7625v6vawp2e 15 20     _SP work_zpfso6pk3vf5df7625v6vawp2e 15 21 copyright copyright NN work_zpfso6pk3vf5df7625v6vawp2e 15 22   _SP work_zpfso6pk3vf5df7625v6vawp2e 15 23 holders holder NNS work_zpfso6pk3vf5df7625v6vawp2e 15 24 . . . work_zpfso6pk3vf5df7625v6vawp2e 16 1 Terms term NNS work_zpfso6pk3vf5df7625v6vawp2e 16 2   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 16 4   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 5 conditions condition NNS work_zpfso6pk3vf5df7625v6vawp2e 16 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 7 for for IN work_zpfso6pk3vf5df7625v6vawp2e 16 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 9 use use VB work_zpfso6pk3vf5df7625v6vawp2e 16 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 11 of of IN work_zpfso6pk3vf5df7625v6vawp2e 16 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 13 this this DT work_zpfso6pk3vf5df7625v6vawp2e 16 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 15 material material NN work_zpfso6pk3vf5df7625v6vawp2e 16 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 17 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 16 18   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 19 defined define VBN work_zpfso6pk3vf5df7625v6vawp2e 16 20   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 21 in in IN work_zpfso6pk3vf5df7625v6vawp2e 16 22     _SP work_zpfso6pk3vf5df7625v6vawp2e 16 23 the the DT work_zpfso6pk3vf5df7625v6vawp2e 16 24   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 25 End end NN work_zpfso6pk3vf5df7625v6vawp2e 16 26   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 27 User User NNP work_zpfso6pk3vf5df7625v6vawp2e 16 28   _SP work_zpfso6pk3vf5df7625v6vawp2e 16 29 Agreement Agreement NNP work_zpfso6pk3vf5df7625v6vawp2e 16 30       _SP work_zpfso6pk3vf5df7625v6vawp2e 16 31 . . . work_zpfso6pk3vf5df7625v6vawp2e 17 1 www.reading.ac.uk/centaur www.reading.ac.uk/centaur VB work_zpfso6pk3vf5df7625v6vawp2e 17 2         _SP work_zpfso6pk3vf5df7625v6vawp2e 17 3 CentAUR centaur NN work_zpfso6pk3vf5df7625v6vawp2e 17 4     _SP work_zpfso6pk3vf5df7625v6vawp2e 17 5 Central Central NNP work_zpfso6pk3vf5df7625v6vawp2e 17 6   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 7 Archive archive JJ work_zpfso6pk3vf5df7625v6vawp2e 17 8   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 9 at at IN work_zpfso6pk3vf5df7625v6vawp2e 17 10   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 17 12   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 13 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 17 14   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 15 of of IN work_zpfso6pk3vf5df7625v6vawp2e 17 16   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 17 Reading Reading NNP work_zpfso6pk3vf5df7625v6vawp2e 17 18     _SP work_zpfso6pk3vf5df7625v6vawp2e 17 19 http://centaur.reading.ac.uk/licence http://centaur.reading.ac.uk/licence NNP work_zpfso6pk3vf5df7625v6vawp2e 17 20 http://www.reading.ac.uk/centaur http://www.reading.ac.uk/centaur NNP work_zpfso6pk3vf5df7625v6vawp2e 17 21 Reading reading NN work_zpfso6pk3vf5df7625v6vawp2e 17 22 ’s ’s '' work_zpfso6pk3vf5df7625v6vawp2e 17 23   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 24 research research NN work_zpfso6pk3vf5df7625v6vawp2e 17 25   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 26 outputs output VBZ work_zpfso6pk3vf5df7625v6vawp2e 17 27   _SP work_zpfso6pk3vf5df7625v6vawp2e 17 28 online online RB work_zpfso6pk3vf5df7625v6vawp2e 17 29 Estimating Estimating NNP work_zpfso6pk3vf5df7625v6vawp2e 17 30 the the DT work_zpfso6pk3vf5df7625v6vawp2e 17 31 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 17 32 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 17 33 of of IN work_zpfso6pk3vf5df7625v6vawp2e 17 34 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 17 35 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 17 36 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 17 37 on on IN work_zpfso6pk3vf5df7625v6vawp2e 17 38 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 17 39 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 17 40 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 17 41 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 17 42 and and CC work_zpfso6pk3vf5df7625v6vawp2e 17 43 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 17 44 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 17 45 Abstract Abstract NNP work_zpfso6pk3vf5df7625v6vawp2e 17 46 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 17 47 propose propose VBP work_zpfso6pk3vf5df7625v6vawp2e 17 48 that that IN work_zpfso6pk3vf5df7625v6vawp2e 17 49 the the DT work_zpfso6pk3vf5df7625v6vawp2e 17 50 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 17 51 root root NN work_zpfso6pk3vf5df7625v6vawp2e 17 52 of of IN work_zpfso6pk3vf5df7625v6vawp2e 17 53 a a DT work_zpfso6pk3vf5df7625v6vawp2e 17 54 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 17 55 density density NN work_zpfso6pk3vf5df7625v6vawp2e 17 56 function function NN work_zpfso6pk3vf5df7625v6vawp2e 17 57 can can MD work_zpfso6pk3vf5df7625v6vawp2e 17 58 be be VB work_zpfso6pk3vf5df7625v6vawp2e 17 59 represented represent VBN work_zpfso6pk3vf5df7625v6vawp2e 17 60 as as IN work_zpfso6pk3vf5df7625v6vawp2e 17 61 a a DT work_zpfso6pk3vf5df7625v6vawp2e 17 62 linear linear JJ work_zpfso6pk3vf5df7625v6vawp2e 17 63 combination combination NN work_zpfso6pk3vf5df7625v6vawp2e 17 64 of of IN work_zpfso6pk3vf5df7625v6vawp2e 17 65 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 17 66 kernels kernel NNS work_zpfso6pk3vf5df7625v6vawp2e 17 67 . . . work_zpfso6pk3vf5df7625v6vawp2e 18 1 It -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 18 2 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 18 3 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 18 4 that that IN work_zpfso6pk3vf5df7625v6vawp2e 18 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 18 6 if if IN work_zpfso6pk3vf5df7625v6vawp2e 18 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 18 8 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 18 9 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 18 10 centres centre VBZ work_zpfso6pk3vf5df7625v6vawp2e 18 11 and and CC work_zpfso6pk3vf5df7625v6vawp2e 18 12 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 18 13 width width NN work_zpfso6pk3vf5df7625v6vawp2e 18 14 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 18 15 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 18 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 18 17 then then RB work_zpfso6pk3vf5df7625v6vawp2e 18 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 18 19 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 18 20 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 18 21 parameter parameter NN work_zpfso6pk3vf5df7625v6vawp2e 18 22 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 18 23 can can MD work_zpfso6pk3vf5df7625v6vawp2e 18 24 be be VB work_zpfso6pk3vf5df7625v6vawp2e 18 25 formulated formulate VBN work_zpfso6pk3vf5df7625v6vawp2e 18 26 as as IN work_zpfso6pk3vf5df7625v6vawp2e 18 27 a a DT work_zpfso6pk3vf5df7625v6vawp2e 18 28 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 18 29 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 18 30 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 18 31 on on IN work_zpfso6pk3vf5df7625v6vawp2e 18 32 sphere sphere JJS work_zpfso6pk3vf5df7625v6vawp2e 18 33 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 18 34 . . . work_zpfso6pk3vf5df7625v6vawp2e 19 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 19 2 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 19 3 order order NN work_zpfso6pk3vf5df7625v6vawp2e 19 4 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 19 5 geometry geometry NN work_zpfso6pk3vf5df7625v6vawp2e 19 6 of of IN work_zpfso6pk3vf5df7625v6vawp2e 19 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 19 8 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 19 9 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 19 10 and and CC work_zpfso6pk3vf5df7625v6vawp2e 19 11 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 19 12 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 19 13 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 19 14 initially initially RB work_zpfso6pk3vf5df7625v6vawp2e 19 15 explored explore VBN work_zpfso6pk3vf5df7625v6vawp2e 19 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 19 17 then then RB work_zpfso6pk3vf5df7625v6vawp2e 19 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 19 19 well well RB work_zpfso6pk3vf5df7625v6vawp2e 19 20 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 19 21 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 19 22 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 19 23 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 19 24 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 19 25 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 19 26 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 19 27 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 19 28 to to TO work_zpfso6pk3vf5df7625v6vawp2e 19 29 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 19 30 the the DT work_zpfso6pk3vf5df7625v6vawp2e 19 31 model model NN work_zpfso6pk3vf5df7625v6vawp2e 19 32 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 19 33 . . . work_zpfso6pk3vf5df7625v6vawp2e 20 1 For for IN work_zpfso6pk3vf5df7625v6vawp2e 20 2 completeness completeness JJ work_zpfso6pk3vf5df7625v6vawp2e 20 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 20 4 k- k- NNP work_zpfso6pk3vf5df7625v6vawp2e 20 5 means mean NNS work_zpfso6pk3vf5df7625v6vawp2e 20 6 clustering cluster VBG work_zpfso6pk3vf5df7625v6vawp2e 20 7 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 20 8 and and CC work_zpfso6pk3vf5df7625v6vawp2e 20 9 a a DT work_zpfso6pk3vf5df7625v6vawp2e 20 10 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 20 11 search search NN work_zpfso6pk3vf5df7625v6vawp2e 20 12 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 20 13 employed employ VBN work_zpfso6pk3vf5df7625v6vawp2e 20 14 to to TO work_zpfso6pk3vf5df7625v6vawp2e 20 15 determine determine VB work_zpfso6pk3vf5df7625v6vawp2e 20 16 the the DT work_zpfso6pk3vf5df7625v6vawp2e 20 17 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 20 18 and and CC work_zpfso6pk3vf5df7625v6vawp2e 20 19 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 20 20 width width NN work_zpfso6pk3vf5df7625v6vawp2e 20 21 respectively respectively RB work_zpfso6pk3vf5df7625v6vawp2e 20 22 . . . work_zpfso6pk3vf5df7625v6vawp2e 21 1 Simulated simulate VBN work_zpfso6pk3vf5df7625v6vawp2e 21 2 examples example NNS work_zpfso6pk3vf5df7625v6vawp2e 21 3 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 21 4 employed employ VBN work_zpfso6pk3vf5df7625v6vawp2e 21 5 to to TO work_zpfso6pk3vf5df7625v6vawp2e 21 6 demonstrate demonstrate VB work_zpfso6pk3vf5df7625v6vawp2e 21 7 that that IN work_zpfso6pk3vf5df7625v6vawp2e 21 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 21 9 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 21 10 approach approach NN work_zpfso6pk3vf5df7625v6vawp2e 21 11 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 21 12 effective effective JJ work_zpfso6pk3vf5df7625v6vawp2e 21 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 21 14 constructing construct VBG work_zpfso6pk3vf5df7625v6vawp2e 21 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 21 16 estimate estimate NN work_zpfso6pk3vf5df7625v6vawp2e 21 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 21 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 21 19 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 21 20 root root NN work_zpfso6pk3vf5df7625v6vawp2e 21 21 of of IN work_zpfso6pk3vf5df7625v6vawp2e 21 22 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 21 23 density density NN work_zpfso6pk3vf5df7625v6vawp2e 21 24 function function NN work_zpfso6pk3vf5df7625v6vawp2e 21 25 . . . work_zpfso6pk3vf5df7625v6vawp2e 22 1 1 1 LS work_zpfso6pk3vf5df7625v6vawp2e 22 2 Introduction introduction NN work_zpfso6pk3vf5df7625v6vawp2e 22 3 The the DT work_zpfso6pk3vf5df7625v6vawp2e 22 4 importance importance NN work_zpfso6pk3vf5df7625v6vawp2e 22 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 22 6 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 22 7 density density NN work_zpfso6pk3vf5df7625v6vawp2e 22 8 function function NN work_zpfso6pk3vf5df7625v6vawp2e 22 9 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 22 10 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 22 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 22 12 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 22 13 evidenced evidence VBN work_zpfso6pk3vf5df7625v6vawp2e 22 14 by by IN work_zpfso6pk3vf5df7625v6vawp2e 22 15 intensive intensive JJ work_zpfso6pk3vf5df7625v6vawp2e 22 16 the- the- DT work_zpfso6pk3vf5df7625v6vawp2e 22 17 oretic oretic JJ work_zpfso6pk3vf5df7625v6vawp2e 22 18 researches research NNS work_zpfso6pk3vf5df7625v6vawp2e 22 19 and and CC work_zpfso6pk3vf5df7625v6vawp2e 22 20 many many JJ work_zpfso6pk3vf5df7625v6vawp2e 22 21 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 22 22 analysis analysis NN work_zpfso6pk3vf5df7625v6vawp2e 22 23 and and CC work_zpfso6pk3vf5df7625v6vawp2e 22 24 pattern pattern NN work_zpfso6pk3vf5df7625v6vawp2e 22 25 recognition recognition NN work_zpfso6pk3vf5df7625v6vawp2e 22 26 applications application NNS work_zpfso6pk3vf5df7625v6vawp2e 22 27 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 22 28 McLach- mclach- NN work_zpfso6pk3vf5df7625v6vawp2e 22 29 lan lan NN work_zpfso6pk3vf5df7625v6vawp2e 22 30 and and CC work_zpfso6pk3vf5df7625v6vawp2e 22 31 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 22 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 33 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 22 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 35 Silverman Silverman NNP work_zpfso6pk3vf5df7625v6vawp2e 22 36 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 37 1986 1986 CD work_zpfso6pk3vf5df7625v6vawp2e 22 38 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 39 Duda Duda NNP work_zpfso6pk3vf5df7625v6vawp2e 22 40 and and CC work_zpfso6pk3vf5df7625v6vawp2e 22 41 Hart Hart NNP work_zpfso6pk3vf5df7625v6vawp2e 22 42 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 43 1973 1973 CD work_zpfso6pk3vf5df7625v6vawp2e 22 44 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 45 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 22 46 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 22 47 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 22 48 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 22 49 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 50 2010 2010 CD work_zpfso6pk3vf5df7625v6vawp2e 22 51 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 52 Rutkowski Rutkowski NNP work_zpfso6pk3vf5df7625v6vawp2e 22 53 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 54 2004 2004 CD work_zpfso6pk3vf5df7625v6vawp2e 22 55 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 56 Yin Yin NNP work_zpfso6pk3vf5df7625v6vawp2e 22 57 and and CC work_zpfso6pk3vf5df7625v6vawp2e 22 58 Allinson Allinson NNP work_zpfso6pk3vf5df7625v6vawp2e 22 59 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 60 2001 2001 CD work_zpfso6pk3vf5df7625v6vawp2e 22 61 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 62 Dempster Dempster NNP work_zpfso6pk3vf5df7625v6vawp2e 22 63 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 22 64 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 22 65 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 22 66 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 67 1977 1977 CD work_zpfso6pk3vf5df7625v6vawp2e 22 68 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 69 Parzen Parzen NNP work_zpfso6pk3vf5df7625v6vawp2e 22 70 , , , work_zpfso6pk3vf5df7625v6vawp2e 22 71 1962 1962 CD work_zpfso6pk3vf5df7625v6vawp2e 22 72 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 22 73 . . . work_zpfso6pk3vf5df7625v6vawp2e 23 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 23 2 Parzen Parzen NNP work_zpfso6pk3vf5df7625v6vawp2e 23 3 window window NN work_zpfso6pk3vf5df7625v6vawp2e 23 4 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 23 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 23 6 PW PW NNP work_zpfso6pk3vf5df7625v6vawp2e 23 7 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 23 8 and and CC work_zpfso6pk3vf5df7625v6vawp2e 23 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 23 10 finite finite JJ work_zpfso6pk3vf5df7625v6vawp2e 23 11 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 23 12 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 23 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 23 14 especially especially RB work_zpfso6pk3vf5df7625v6vawp2e 23 15 a a DT work_zpfso6pk3vf5df7625v6vawp2e 23 16 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 23 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 23 18 Gaussians Gaussians NNPS work_zpfso6pk3vf5df7625v6vawp2e 23 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 23 20 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 23 21 two two CD work_zpfso6pk3vf5df7625v6vawp2e 23 22 widely widely RB work_zpfso6pk3vf5df7625v6vawp2e 23 23 researched research VBN work_zpfso6pk3vf5df7625v6vawp2e 23 24 and and CC work_zpfso6pk3vf5df7625v6vawp2e 23 25 popular popular JJ work_zpfso6pk3vf5df7625v6vawp2e 23 26 estimators estimator NNS work_zpfso6pk3vf5df7625v6vawp2e 23 27 . . . work_zpfso6pk3vf5df7625v6vawp2e 24 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 24 2 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 24 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 4 Gaussians Gaussians NNP work_zpfso6pk3vf5df7625v6vawp2e 24 5 model model NN work_zpfso6pk3vf5df7625v6vawp2e 24 6 represents represent VBZ work_zpfso6pk3vf5df7625v6vawp2e 24 7 an an DT work_zpfso6pk3vf5df7625v6vawp2e 24 8 underlying underlie VBG work_zpfso6pk3vf5df7625v6vawp2e 24 9 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 24 10 as as IN work_zpfso6pk3vf5df7625v6vawp2e 24 11 a a DT work_zpfso6pk3vf5df7625v6vawp2e 24 12 linear linear JJ work_zpfso6pk3vf5df7625v6vawp2e 24 13 combination combination NN work_zpfso6pk3vf5df7625v6vawp2e 24 14 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 15 Gaus- Gaus- NNP work_zpfso6pk3vf5df7625v6vawp2e 24 16 sian sian NNP work_zpfso6pk3vf5df7625v6vawp2e 24 17 kernels kernels NNP work_zpfso6pk3vf5df7625v6vawp2e 24 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 19 and and CC work_zpfso6pk3vf5df7625v6vawp2e 24 20 the the DT work_zpfso6pk3vf5df7625v6vawp2e 24 21 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 24 22 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 24 23 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 24 24 ML ML NNP work_zpfso6pk3vf5df7625v6vawp2e 24 25 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 24 26 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 24 27 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 28 the the DT work_zpfso6pk3vf5df7625v6vawp2e 24 29 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 24 30 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 24 31 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 24 32 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 24 33 Department Department NNP work_zpfso6pk3vf5df7625v6vawp2e 24 34 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 35 Computer Computer NNP work_zpfso6pk3vf5df7625v6vawp2e 24 36 Science Science NNP work_zpfso6pk3vf5df7625v6vawp2e 24 37 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 38 School School NNP work_zpfso6pk3vf5df7625v6vawp2e 24 39 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 40 Mathematical Mathematical NNP work_zpfso6pk3vf5df7625v6vawp2e 24 41 and and CC work_zpfso6pk3vf5df7625v6vawp2e 24 42 Physical Physical NNP work_zpfso6pk3vf5df7625v6vawp2e 24 43 Sciences Sciences NNPS work_zpfso6pk3vf5df7625v6vawp2e 24 44 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 45 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 24 46 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 47 Reading Reading NNP work_zpfso6pk3vf5df7625v6vawp2e 24 48 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 49 UK UK NNP work_zpfso6pk3vf5df7625v6vawp2e 24 50 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 51 e e NN work_zpfso6pk3vf5df7625v6vawp2e 24 52 - - NN work_zpfso6pk3vf5df7625v6vawp2e 24 53 mail mail NN work_zpfso6pk3vf5df7625v6vawp2e 24 54 : : : work_zpfso6pk3vf5df7625v6vawp2e 24 55 x.hong@reading.ac.uk x.hong@reading.ac.uk ADD work_zpfso6pk3vf5df7625v6vawp2e 24 56 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 24 57 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 24 58 Discipline Discipline NNP work_zpfso6pk3vf5df7625v6vawp2e 24 59 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 60 Business Business NNP work_zpfso6pk3vf5df7625v6vawp2e 24 61 Analytics Analytics NNPS work_zpfso6pk3vf5df7625v6vawp2e 24 62 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 63 The the DT work_zpfso6pk3vf5df7625v6vawp2e 24 64 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 24 65 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 66 Sydney Sydney NNP work_zpfso6pk3vf5df7625v6vawp2e 24 67 Business Business NNP work_zpfso6pk3vf5df7625v6vawp2e 24 68 School School NNP work_zpfso6pk3vf5df7625v6vawp2e 24 69 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 70 The the DT work_zpfso6pk3vf5df7625v6vawp2e 24 71 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 24 72 of of IN work_zpfso6pk3vf5df7625v6vawp2e 24 73 Sydney Sydney NNP work_zpfso6pk3vf5df7625v6vawp2e 24 74 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 75 NSW NSW NNP work_zpfso6pk3vf5df7625v6vawp2e 24 76 2006 2006 CD work_zpfso6pk3vf5df7625v6vawp2e 24 77 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 78 Australia Australia NNP work_zpfso6pk3vf5df7625v6vawp2e 24 79 , , , work_zpfso6pk3vf5df7625v6vawp2e 24 80 e e NN work_zpfso6pk3vf5df7625v6vawp2e 24 81 - - NN work_zpfso6pk3vf5df7625v6vawp2e 24 82 mail mail NN work_zpfso6pk3vf5df7625v6vawp2e 24 83 : : : work_zpfso6pk3vf5df7625v6vawp2e 24 84 junbin.gao@sydney.edu.au junbin.gao@sydney.edu.au NNP work_zpfso6pk3vf5df7625v6vawp2e 24 85 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 24 86 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 24 87 and and CC work_zpfso6pk3vf5df7625v6vawp2e 24 88 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 24 89 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 24 90 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 24 91 can can MD work_zpfso6pk3vf5df7625v6vawp2e 24 92 be be VB work_zpfso6pk3vf5df7625v6vawp2e 24 93 obtained obtain VBN work_zpfso6pk3vf5df7625v6vawp2e 24 94 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 24 95 the the DT work_zpfso6pk3vf5df7625v6vawp2e 24 96 expectation- expectation- FW work_zpfso6pk3vf5df7625v6vawp2e 24 97 maximization maximization NN work_zpfso6pk3vf5df7625v6vawp2e 24 98 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 24 99 EM EM NNP work_zpfso6pk3vf5df7625v6vawp2e 24 100 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 24 101 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 24 102 . . . work_zpfso6pk3vf5df7625v6vawp2e 25 1 Alternatively alternatively RB work_zpfso6pk3vf5df7625v6vawp2e 25 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 25 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 25 4 Parzen Parzen NNP work_zpfso6pk3vf5df7625v6vawp2e 25 5 window window NN work_zpfso6pk3vf5df7625v6vawp2e 25 6 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 25 7 PW pw NN work_zpfso6pk3vf5df7625v6vawp2e 25 8 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 25 9 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 25 10 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 25 11 Parzen Parzen NNP work_zpfso6pk3vf5df7625v6vawp2e 25 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 25 13 1962 1962 CD work_zpfso6pk3vf5df7625v6vawp2e 25 14 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 25 15 can can MD work_zpfso6pk3vf5df7625v6vawp2e 25 16 be be VB work_zpfso6pk3vf5df7625v6vawp2e 25 17 regarded regard VBN work_zpfso6pk3vf5df7625v6vawp2e 25 18 as as IN work_zpfso6pk3vf5df7625v6vawp2e 25 19 a a DT work_zpfso6pk3vf5df7625v6vawp2e 25 20 special special JJ work_zpfso6pk3vf5df7625v6vawp2e 25 21 case case NN work_zpfso6pk3vf5df7625v6vawp2e 25 22 of of IN work_zpfso6pk3vf5df7625v6vawp2e 25 23 the the DT work_zpfso6pk3vf5df7625v6vawp2e 25 24 finite finite JJ work_zpfso6pk3vf5df7625v6vawp2e 25 25 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 25 26 model model NN work_zpfso6pk3vf5df7625v6vawp2e 25 27 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 25 28 McLachlan McLachlan NNP work_zpfso6pk3vf5df7625v6vawp2e 25 29 and and CC work_zpfso6pk3vf5df7625v6vawp2e 25 30 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 25 31 , , , work_zpfso6pk3vf5df7625v6vawp2e 25 32 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 25 33 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 25 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 25 35 in in IN work_zpfso6pk3vf5df7625v6vawp2e 25 36 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 25 37 the the DT work_zpfso6pk3vf5df7625v6vawp2e 25 38 number number NN work_zpfso6pk3vf5df7625v6vawp2e 25 39 of of IN work_zpfso6pk3vf5df7625v6vawp2e 25 40 mixtures mixture NNS work_zpfso6pk3vf5df7625v6vawp2e 25 41 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 25 42 equal equal JJ work_zpfso6pk3vf5df7625v6vawp2e 25 43 to to IN work_zpfso6pk3vf5df7625v6vawp2e 25 44 that that DT work_zpfso6pk3vf5df7625v6vawp2e 25 45 of of IN work_zpfso6pk3vf5df7625v6vawp2e 25 46 the the DT work_zpfso6pk3vf5df7625v6vawp2e 25 47 training training NN work_zpfso6pk3vf5df7625v6vawp2e 25 48 data data NN work_zpfso6pk3vf5df7625v6vawp2e 25 49 samples sample NNS work_zpfso6pk3vf5df7625v6vawp2e 25 50 and and CC work_zpfso6pk3vf5df7625v6vawp2e 25 51 all all PDT work_zpfso6pk3vf5df7625v6vawp2e 25 52 the the DT work_zpfso6pk3vf5df7625v6vawp2e 25 53 mixing mix VBG work_zpfso6pk3vf5df7625v6vawp2e 25 54 weights weight NNS work_zpfso6pk3vf5df7625v6vawp2e 25 55 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 25 56 equal equal JJ work_zpfso6pk3vf5df7625v6vawp2e 25 57 , , , work_zpfso6pk3vf5df7625v6vawp2e 25 58 providing provide VBG work_zpfso6pk3vf5df7625v6vawp2e 25 59 as as IN work_zpfso6pk3vf5df7625v6vawp2e 25 60 a a DT work_zpfso6pk3vf5df7625v6vawp2e 25 61 simple simple JJ work_zpfso6pk3vf5df7625v6vawp2e 25 62 practical practical JJ work_zpfso6pk3vf5df7625v6vawp2e 25 63 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 25 64 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 25 65 . . . work_zpfso6pk3vf5df7625v6vawp2e 26 1 However however RB work_zpfso6pk3vf5df7625v6vawp2e 26 2 if if IN work_zpfso6pk3vf5df7625v6vawp2e 26 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 26 4 number number NN work_zpfso6pk3vf5df7625v6vawp2e 26 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 26 6 training train VBG work_zpfso6pk3vf5df7625v6vawp2e 26 7 data data NN work_zpfso6pk3vf5df7625v6vawp2e 26 8 samples sample NNS work_zpfso6pk3vf5df7625v6vawp2e 26 9 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 26 10 very very RB work_zpfso6pk3vf5df7625v6vawp2e 26 11 large large JJ work_zpfso6pk3vf5df7625v6vawp2e 26 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 26 13 then then RB work_zpfso6pk3vf5df7625v6vawp2e 26 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 26 15 point point NN work_zpfso6pk3vf5df7625v6vawp2e 26 16 density density NN work_zpfso6pk3vf5df7625v6vawp2e 26 17 estimate estimate NN work_zpfso6pk3vf5df7625v6vawp2e 26 18 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 26 19 the the DT work_zpfso6pk3vf5df7625v6vawp2e 26 20 PW PW NNP work_zpfso6pk3vf5df7625v6vawp2e 26 21 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 26 22 for for IN work_zpfso6pk3vf5df7625v6vawp2e 26 23 a a DT work_zpfso6pk3vf5df7625v6vawp2e 26 24 future future JJ work_zpfso6pk3vf5df7625v6vawp2e 26 25 data data NN work_zpfso6pk3vf5df7625v6vawp2e 26 26 sample sample NN work_zpfso6pk3vf5df7625v6vawp2e 26 27 can can MD work_zpfso6pk3vf5df7625v6vawp2e 26 28 be be VB work_zpfso6pk3vf5df7625v6vawp2e 26 29 computationally computationally RB work_zpfso6pk3vf5df7625v6vawp2e 26 30 expensive expensive JJ work_zpfso6pk3vf5df7625v6vawp2e 26 31 . . . work_zpfso6pk3vf5df7625v6vawp2e 27 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 27 2 as- as- NNP work_zpfso6pk3vf5df7625v6vawp2e 27 3 sociated sociate VBD work_zpfso6pk3vf5df7625v6vawp2e 27 4 ML ML NNP work_zpfso6pk3vf5df7625v6vawp2e 27 5 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 27 6 in in IN work_zpfso6pk3vf5df7625v6vawp2e 27 7 a a DT work_zpfso6pk3vf5df7625v6vawp2e 27 8 general general JJ work_zpfso6pk3vf5df7625v6vawp2e 27 9 finite finite JJ work_zpfso6pk3vf5df7625v6vawp2e 27 10 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 27 11 Gaussian Gaussian NNP work_zpfso6pk3vf5df7625v6vawp2e 27 12 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 27 13 generally generally RB work_zpfso6pk3vf5df7625v6vawp2e 27 14 a a DT work_zpfso6pk3vf5df7625v6vawp2e 27 15 highly highly RB work_zpfso6pk3vf5df7625v6vawp2e 27 16 nonlinear nonlinear JJ work_zpfso6pk3vf5df7625v6vawp2e 27 17 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 27 18 process process NN work_zpfso6pk3vf5df7625v6vawp2e 27 19 requiring require VBG work_zpfso6pk3vf5df7625v6vawp2e 27 20 extensive extensive JJ work_zpfso6pk3vf5df7625v6vawp2e 27 21 computation computation NN work_zpfso6pk3vf5df7625v6vawp2e 27 22 , , , work_zpfso6pk3vf5df7625v6vawp2e 27 23 while while IN work_zpfso6pk3vf5df7625v6vawp2e 27 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 27 25 EM EM NNP work_zpfso6pk3vf5df7625v6vawp2e 27 26 algo- algo- JJ work_zpfso6pk3vf5df7625v6vawp2e 27 27 rithm rithm NN work_zpfso6pk3vf5df7625v6vawp2e 27 28 for for IN work_zpfso6pk3vf5df7625v6vawp2e 27 29 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 27 30 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 27 31 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 27 32 enjoys enjoy VBZ work_zpfso6pk3vf5df7625v6vawp2e 27 33 an an DT work_zpfso6pk3vf5df7625v6vawp2e 27 34 explicit explicit JJ work_zpfso6pk3vf5df7625v6vawp2e 27 35 iterative iterative JJ work_zpfso6pk3vf5df7625v6vawp2e 27 36 form form NN work_zpfso6pk3vf5df7625v6vawp2e 27 37 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 27 38 Bilmes Bilmes NNP work_zpfso6pk3vf5df7625v6vawp2e 27 39 , , , work_zpfso6pk3vf5df7625v6vawp2e 27 40 1998 1998 CD work_zpfso6pk3vf5df7625v6vawp2e 27 41 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 27 42 . . . work_zpfso6pk3vf5df7625v6vawp2e 28 1 There there EX work_zpfso6pk3vf5df7625v6vawp2e 28 2 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 28 3 also also RB work_zpfso6pk3vf5df7625v6vawp2e 28 4 considerable considerable JJ work_zpfso6pk3vf5df7625v6vawp2e 28 5 interests interest NNS work_zpfso6pk3vf5df7625v6vawp2e 28 6 into into IN work_zpfso6pk3vf5df7625v6vawp2e 28 7 research research NN work_zpfso6pk3vf5df7625v6vawp2e 28 8 on on IN work_zpfso6pk3vf5df7625v6vawp2e 28 9 sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 28 10 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 28 11 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 28 12 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 28 13 can can MD work_zpfso6pk3vf5df7625v6vawp2e 28 14 be be VB work_zpfso6pk3vf5df7625v6vawp2e 28 15 summarized summarize VBN work_zpfso6pk3vf5df7625v6vawp2e 28 16 into into IN work_zpfso6pk3vf5df7625v6vawp2e 28 17 two two CD work_zpfso6pk3vf5df7625v6vawp2e 28 18 categories category NNS work_zpfso6pk3vf5df7625v6vawp2e 28 19 . . . work_zpfso6pk3vf5df7625v6vawp2e 29 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 29 2 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 29 3 category category NN work_zpfso6pk3vf5df7625v6vawp2e 29 4 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 29 5 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 29 6 on on IN work_zpfso6pk3vf5df7625v6vawp2e 29 7 constrained constrained JJ work_zpfso6pk3vf5df7625v6vawp2e 29 8 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 29 9 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 29 10 Weston Weston NNP work_zpfso6pk3vf5df7625v6vawp2e 29 11 et et FW work_zpfso6pk3vf5df7625v6vawp2e 29 12 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 29 13 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 29 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 15 1999 1999 CD work_zpfso6pk3vf5df7625v6vawp2e 29 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 17 Vapnik Vapnik NNP work_zpfso6pk3vf5df7625v6vawp2e 29 18 and and CC work_zpfso6pk3vf5df7625v6vawp2e 29 19 Mukherjee Mukherjee NNP work_zpfso6pk3vf5df7625v6vawp2e 29 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 21 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 29 22 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 23 Girolami Girolami NNP work_zpfso6pk3vf5df7625v6vawp2e 29 24 and and CC work_zpfso6pk3vf5df7625v6vawp2e 29 25 He -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 29 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 27 2003 2003 CD work_zpfso6pk3vf5df7625v6vawp2e 29 28 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 29 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 29 30 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 29 31 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 29 32 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 29 33 , , , work_zpfso6pk3vf5df7625v6vawp2e 29 34 2015 2015 CD work_zpfso6pk3vf5df7625v6vawp2e 29 35 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 29 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 30 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 30 2 second second JJ work_zpfso6pk3vf5df7625v6vawp2e 30 3 category category NN work_zpfso6pk3vf5df7625v6vawp2e 30 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 30 5 sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 30 6 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 30 7 density density NN work_zpfso6pk3vf5df7625v6vawp2e 30 8 estimators estimator NNS work_zpfso6pk3vf5df7625v6vawp2e 30 9 construct construct VBP work_zpfso6pk3vf5df7625v6vawp2e 30 10 the the DT work_zpfso6pk3vf5df7625v6vawp2e 30 11 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 30 12 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 30 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 30 14 a a DT work_zpfso6pk3vf5df7625v6vawp2e 30 15 forward forward JJ work_zpfso6pk3vf5df7625v6vawp2e 30 16 regression regression NN work_zpfso6pk3vf5df7625v6vawp2e 30 17 manner manner NN work_zpfso6pk3vf5df7625v6vawp2e 30 18 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 30 19 Choudhury Choudhury NNP work_zpfso6pk3vf5df7625v6vawp2e 30 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 21 2002,Chen 2002,chen CD work_zpfso6pk3vf5df7625v6vawp2e 30 22 et et FW work_zpfso6pk3vf5df7625v6vawp2e 30 23 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 30 24 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 30 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 26 2004b 2004b NNS work_zpfso6pk3vf5df7625v6vawp2e 30 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 28 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 30 29 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 30 30 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 30 31 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 30 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 33 2004a 2004a CD work_zpfso6pk3vf5df7625v6vawp2e 30 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 35 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 30 36 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 30 37 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 30 38 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 30 39 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 40 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 30 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 42 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 30 43 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 30 44 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 30 45 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 30 46 , , , work_zpfso6pk3vf5df7625v6vawp2e 30 47 2013 2013 CD work_zpfso6pk3vf5df7625v6vawp2e 30 48 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 30 49 . . . work_zpfso6pk3vf5df7625v6vawp2e 31 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 31 2 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 31 3 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 31 4 algorithms algorithm NNS work_zpfso6pk3vf5df7625v6vawp2e 31 5 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 31 6 been be VBN work_zpfso6pk3vf5df7625v6vawp2e 31 7 recently recently RB work_zpfso6pk3vf5df7625v6vawp2e 31 8 researched research VBN work_zpfso6pk3vf5df7625v6vawp2e 31 9 on on IN work_zpfso6pk3vf5df7625v6vawp2e 31 10 many many JJ work_zpfso6pk3vf5df7625v6vawp2e 31 11 types type NNS work_zpfso6pk3vf5df7625v6vawp2e 31 12 of of IN work_zpfso6pk3vf5df7625v6vawp2e 31 13 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 31 14 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 31 15 such such JJ work_zpfso6pk3vf5df7625v6vawp2e 31 16 as as IN work_zpfso6pk3vf5df7625v6vawp2e 31 17 the the DT work_zpfso6pk3vf5df7625v6vawp2e 31 18 Stiefel Stiefel NNP work_zpfso6pk3vf5df7625v6vawp2e 31 19 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 31 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 31 21 Grassmann Grassmann NNP work_zpfso6pk3vf5df7625v6vawp2e 31 22 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 31 23 and and CC work_zpfso6pk3vf5df7625v6vawp2e 31 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 31 25 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 31 26 of of IN work_zpfso6pk3vf5df7625v6vawp2e 31 27 positive positive JJ work_zpfso6pk3vf5df7625v6vawp2e 31 28 definite definite JJ work_zpfso6pk3vf5df7625v6vawp2e 31 29 matrices matrix NNS work_zpfso6pk3vf5df7625v6vawp2e 31 30 , , , work_zpfso6pk3vf5df7625v6vawp2e 31 31 see see VB work_zpfso6pk3vf5df7625v6vawp2e 31 32 Section section NN work_zpfso6pk3vf5df7625v6vawp2e 31 33 3.4 3.4 CD work_zpfso6pk3vf5df7625v6vawp2e 31 34 of of IN work_zpfso6pk3vf5df7625v6vawp2e 31 35 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 31 36 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 31 37 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 31 38 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 31 39 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 31 40 , , , work_zpfso6pk3vf5df7625v6vawp2e 31 41 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 31 42 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 31 43 . . . work_zpfso6pk3vf5df7625v6vawp2e 32 1 Since since IN work_zpfso6pk3vf5df7625v6vawp2e 32 2 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 32 3 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 32 4 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 32 5 directly directly RB work_zpfso6pk3vf5df7625v6vawp2e 32 6 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 32 7 on on IN work_zpfso6pk3vf5df7625v6vawp2e 32 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 32 9 curved curved JJ work_zpfso6pk3vf5df7625v6vawp2e 32 10 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 32 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 32 12 one one PRP work_zpfso6pk3vf5df7625v6vawp2e 32 13 can can MD work_zpfso6pk3vf5df7625v6vawp2e 32 14 elim- elim- RB work_zpfso6pk3vf5df7625v6vawp2e 32 15 inate inate VB work_zpfso6pk3vf5df7625v6vawp2e 32 16 those those DT work_zpfso6pk3vf5df7625v6vawp2e 32 17 constraints constraint NNS work_zpfso6pk3vf5df7625v6vawp2e 32 18 such such JJ work_zpfso6pk3vf5df7625v6vawp2e 32 19 as as IN work_zpfso6pk3vf5df7625v6vawp2e 32 20 orthogonality orthogonality NN work_zpfso6pk3vf5df7625v6vawp2e 32 21 to to TO work_zpfso6pk3vf5df7625v6vawp2e 32 22 obtain obtain VB work_zpfso6pk3vf5df7625v6vawp2e 32 23 an an DT work_zpfso6pk3vf5df7625v6vawp2e 32 24 unconstrained unconstrained JJ work_zpfso6pk3vf5df7625v6vawp2e 32 25 optimisa- optimisa- NN work_zpfso6pk3vf5df7625v6vawp2e 32 26 tion tion NN work_zpfso6pk3vf5df7625v6vawp2e 32 27 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 32 28 that that IN work_zpfso6pk3vf5df7625v6vawp2e 32 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 32 30 by by IN work_zpfso6pk3vf5df7625v6vawp2e 32 31 construction construction NN work_zpfso6pk3vf5df7625v6vawp2e 32 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 32 33 will will MD work_zpfso6pk3vf5df7625v6vawp2e 32 34 only only RB work_zpfso6pk3vf5df7625v6vawp2e 32 35 use use VB work_zpfso6pk3vf5df7625v6vawp2e 32 36 feasible feasible JJ work_zpfso6pk3vf5df7625v6vawp2e 32 37 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 32 38 . . . work_zpfso6pk3vf5df7625v6vawp2e 33 1 This this DT work_zpfso6pk3vf5df7625v6vawp2e 33 2 allows allow VBZ work_zpfso6pk3vf5df7625v6vawp2e 33 3 one one PRP work_zpfso6pk3vf5df7625v6vawp2e 33 4 to to TO work_zpfso6pk3vf5df7625v6vawp2e 33 5 incorporate incorporate VB work_zpfso6pk3vf5df7625v6vawp2e 33 6 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 33 7 geometry geometry NN work_zpfso6pk3vf5df7625v6vawp2e 33 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 33 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 33 10 resulting result VBG work_zpfso6pk3vf5df7625v6vawp2e 33 11 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 33 12 problems problem NNS work_zpfso6pk3vf5df7625v6vawp2e 33 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 33 14 thus thus RB work_zpfso6pk3vf5df7625v6vawp2e 33 15 pro- pro- NN work_zpfso6pk3vf5df7625v6vawp2e 33 16 ducing duce VBG work_zpfso6pk3vf5df7625v6vawp2e 33 17 far far RB work_zpfso6pk3vf5df7625v6vawp2e 33 18 more more RBR work_zpfso6pk3vf5df7625v6vawp2e 33 19 accurate accurate JJ work_zpfso6pk3vf5df7625v6vawp2e 33 20 numerical numerical JJ work_zpfso6pk3vf5df7625v6vawp2e 33 21 results result NNS work_zpfso6pk3vf5df7625v6vawp2e 33 22 . . . work_zpfso6pk3vf5df7625v6vawp2e 34 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 34 2 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 34 3 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 34 4 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 34 5 been be VBN work_zpfso6pk3vf5df7625v6vawp2e 34 6 successfully successfully RB work_zpfso6pk3vf5df7625v6vawp2e 34 7 applied apply VBN work_zpfso6pk3vf5df7625v6vawp2e 34 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 34 9 machine machine NN work_zpfso6pk3vf5df7625v6vawp2e 34 10 learning learning NN work_zpfso6pk3vf5df7625v6vawp2e 34 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 12 computer computer NN work_zpfso6pk3vf5df7625v6vawp2e 34 13 vision vision NN work_zpfso6pk3vf5df7625v6vawp2e 34 14 and and CC work_zpfso6pk3vf5df7625v6vawp2e 34 15 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 34 16 mining mining NN work_zpfso6pk3vf5df7625v6vawp2e 34 17 tasks task NNS work_zpfso6pk3vf5df7625v6vawp2e 34 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 19 including include VBG work_zpfso6pk3vf5df7625v6vawp2e 34 20 fixed fix VBN work_zpfso6pk3vf5df7625v6vawp2e 34 21 low low JJ work_zpfso6pk3vf5df7625v6vawp2e 34 22 rank rank NN work_zpfso6pk3vf5df7625v6vawp2e 34 23 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 34 24 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 34 25 Mishra Mishra NNP work_zpfso6pk3vf5df7625v6vawp2e 34 26 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 34 27 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 34 28 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 34 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 30 2013 2013 CD work_zpfso6pk3vf5df7625v6vawp2e 34 31 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 34 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 33 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 34 34 dictionary dictionary JJ work_zpfso6pk3vf5df7625v6vawp2e 34 35 learning learning NN work_zpfso6pk3vf5df7625v6vawp2e 34 36 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 34 37 Harandi Harandi NNP work_zpfso6pk3vf5df7625v6vawp2e 34 38 et et FW work_zpfso6pk3vf5df7625v6vawp2e 34 39 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 34 40 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 34 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 42 2014 2014 CD work_zpfso6pk3vf5df7625v6vawp2e 34 43 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 34 44 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 45 and and CC work_zpfso6pk3vf5df7625v6vawp2e 34 46 computer computer NN work_zpfso6pk3vf5df7625v6vawp2e 34 47 vision vision NN work_zpfso6pk3vf5df7625v6vawp2e 34 48 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 34 49 Lui Lui NNP work_zpfso6pk3vf5df7625v6vawp2e 34 50 , , , work_zpfso6pk3vf5df7625v6vawp2e 34 51 2012 2012 CD work_zpfso6pk3vf5df7625v6vawp2e 34 52 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 34 53 . . . work_zpfso6pk3vf5df7625v6vawp2e 35 1 Since since IN work_zpfso6pk3vf5df7625v6vawp2e 35 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 35 3 constraint constraint NN work_zpfso6pk3vf5df7625v6vawp2e 35 4 on on IN work_zpfso6pk3vf5df7625v6vawp2e 35 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 35 6 mixing mix VBG work_zpfso6pk3vf5df7625v6vawp2e 35 7 coefficients coefficient NNS work_zpfso6pk3vf5df7625v6vawp2e 35 8 of of IN work_zpfso6pk3vf5df7625v6vawp2e 35 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 35 10 finite finite JJ work_zpfso6pk3vf5df7625v6vawp2e 35 11 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 35 12 model model NN work_zpfso6pk3vf5df7625v6vawp2e 35 13 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 35 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 35 15 multinomial multinomial JJ work_zpfso6pk3vf5df7625v6vawp2e 35 16 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 35 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 35 18 recently recently RB work_zpfso6pk3vf5df7625v6vawp2e 35 19 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 35 20 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 35 21 introduced introduce VBN work_zpfso6pk3vf5df7625v6vawp2e 35 22 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 35 23 trust trust NN work_zpfso6pk3vf5df7625v6vawp2e 35 24 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 35 25 region region NN work_zpfso6pk3vf5df7625v6vawp2e 35 26 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 35 27 RTR rtr NN work_zpfso6pk3vf5df7625v6vawp2e 35 28 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 35 29 algorithm algorithm VB work_zpfso6pk3vf5df7625v6vawp2e 35 30 for for IN work_zpfso6pk3vf5df7625v6vawp2e 35 31 sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 35 32 fi- fi- XX work_zpfso6pk3vf5df7625v6vawp2e 35 33 nite nite JJ work_zpfso6pk3vf5df7625v6vawp2e 35 34 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 35 35 model model NN work_zpfso6pk3vf5df7625v6vawp2e 35 36 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 35 37 on on IN work_zpfso6pk3vf5df7625v6vawp2e 35 38 minimal minimal JJ work_zpfso6pk3vf5df7625v6vawp2e 35 39 integrated integrate VBN work_zpfso6pk3vf5df7625v6vawp2e 35 40 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 35 41 error error NN work_zpfso6pk3vf5df7625v6vawp2e 35 42 criterion criterion NN work_zpfso6pk3vf5df7625v6vawp2e 35 43 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 35 44 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 35 45 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 35 46 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 35 47 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 35 48 , , , work_zpfso6pk3vf5df7625v6vawp2e 35 49 2015 2015 CD work_zpfso6pk3vf5df7625v6vawp2e 35 50 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 35 51 . . . work_zpfso6pk3vf5df7625v6vawp2e 36 1 Note note VB work_zpfso6pk3vf5df7625v6vawp2e 36 2 that that IN work_zpfso6pk3vf5df7625v6vawp2e 36 3 all all PDT work_zpfso6pk3vf5df7625v6vawp2e 36 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 36 5 aforementioned aforementioned JJ work_zpfso6pk3vf5df7625v6vawp2e 36 6 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 36 7 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 36 8 algorithms algorithm NNS work_zpfso6pk3vf5df7625v6vawp2e 36 9 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 36 10 aimed aim VBN work_zpfso6pk3vf5df7625v6vawp2e 36 11 at at IN work_zpfso6pk3vf5df7625v6vawp2e 36 12 directly directly RB work_zpfso6pk3vf5df7625v6vawp2e 36 13 estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 36 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 36 15 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 36 16 density density NN work_zpfso6pk3vf5df7625v6vawp2e 36 17 function function NN work_zpfso6pk3vf5df7625v6vawp2e 36 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 37 1 However however RB work_zpfso6pk3vf5df7625v6vawp2e 37 2 in in IN work_zpfso6pk3vf5df7625v6vawp2e 37 3 this this DT work_zpfso6pk3vf5df7625v6vawp2e 37 4 work work NN work_zpfso6pk3vf5df7625v6vawp2e 37 5 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 37 6 investigate investigate VBP work_zpfso6pk3vf5df7625v6vawp2e 37 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 37 8 less less RBR work_zpfso6pk3vf5df7625v6vawp2e 37 9 studied studied JJ work_zpfso6pk3vf5df7625v6vawp2e 37 10 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 37 11 of of IN work_zpfso6pk3vf5df7625v6vawp2e 37 12 estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 37 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 37 14 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 37 15 root root NN work_zpfso6pk3vf5df7625v6vawp2e 37 16 of of IN work_zpfso6pk3vf5df7625v6vawp2e 37 17 the the DT work_zpfso6pk3vf5df7625v6vawp2e 37 18 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 37 19 density density NN work_zpfso6pk3vf5df7625v6vawp2e 37 20 function function NN work_zpfso6pk3vf5df7625v6vawp2e 37 21 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 37 22 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 37 23 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 37 24 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 37 25 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 37 26 Pinheiro Pinheiro NNP work_zpfso6pk3vf5df7625v6vawp2e 37 27 and and CC work_zpfso6pk3vf5df7625v6vawp2e 37 28 Vidakovic Vidakovic NNP work_zpfso6pk3vf5df7625v6vawp2e 37 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 37 30 1998 1998 CD work_zpfso6pk3vf5df7625v6vawp2e 37 31 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 37 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 37 33 i.e. i.e. FW work_zpfso6pk3vf5df7625v6vawp2e 37 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 37 35 the the DT work_zpfso6pk3vf5df7625v6vawp2e 37 36 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 37 37 root root NN work_zpfso6pk3vf5df7625v6vawp2e 37 38 of of IN work_zpfso6pk3vf5df7625v6vawp2e 37 39 a a DT work_zpfso6pk3vf5df7625v6vawp2e 37 40 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 37 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 37 42 rather rather RB work_zpfso6pk3vf5df7625v6vawp2e 37 43 than than IN work_zpfso6pk3vf5df7625v6vawp2e 37 44 the the DT work_zpfso6pk3vf5df7625v6vawp2e 37 45 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 37 46 itself -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 37 47 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 37 48 a a DT work_zpfso6pk3vf5df7625v6vawp2e 37 49 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 37 50 of of IN work_zpfso6pk3vf5df7625v6vawp2e 37 51 Gaussians Gaussians NNPS work_zpfso6pk3vf5df7625v6vawp2e 37 52 . . . work_zpfso6pk3vf5df7625v6vawp2e 38 1 Clearly clearly RB work_zpfso6pk3vf5df7625v6vawp2e 38 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 38 3 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 38 4 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 38 5 can can MD work_zpfso6pk3vf5df7625v6vawp2e 38 6 be be VB work_zpfso6pk3vf5df7625v6vawp2e 38 7 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 38 8 similarly similarly RB work_zpfso6pk3vf5df7625v6vawp2e 38 9 in in IN work_zpfso6pk3vf5df7625v6vawp2e 38 10 many many JJ work_zpfso6pk3vf5df7625v6vawp2e 38 11 applications application NNS work_zpfso6pk3vf5df7625v6vawp2e 38 12 as as IN work_zpfso6pk3vf5df7625v6vawp2e 38 13 can can MD work_zpfso6pk3vf5df7625v6vawp2e 38 14 a a DT work_zpfso6pk3vf5df7625v6vawp2e 38 15 PDF pdf NN work_zpfso6pk3vf5df7625v6vawp2e 38 16 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 38 17 . . . work_zpfso6pk3vf5df7625v6vawp2e 39 1 However however RB work_zpfso6pk3vf5df7625v6vawp2e 39 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 39 3 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 39 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 39 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 39 6 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 39 7 root root NN work_zpfso6pk3vf5df7625v6vawp2e 39 8 of of IN work_zpfso6pk3vf5df7625v6vawp2e 39 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 39 10 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 39 11 density density NN work_zpfso6pk3vf5df7625v6vawp2e 39 12 function function NN work_zpfso6pk3vf5df7625v6vawp2e 39 13 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 39 14 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 39 15 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 39 16 poses pose VBZ work_zpfso6pk3vf5df7625v6vawp2e 39 17 as as IN work_zpfso6pk3vf5df7625v6vawp2e 39 18 a a DT work_zpfso6pk3vf5df7625v6vawp2e 39 19 different different JJ work_zpfso6pk3vf5df7625v6vawp2e 39 20 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 39 21 , , , work_zpfso6pk3vf5df7625v6vawp2e 39 22 and and CC work_zpfso6pk3vf5df7625v6vawp2e 39 23 new new JJ work_zpfso6pk3vf5df7625v6vawp2e 39 24 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 39 25 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 39 26 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 39 27 required require VBN work_zpfso6pk3vf5df7625v6vawp2e 39 28 . . . work_zpfso6pk3vf5df7625v6vawp2e 40 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 40 2 this this DT work_zpfso6pk3vf5df7625v6vawp2e 40 3 paper paper NN work_zpfso6pk3vf5df7625v6vawp2e 40 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 40 5 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 40 6 introduce introduce VBP work_zpfso6pk3vf5df7625v6vawp2e 40 7 / / SYM work_zpfso6pk3vf5df7625v6vawp2e 40 8 extend extend VB work_zpfso6pk3vf5df7625v6vawp2e 40 9 a a DT work_zpfso6pk3vf5df7625v6vawp2e 40 10 fast fast JJ work_zpfso6pk3vf5df7625v6vawp2e 40 11 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 40 12 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 40 13 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 40 14 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 40 15 on on IN work_zpfso6pk3vf5df7625v6vawp2e 40 16 a a DT work_zpfso6pk3vf5df7625v6vawp2e 40 17 linear linear JJ work_zpfso6pk3vf5df7625v6vawp2e 40 18 combination combination NN work_zpfso6pk3vf5df7625v6vawp2e 40 19 of of IN work_zpfso6pk3vf5df7625v6vawp2e 40 20 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 40 21 kernels kernel NNS work_zpfso6pk3vf5df7625v6vawp2e 40 22 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 40 23 represents represent VBZ work_zpfso6pk3vf5df7625v6vawp2e 40 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 40 25 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 40 26 root root NN work_zpfso6pk3vf5df7625v6vawp2e 40 27 of of IN work_zpfso6pk3vf5df7625v6vawp2e 40 28 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 40 29 density density NN work_zpfso6pk3vf5df7625v6vawp2e 40 30 function function NN work_zpfso6pk3vf5df7625v6vawp2e 40 31 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 40 32 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 40 33 and and CC work_zpfso6pk3vf5df7625v6vawp2e 40 34 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 40 35 , , , work_zpfso6pk3vf5df7625v6vawp2e 40 36 2016 2016 CD work_zpfso6pk3vf5df7625v6vawp2e 40 37 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 40 38 . . . work_zpfso6pk3vf5df7625v6vawp2e 41 1 Initially initially RB work_zpfso6pk3vf5df7625v6vawp2e 41 2 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 41 3 apply apply VBP work_zpfso6pk3vf5df7625v6vawp2e 41 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 41 5 k k NN work_zpfso6pk3vf5df7625v6vawp2e 41 6 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 41 7 means means NN work_zpfso6pk3vf5df7625v6vawp2e 41 8 clustering cluster VBG work_zpfso6pk3vf5df7625v6vawp2e 41 9 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 41 10 and and CC work_zpfso6pk3vf5df7625v6vawp2e 41 11 a a DT work_zpfso6pk3vf5df7625v6vawp2e 41 12 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 41 13 search search NN work_zpfso6pk3vf5df7625v6vawp2e 41 14 to to TO work_zpfso6pk3vf5df7625v6vawp2e 41 15 determine determine VB work_zpfso6pk3vf5df7625v6vawp2e 41 16 the the DT work_zpfso6pk3vf5df7625v6vawp2e 41 17 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 41 18 and and CC work_zpfso6pk3vf5df7625v6vawp2e 41 19 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 41 20 width width NN work_zpfso6pk3vf5df7625v6vawp2e 41 21 . . . work_zpfso6pk3vf5df7625v6vawp2e 42 1 It -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 42 2 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 42 3 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 42 4 that that IN work_zpfso6pk3vf5df7625v6vawp2e 42 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 42 6 underlying underlie VBG work_zpfso6pk3vf5df7625v6vawp2e 42 7 parameter parameter NN work_zpfso6pk3vf5df7625v6vawp2e 42 8 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 42 9 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 42 10 can can MD work_zpfso6pk3vf5df7625v6vawp2e 42 11 be be VB work_zpfso6pk3vf5df7625v6vawp2e 42 12 formulated formulate VBN work_zpfso6pk3vf5df7625v6vawp2e 42 13 as as IN work_zpfso6pk3vf5df7625v6vawp2e 42 14 a a DT work_zpfso6pk3vf5df7625v6vawp2e 42 15 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 42 16 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 42 17 on on IN work_zpfso6pk3vf5df7625v6vawp2e 42 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 42 19 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 42 20 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 42 21 . . . work_zpfso6pk3vf5df7625v6vawp2e 43 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 43 2 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 43 3 order order NN work_zpfso6pk3vf5df7625v6vawp2e 43 4 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 43 5 geom- geom- NN work_zpfso6pk3vf5df7625v6vawp2e 43 6 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 43 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 43 8 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 43 9 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 43 10 of of IN work_zpfso6pk3vf5df7625v6vawp2e 43 11 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 43 12 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 43 13 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 43 14 on on IN work_zpfso6pk3vf5df7625v6vawp2e 43 15 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 43 16 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 43 17 etry etry NN work_zpfso6pk3vf5df7625v6vawp2e 43 18 of of IN work_zpfso6pk3vf5df7625v6vawp2e 43 19 the the DT work_zpfso6pk3vf5df7625v6vawp2e 43 20 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 43 21 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 43 22 and and CC work_zpfso6pk3vf5df7625v6vawp2e 43 23 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 43 24 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 43 25 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 43 26 explored explore VBN work_zpfso6pk3vf5df7625v6vawp2e 43 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 43 28 and and CC work_zpfso6pk3vf5df7625v6vawp2e 43 29 the the DT work_zpfso6pk3vf5df7625v6vawp2e 43 30 well well RB work_zpfso6pk3vf5df7625v6vawp2e 43 31 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 43 32 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 43 33 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 43 34 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 43 35 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 43 36 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 43 37 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 43 38 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 43 39 to to TO work_zpfso6pk3vf5df7625v6vawp2e 43 40 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 43 41 the the DT work_zpfso6pk3vf5df7625v6vawp2e 43 42 model model NN work_zpfso6pk3vf5df7625v6vawp2e 43 43 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 43 44 . . . work_zpfso6pk3vf5df7625v6vawp2e 44 1 Numerical numerical JJ work_zpfso6pk3vf5df7625v6vawp2e 44 2 examples example NNS work_zpfso6pk3vf5df7625v6vawp2e 44 3 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 44 4 employed employ VBN work_zpfso6pk3vf5df7625v6vawp2e 44 5 to to TO work_zpfso6pk3vf5df7625v6vawp2e 44 6 demonstrate demonstrate VB work_zpfso6pk3vf5df7625v6vawp2e 44 7 that that IN work_zpfso6pk3vf5df7625v6vawp2e 44 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 44 9 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 44 10 approach approach NN work_zpfso6pk3vf5df7625v6vawp2e 44 11 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 44 12 effective effective JJ work_zpfso6pk3vf5df7625v6vawp2e 44 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 44 14 constructing construct VBG work_zpfso6pk3vf5df7625v6vawp2e 44 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 44 16 estimate estimate NN work_zpfso6pk3vf5df7625v6vawp2e 44 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 44 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 44 19 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 44 20 root root NN work_zpfso6pk3vf5df7625v6vawp2e 44 21 of of IN work_zpfso6pk3vf5df7625v6vawp2e 44 22 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 44 23 density density NN work_zpfso6pk3vf5df7625v6vawp2e 44 24 func- func- NNP work_zpfso6pk3vf5df7625v6vawp2e 44 25 tion tion NN work_zpfso6pk3vf5df7625v6vawp2e 44 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 45 1 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 45 2 Preliminary preliminary JJ work_zpfso6pk3vf5df7625v6vawp2e 45 3 on on IN work_zpfso6pk3vf5df7625v6vawp2e 45 4 Sphere Sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 45 5 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 45 6 This this DT work_zpfso6pk3vf5df7625v6vawp2e 45 7 section section NN work_zpfso6pk3vf5df7625v6vawp2e 45 8 briefly briefly RB work_zpfso6pk3vf5df7625v6vawp2e 45 9 introduces introduce VBZ work_zpfso6pk3vf5df7625v6vawp2e 45 10 the the DT work_zpfso6pk3vf5df7625v6vawp2e 45 11 concept concept NN work_zpfso6pk3vf5df7625v6vawp2e 45 12 of of IN work_zpfso6pk3vf5df7625v6vawp2e 45 13 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 45 14 manifold manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 45 15 and and CC work_zpfso6pk3vf5df7625v6vawp2e 45 16 the the DT work_zpfso6pk3vf5df7625v6vawp2e 45 17 necessary necessary JJ work_zpfso6pk3vf5df7625v6vawp2e 45 18 ingredients ingredient NNS work_zpfso6pk3vf5df7625v6vawp2e 45 19 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 45 20 in in IN work_zpfso6pk3vf5df7625v6vawp2e 45 21 the the DT work_zpfso6pk3vf5df7625v6vawp2e 45 22 retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 45 23 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 45 24 framework framework NN work_zpfso6pk3vf5df7625v6vawp2e 45 25 of of IN work_zpfso6pk3vf5df7625v6vawp2e 45 26 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 45 27 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 45 28 . . . work_zpfso6pk3vf5df7625v6vawp2e 46 1 As as IN work_zpfso6pk3vf5df7625v6vawp2e 46 2 a a DT work_zpfso6pk3vf5df7625v6vawp2e 46 3 reference reference NN work_zpfso6pk3vf5df7625v6vawp2e 46 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 46 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 46 6 main main JJ work_zpfso6pk3vf5df7625v6vawp2e 46 7 notations notation NNS work_zpfso6pk3vf5df7625v6vawp2e 46 8 on on IN work_zpfso6pk3vf5df7625v6vawp2e 46 9 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 46 10 geometry geometry NN work_zpfso6pk3vf5df7625v6vawp2e 46 11 on on IN work_zpfso6pk3vf5df7625v6vawp2e 46 12 sphere sphere JJS work_zpfso6pk3vf5df7625v6vawp2e 46 13 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 46 14 in in IN work_zpfso6pk3vf5df7625v6vawp2e 46 15 this this DT work_zpfso6pk3vf5df7625v6vawp2e 46 16 section section NN work_zpfso6pk3vf5df7625v6vawp2e 46 17 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 46 18 summarized summarize VBN work_zpfso6pk3vf5df7625v6vawp2e 46 19 in in IN work_zpfso6pk3vf5df7625v6vawp2e 46 20 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 46 21 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 46 22 . . . work_zpfso6pk3vf5df7625v6vawp2e 47 1 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 47 2 refer refer VBP work_zpfso6pk3vf5df7625v6vawp2e 47 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 47 4 readers reader NNS work_zpfso6pk3vf5df7625v6vawp2e 47 5 to to IN work_zpfso6pk3vf5df7625v6vawp2e 47 6 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 47 7 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 47 8 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 47 9 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 47 10 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 47 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 47 12 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 47 13 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 47 14 for for IN work_zpfso6pk3vf5df7625v6vawp2e 47 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 47 16 general general JJ work_zpfso6pk3vf5df7625v6vawp2e 47 17 concepts concept NNS work_zpfso6pk3vf5df7625v6vawp2e 47 18 of of IN work_zpfso6pk3vf5df7625v6vawp2e 47 19 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 47 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 48 1 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 48 2 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 48 3 Notations notation NNS work_zpfso6pk3vf5df7625v6vawp2e 48 4 for for IN work_zpfso6pk3vf5df7625v6vawp2e 48 5 Sphere Sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 48 6 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 48 7 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 48 8 SM−1,g SM−1,g NNP work_zpfso6pk3vf5df7625v6vawp2e 48 9 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 10 Sphere Sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 48 11 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 48 12 for for IN work_zpfso6pk3vf5df7625v6vawp2e 48 13 parameter parameter NNP work_zpfso6pk3vf5df7625v6vawp2e 48 14 matrix matrix NNP work_zpfso6pk3vf5df7625v6vawp2e 48 15 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 16 and and CC work_zpfso6pk3vf5df7625v6vawp2e 48 17 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 18 inner inner JJ work_zpfso6pk3vf5df7625v6vawp2e 48 19 product product NN work_zpfso6pk3vf5df7625v6vawp2e 48 20 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 21 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 22 manifold manifold JJ work_zpfso6pk3vf5df7625v6vawp2e 48 23 Tθ tθ IN work_zpfso6pk3vf5df7625v6vawp2e 48 24 SM−1 sm−1 JJ work_zpfso6pk3vf5df7625v6vawp2e 48 25 Tangent Tangent NNP work_zpfso6pk3vf5df7625v6vawp2e 48 26 space space NN work_zpfso6pk3vf5df7625v6vawp2e 48 27 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 28 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 29 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 48 30 manifold manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 48 31 uθ uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 48 33 vθ vθ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 34 Tangent Tangent NNP work_zpfso6pk3vf5df7625v6vawp2e 48 35 vectors vector NNS work_zpfso6pk3vf5df7625v6vawp2e 48 36 at at IN work_zpfso6pk3vf5df7625v6vawp2e 48 37 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 38 Projθ Projθ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 39 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 48 40 z z NN work_zpfso6pk3vf5df7625v6vawp2e 48 41 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 42 Orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 48 43 projector projector NN work_zpfso6pk3vf5df7625v6vawp2e 48 44 from from IN work_zpfso6pk3vf5df7625v6vawp2e 48 45 a a DT work_zpfso6pk3vf5df7625v6vawp2e 48 46 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 48 47 in in IN work_zpfso6pk3vf5df7625v6vawp2e 48 48 ambient ambient JJ work_zpfso6pk3vf5df7625v6vawp2e 48 49 space space NN work_zpfso6pk3vf5df7625v6vawp2e 48 50 onto onto IN work_zpfso6pk3vf5df7625v6vawp2e 48 51 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 52 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 48 53 space space NN work_zpfso6pk3vf5df7625v6vawp2e 48 54 at at IN work_zpfso6pk3vf5df7625v6vawp2e 48 55 θ θ NN work_zpfso6pk3vf5df7625v6vawp2e 48 56 gradF(θ gradF(θ , work_zpfso6pk3vf5df7625v6vawp2e 48 57 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 58 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 48 59 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 48 60 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 61 F(θ f(θ NN work_zpfso6pk3vf5df7625v6vawp2e 48 62 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 63 on on IN work_zpfso6pk3vf5df7625v6vawp2e 48 64 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 65 manifold manifold JJ work_zpfso6pk3vf5df7625v6vawp2e 48 66 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 48 67 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 68 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 69 Classical classical JJ work_zpfso6pk3vf5df7625v6vawp2e 48 70 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 48 71 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 72 F(θ f(θ NN work_zpfso6pk3vf5df7625v6vawp2e 48 73 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 74 as as IN work_zpfso6pk3vf5df7625v6vawp2e 48 75 seen see VBN work_zpfso6pk3vf5df7625v6vawp2e 48 76 in in IN work_zpfso6pk3vf5df7625v6vawp2e 48 77 Euclidean euclidean JJ work_zpfso6pk3vf5df7625v6vawp2e 48 78 space space NN work_zpfso6pk3vf5df7625v6vawp2e 48 79 Expθ Expθ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 80 Retraction Retraction NNP work_zpfso6pk3vf5df7625v6vawp2e 48 81 mapping mapping NN work_zpfso6pk3vf5df7625v6vawp2e 48 82 Tθk+1←θk Tθk+1←θk NNP work_zpfso6pk3vf5df7625v6vawp2e 48 83 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 48 84 uθk uθk NNP work_zpfso6pk3vf5df7625v6vawp2e 48 85 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 86 Vector Vector NNP work_zpfso6pk3vf5df7625v6vawp2e 48 87 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 48 88 The the DT work_zpfso6pk3vf5df7625v6vawp2e 48 89 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 48 90 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 48 91 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 48 92 the the DT work_zpfso6pk3vf5df7625v6vawp2e 48 93 set set NN work_zpfso6pk3vf5df7625v6vawp2e 48 94 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 95 unit unit NN work_zpfso6pk3vf5df7625v6vawp2e 48 96 Frobenius Frobenius NNP work_zpfso6pk3vf5df7625v6vawp2e 48 97 norm norm NN work_zpfso6pk3vf5df7625v6vawp2e 48 98 vectors vector NNS work_zpfso6pk3vf5df7625v6vawp2e 48 99 of of IN work_zpfso6pk3vf5df7625v6vawp2e 48 100 size size NN work_zpfso6pk3vf5df7625v6vawp2e 48 101 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 48 102 , , , work_zpfso6pk3vf5df7625v6vawp2e 48 103 denoted denote VBD work_zpfso6pk3vf5df7625v6vawp2e 48 104 as as IN work_zpfso6pk3vf5df7625v6vawp2e 48 105 SM−1 SM−1 NNP work_zpfso6pk3vf5df7625v6vawp2e 48 106 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 48 107 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 48 108 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 48 109 ∈RM ∈RM NNP work_zpfso6pk3vf5df7625v6vawp2e 48 110 : : : work_zpfso6pk3vf5df7625v6vawp2e 48 111 ∥θ∥2 ∥θ∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 48 112 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 48 113 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 48 114 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 48 115 . . . work_zpfso6pk3vf5df7625v6vawp2e 49 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 49 2 1 1 LS work_zpfso6pk3vf5df7625v6vawp2e 49 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 49 4 It -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 49 5 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 49 6 endowed endow VBN work_zpfso6pk3vf5df7625v6vawp2e 49 7 with with IN work_zpfso6pk3vf5df7625v6vawp2e 49 8 a a DT work_zpfso6pk3vf5df7625v6vawp2e 49 9 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 49 10 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 49 11 structure structure NN work_zpfso6pk3vf5df7625v6vawp2e 49 12 by by IN work_zpfso6pk3vf5df7625v6vawp2e 49 13 considering consider VBG work_zpfso6pk3vf5df7625v6vawp2e 49 14 it -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 49 15 as as IN work_zpfso6pk3vf5df7625v6vawp2e 49 16 a a DT work_zpfso6pk3vf5df7625v6vawp2e 49 17 Rieman- Rieman- NNP work_zpfso6pk3vf5df7625v6vawp2e 49 18 nian nian JJ work_zpfso6pk3vf5df7625v6vawp2e 49 19 submanifold submanifold NN work_zpfso6pk3vf5df7625v6vawp2e 49 20 of of IN work_zpfso6pk3vf5df7625v6vawp2e 49 21 the the DT work_zpfso6pk3vf5df7625v6vawp2e 49 22 embedding embed VBG work_zpfso6pk3vf5df7625v6vawp2e 49 23 Euclidean euclidean JJ work_zpfso6pk3vf5df7625v6vawp2e 49 24 space space NN work_zpfso6pk3vf5df7625v6vawp2e 49 25 RM RM NNP work_zpfso6pk3vf5df7625v6vawp2e 49 26 endowed endow VBN work_zpfso6pk3vf5df7625v6vawp2e 49 27 with with IN work_zpfso6pk3vf5df7625v6vawp2e 49 28 the the DT work_zpfso6pk3vf5df7625v6vawp2e 49 29 usual usual JJ work_zpfso6pk3vf5df7625v6vawp2e 49 30 inner inner JJ work_zpfso6pk3vf5df7625v6vawp2e 49 31 product product NN work_zpfso6pk3vf5df7625v6vawp2e 49 32 g(uθ g(uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 49 33 , , , work_zpfso6pk3vf5df7625v6vawp2e 49 34 vθ vθ NN work_zpfso6pk3vf5df7625v6vawp2e 49 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 49 36 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 49 37 uTθ uTθ NNP work_zpfso6pk3vf5df7625v6vawp2e 49 38 vθ vθ NN work_zpfso6pk3vf5df7625v6vawp2e 49 39 , , , work_zpfso6pk3vf5df7625v6vawp2e 49 40 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 49 41 2 2 LS work_zpfso6pk3vf5df7625v6vawp2e 49 42 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 49 43 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 49 44 uθ uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 49 45 , , , work_zpfso6pk3vf5df7625v6vawp2e 49 46 vθ vθ VB work_zpfso6pk3vf5df7625v6vawp2e 49 47 ∈ ∈ NNP work_zpfso6pk3vf5df7625v6vawp2e 49 48 Tθ tθ IN work_zpfso6pk3vf5df7625v6vawp2e 49 49 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 49 50 ⊂ ⊂ CD work_zpfso6pk3vf5df7625v6vawp2e 49 51 RM RM NNP work_zpfso6pk3vf5df7625v6vawp2e 49 52 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 49 53 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 49 54 vectors vector NNS work_zpfso6pk3vf5df7625v6vawp2e 49 55 to to TO work_zpfso6pk3vf5df7625v6vawp2e 49 56 SM−1 sm−1 VB work_zpfso6pk3vf5df7625v6vawp2e 49 57 at at IN work_zpfso6pk3vf5df7625v6vawp2e 49 58 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 49 59 . . . work_zpfso6pk3vf5df7625v6vawp2e 50 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 50 2 inner inner JJ work_zpfso6pk3vf5df7625v6vawp2e 50 3 product product NN work_zpfso6pk3vf5df7625v6vawp2e 50 4 on on IN work_zpfso6pk3vf5df7625v6vawp2e 50 5 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 50 6 determines determine VBZ work_zpfso6pk3vf5df7625v6vawp2e 50 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 50 8 geometry geometry NN work_zpfso6pk3vf5df7625v6vawp2e 50 9 such such JJ work_zpfso6pk3vf5df7625v6vawp2e 50 10 as as IN work_zpfso6pk3vf5df7625v6vawp2e 50 11 distance distance NN work_zpfso6pk3vf5df7625v6vawp2e 50 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 50 13 angle angle NN work_zpfso6pk3vf5df7625v6vawp2e 50 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 50 15 curvature curvature JJ work_zpfso6pk3vf5df7625v6vawp2e 50 16 on on IN work_zpfso6pk3vf5df7625v6vawp2e 50 17 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 50 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 51 1 Note note VB work_zpfso6pk3vf5df7625v6vawp2e 51 2 that that IN work_zpfso6pk3vf5df7625v6vawp2e 51 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 51 4 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 51 5 space space NN work_zpfso6pk3vf5df7625v6vawp2e 51 6 Tθ tθ DT work_zpfso6pk3vf5df7625v6vawp2e 51 7 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 51 8 at at IN work_zpfso6pk3vf5df7625v6vawp2e 51 9 element element NN work_zpfso6pk3vf5df7625v6vawp2e 51 10 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 51 11 can can MD work_zpfso6pk3vf5df7625v6vawp2e 51 12 be be VB work_zpfso6pk3vf5df7625v6vawp2e 51 13 described describe VBN work_zpfso6pk3vf5df7625v6vawp2e 51 14 by by IN work_zpfso6pk3vf5df7625v6vawp2e 51 15 Tθ tθ DT work_zpfso6pk3vf5df7625v6vawp2e 51 16 SM−1 SM−1 NNP work_zpfso6pk3vf5df7625v6vawp2e 51 17 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 51 18 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 51 19 uθ uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 51 20 : : : work_zpfso6pk3vf5df7625v6vawp2e 51 21 uTθ uTθ NNP work_zpfso6pk3vf5df7625v6vawp2e 51 22 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 51 23 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 51 24 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 51 25 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 51 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 52 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 52 2 3 3 LS work_zpfso6pk3vf5df7625v6vawp2e 52 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 52 4 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 52 5 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 52 6 and and CC work_zpfso6pk3vf5df7625v6vawp2e 52 7 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 52 8 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 52 9 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 52 10 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 52 11 : : : work_zpfso6pk3vf5df7625v6vawp2e 52 12 Let let VB work_zpfso6pk3vf5df7625v6vawp2e 52 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 52 14 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 52 15 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 52 16 of of IN work_zpfso6pk3vf5df7625v6vawp2e 52 17 a a DT work_zpfso6pk3vf5df7625v6vawp2e 52 18 scalar scalar JJ work_zpfso6pk3vf5df7625v6vawp2e 52 19 function function NN work_zpfso6pk3vf5df7625v6vawp2e 52 20 F(θ F(θ VBN work_zpfso6pk3vf5df7625v6vawp2e 52 21 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 52 22 on on IN work_zpfso6pk3vf5df7625v6vawp2e 52 23 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 52 24 be be VB work_zpfso6pk3vf5df7625v6vawp2e 52 25 denoted denote VBN work_zpfso6pk3vf5df7625v6vawp2e 52 26 by by IN work_zpfso6pk3vf5df7625v6vawp2e 52 27 gradF(θ gradf(θ NN work_zpfso6pk3vf5df7625v6vawp2e 52 28 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 52 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 52 30 and and CC work_zpfso6pk3vf5df7625v6vawp2e 52 31 its -PRON- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 52 32 classical classical JJ work_zpfso6pk3vf5df7625v6vawp2e 52 33 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 52 34 as as IN work_zpfso6pk3vf5df7625v6vawp2e 52 35 seen see VBN work_zpfso6pk3vf5df7625v6vawp2e 52 36 in in IN work_zpfso6pk3vf5df7625v6vawp2e 52 37 the the DT work_zpfso6pk3vf5df7625v6vawp2e 52 38 Euclidean euclidean JJ work_zpfso6pk3vf5df7625v6vawp2e 52 39 space space NN work_zpfso6pk3vf5df7625v6vawp2e 52 40 as as IN work_zpfso6pk3vf5df7625v6vawp2e 52 41 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 52 42 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 52 43 . . . work_zpfso6pk3vf5df7625v6vawp2e 53 1 Then then RB work_zpfso6pk3vf5df7625v6vawp2e 53 2 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 53 3 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 53 4 gradF(θ gradF(θ , work_zpfso6pk3vf5df7625v6vawp2e 53 5 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 6 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 53 7 Projθ Projθ NNP work_zpfso6pk3vf5df7625v6vawp2e 53 8 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 53 9 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 53 10 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 53 13 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 53 14 4 4 LS work_zpfso6pk3vf5df7625v6vawp2e 53 15 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 16 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 53 17 Projθ Projθ NNP work_zpfso6pk3vf5df7625v6vawp2e 53 18 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 53 19 z z NN work_zpfso6pk3vf5df7625v6vawp2e 53 20 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 21 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 53 22 the the DT work_zpfso6pk3vf5df7625v6vawp2e 53 23 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 53 24 projection projection NN work_zpfso6pk3vf5df7625v6vawp2e 53 25 onto onto IN work_zpfso6pk3vf5df7625v6vawp2e 53 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 53 27 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 53 28 space space NN work_zpfso6pk3vf5df7625v6vawp2e 53 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 53 30 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 53 31 can can MD work_zpfso6pk3vf5df7625v6vawp2e 53 32 be be VB work_zpfso6pk3vf5df7625v6vawp2e 53 33 computed compute VBN work_zpfso6pk3vf5df7625v6vawp2e 53 34 as as IN work_zpfso6pk3vf5df7625v6vawp2e 53 35 ProjX(z projx(z NN work_zpfso6pk3vf5df7625v6vawp2e 53 36 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 37 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 53 38 z−(θ z−(θ UH work_zpfso6pk3vf5df7625v6vawp2e 53 39 Tz)θ Tz)θ NNP work_zpfso6pk3vf5df7625v6vawp2e 53 40 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 53 41 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 53 42 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 53 43 in in IN work_zpfso6pk3vf5df7625v6vawp2e 53 44 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 53 45 z z NNP work_zpfso6pk3vf5df7625v6vawp2e 53 46 represents represent VBZ work_zpfso6pk3vf5df7625v6vawp2e 53 47 a a DT work_zpfso6pk3vf5df7625v6vawp2e 53 48 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 53 49 in in IN work_zpfso6pk3vf5df7625v6vawp2e 53 50 the the DT work_zpfso6pk3vf5df7625v6vawp2e 53 51 ambient ambient JJ work_zpfso6pk3vf5df7625v6vawp2e 53 52 space space NN work_zpfso6pk3vf5df7625v6vawp2e 53 53 . . . work_zpfso6pk3vf5df7625v6vawp2e 54 1 Retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 54 2 mapping mapping NN work_zpfso6pk3vf5df7625v6vawp2e 54 3 : : : work_zpfso6pk3vf5df7625v6vawp2e 54 4 An an DT work_zpfso6pk3vf5df7625v6vawp2e 54 5 important important JJ work_zpfso6pk3vf5df7625v6vawp2e 54 6 concept concept NN work_zpfso6pk3vf5df7625v6vawp2e 54 7 in in IN work_zpfso6pk3vf5df7625v6vawp2e 54 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 54 9 recent recent JJ work_zpfso6pk3vf5df7625v6vawp2e 54 10 retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 54 11 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 54 12 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 54 13 frame- frame- NN work_zpfso6pk3vf5df7625v6vawp2e 54 14 work work NN work_zpfso6pk3vf5df7625v6vawp2e 54 15 of of IN work_zpfso6pk3vf5df7625v6vawp2e 54 16 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 54 17 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 54 18 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 54 19 the the DT work_zpfso6pk3vf5df7625v6vawp2e 54 20 retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 54 21 mapping mapping NN work_zpfso6pk3vf5df7625v6vawp2e 54 22 , , , work_zpfso6pk3vf5df7625v6vawp2e 54 23 see see VB work_zpfso6pk3vf5df7625v6vawp2e 54 24 Section section NN work_zpfso6pk3vf5df7625v6vawp2e 54 25 4.1 4.1 CD work_zpfso6pk3vf5df7625v6vawp2e 54 26 of of IN work_zpfso6pk3vf5df7625v6vawp2e 54 27 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 54 28 Ab- Ab- NNP work_zpfso6pk3vf5df7625v6vawp2e 54 29 sil sil NNP work_zpfso6pk3vf5df7625v6vawp2e 54 30 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 54 31 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 54 32 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 54 33 , , , work_zpfso6pk3vf5df7625v6vawp2e 54 34 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 54 35 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 54 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 55 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 55 2 exponential exponential JJ work_zpfso6pk3vf5df7625v6vawp2e 55 3 map map NN work_zpfso6pk3vf5df7625v6vawp2e 55 4 ExpX ExpX NNP work_zpfso6pk3vf5df7625v6vawp2e 55 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 55 6 defined define VBN work_zpfso6pk3vf5df7625v6vawp2e 55 7 by by IN work_zpfso6pk3vf5df7625v6vawp2e 55 8 Expθ Expθ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 9 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 55 10 λ λ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 11 uθ uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 12 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 55 13 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 55 14 cos cos NNP work_zpfso6pk3vf5df7625v6vawp2e 55 15 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 55 16 ∥λ ∥λ IN work_zpfso6pk3vf5df7625v6vawp2e 55 17 uθ∥2 uθ∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 55 18 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 55 19 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 20 + + CC work_zpfso6pk3vf5df7625v6vawp2e 55 21 sin(∥λ sin(∥λ SYM work_zpfso6pk3vf5df7625v6vawp2e 55 22 uθ∥2 uθ∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 55 23 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 55 24 ∥uθ∥2 ∥uθ∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 55 25 uθ uθ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 55 27 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 55 28 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 55 29 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 55 30 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 55 31 the the DT work_zpfso6pk3vf5df7625v6vawp2e 55 32 canonical canonical JJ work_zpfso6pk3vf5df7625v6vawp2e 55 33 choice choice NN work_zpfso6pk3vf5df7625v6vawp2e 55 34 for for IN work_zpfso6pk3vf5df7625v6vawp2e 55 35 the the DT work_zpfso6pk3vf5df7625v6vawp2e 55 36 retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 55 37 mapping mapping NN work_zpfso6pk3vf5df7625v6vawp2e 55 38 , , , work_zpfso6pk3vf5df7625v6vawp2e 55 39 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 55 40 the the DT work_zpfso6pk3vf5df7625v6vawp2e 55 41 scalar scalar NN work_zpfso6pk3vf5df7625v6vawp2e 55 42 λ λ NNP work_zpfso6pk3vf5df7625v6vawp2e 55 43 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 55 44 a a DT work_zpfso6pk3vf5df7625v6vawp2e 55 45 chosen choose VBN work_zpfso6pk3vf5df7625v6vawp2e 55 46 step step NN work_zpfso6pk3vf5df7625v6vawp2e 55 47 size size NN work_zpfso6pk3vf5df7625v6vawp2e 55 48 . . . work_zpfso6pk3vf5df7625v6vawp2e 56 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 56 2 retraction retraction NN work_zpfso6pk3vf5df7625v6vawp2e 56 3 mapping mapping NN work_zpfso6pk3vf5df7625v6vawp2e 56 4 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 56 5 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 56 6 to to TO work_zpfso6pk3vf5df7625v6vawp2e 56 7 locate locate VB work_zpfso6pk3vf5df7625v6vawp2e 56 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 56 9 next next JJ work_zpfso6pk3vf5df7625v6vawp2e 56 10 iterate iterate NN work_zpfso6pk3vf5df7625v6vawp2e 56 11 on on IN work_zpfso6pk3vf5df7625v6vawp2e 56 12 the the DT work_zpfso6pk3vf5df7625v6vawp2e 56 13 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 56 14 along along IN work_zpfso6pk3vf5df7625v6vawp2e 56 15 a a DT work_zpfso6pk3vf5df7625v6vawp2e 56 16 specified specify VBN work_zpfso6pk3vf5df7625v6vawp2e 56 17 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 56 18 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 56 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 56 20 such such JJ work_zpfso6pk3vf5df7625v6vawp2e 56 21 as as IN work_zpfso6pk3vf5df7625v6vawp2e 56 22 a a DT work_zpfso6pk3vf5df7625v6vawp2e 56 23 search search NN work_zpfso6pk3vf5df7625v6vawp2e 56 24 direction direction NN work_zpfso6pk3vf5df7625v6vawp2e 56 25 in in IN work_zpfso6pk3vf5df7625v6vawp2e 56 26 line line NN work_zpfso6pk3vf5df7625v6vawp2e 56 27 search search NN work_zpfso6pk3vf5df7625v6vawp2e 56 28 in in IN work_zpfso6pk3vf5df7625v6vawp2e 56 29 the the DT work_zpfso6pk3vf5df7625v6vawp2e 56 30 New- New- NNP work_zpfso6pk3vf5df7625v6vawp2e 56 31 ton ton NN work_zpfso6pk3vf5df7625v6vawp2e 56 32 ’s ’ VBZ work_zpfso6pk3vf5df7625v6vawp2e 56 33 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 56 34 or or CC work_zpfso6pk3vf5df7625v6vawp2e 56 35 the the DT work_zpfso6pk3vf5df7625v6vawp2e 56 36 suboptimal suboptimal JJ work_zpfso6pk3vf5df7625v6vawp2e 56 37 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 56 38 direction direction NN work_zpfso6pk3vf5df7625v6vawp2e 56 39 in in IN work_zpfso6pk3vf5df7625v6vawp2e 56 40 the the DT work_zpfso6pk3vf5df7625v6vawp2e 56 41 trust trust NN work_zpfso6pk3vf5df7625v6vawp2e 56 42 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 56 43 region region NN work_zpfso6pk3vf5df7625v6vawp2e 56 44 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 56 45 , , , work_zpfso6pk3vf5df7625v6vawp2e 56 46 see see VB work_zpfso6pk3vf5df7625v6vawp2e 56 47 Chapter chapter NN work_zpfso6pk3vf5df7625v6vawp2e 56 48 7 7 CD work_zpfso6pk3vf5df7625v6vawp2e 56 49 of of IN work_zpfso6pk3vf5df7625v6vawp2e 56 50 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 56 51 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 56 52 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 56 53 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 56 54 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 56 55 , , , work_zpfso6pk3vf5df7625v6vawp2e 56 56 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 56 57 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 56 58 . . . work_zpfso6pk3vf5df7625v6vawp2e 57 1 For for IN work_zpfso6pk3vf5df7625v6vawp2e 57 2 example example NN work_zpfso6pk3vf5df7625v6vawp2e 57 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 57 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 57 5 line line NN work_zpfso6pk3vf5df7625v6vawp2e 57 6 search search NN work_zpfso6pk3vf5df7625v6vawp2e 57 7 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 57 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 57 9 simply simply RB work_zpfso6pk3vf5df7625v6vawp2e 57 10 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 57 11 by by IN work_zpfso6pk3vf5df7625v6vawp2e 57 12 θk+1 θk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 57 13 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 57 14 Expθk Expθk NNP work_zpfso6pk3vf5df7625v6vawp2e 57 15 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 57 16 λkuθk λkuθk JJ work_zpfso6pk3vf5df7625v6vawp2e 57 17 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 57 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 58 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 58 2 7 7 LS work_zpfso6pk3vf5df7625v6vawp2e 58 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 58 4 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 58 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 58 6 search search NN work_zpfso6pk3vf5df7625v6vawp2e 58 7 direction direction NN work_zpfso6pk3vf5df7625v6vawp2e 58 8 uθk uθk NN work_zpfso6pk3vf5df7625v6vawp2e 58 9 ∈ ∈ NNP work_zpfso6pk3vf5df7625v6vawp2e 58 10 Tθk Tθk NNP work_zpfso6pk3vf5df7625v6vawp2e 58 11 S S NNP work_zpfso6pk3vf5df7625v6vawp2e 58 12 M−1 M−1 NNP work_zpfso6pk3vf5df7625v6vawp2e 58 13 and and CC work_zpfso6pk3vf5df7625v6vawp2e 58 14 λk λk NNP work_zpfso6pk3vf5df7625v6vawp2e 58 15 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 58 16 a a DT work_zpfso6pk3vf5df7625v6vawp2e 58 17 chosen choose VBN work_zpfso6pk3vf5df7625v6vawp2e 58 18 step step NN work_zpfso6pk3vf5df7625v6vawp2e 58 19 size size NN work_zpfso6pk3vf5df7625v6vawp2e 58 20 at at IN work_zpfso6pk3vf5df7625v6vawp2e 58 21 iteration iteration NN work_zpfso6pk3vf5df7625v6vawp2e 58 22 step step NN work_zpfso6pk3vf5df7625v6vawp2e 58 23 k. k. NNP work_zpfso6pk3vf5df7625v6vawp2e 58 24 Vector Vector NNP work_zpfso6pk3vf5df7625v6vawp2e 58 25 Transport Transport NNP work_zpfso6pk3vf5df7625v6vawp2e 58 26 : : : work_zpfso6pk3vf5df7625v6vawp2e 58 27 In in IN work_zpfso6pk3vf5df7625v6vawp2e 58 28 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 58 29 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 58 30 algorithms algorithm NNS work_zpfso6pk3vf5df7625v6vawp2e 58 31 , , , work_zpfso6pk3vf5df7625v6vawp2e 58 32 the the DT work_zpfso6pk3vf5df7625v6vawp2e 58 33 second second JJ work_zpfso6pk3vf5df7625v6vawp2e 58 34 derivatives derivative NNS work_zpfso6pk3vf5df7625v6vawp2e 58 35 can can MD work_zpfso6pk3vf5df7625v6vawp2e 58 36 be be VB work_zpfso6pk3vf5df7625v6vawp2e 58 37 approximated approximate VBN work_zpfso6pk3vf5df7625v6vawp2e 58 38 by by IN work_zpfso6pk3vf5df7625v6vawp2e 58 39 comparing compare VBG work_zpfso6pk3vf5df7625v6vawp2e 58 40 the the DT work_zpfso6pk3vf5df7625v6vawp2e 58 41 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 58 42 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 58 43 order order NN work_zpfso6pk3vf5df7625v6vawp2e 58 44 information information NN work_zpfso6pk3vf5df7625v6vawp2e 58 45 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 58 46 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 58 47 vectors vector NNS work_zpfso6pk3vf5df7625v6vawp2e 58 48 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 58 49 at at IN work_zpfso6pk3vf5df7625v6vawp2e 58 50 distinct distinct JJ work_zpfso6pk3vf5df7625v6vawp2e 58 51 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 58 52 on on IN work_zpfso6pk3vf5df7625v6vawp2e 58 53 the the DT work_zpfso6pk3vf5df7625v6vawp2e 58 54 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 58 55 . . . work_zpfso6pk3vf5df7625v6vawp2e 59 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 59 2 notion notion NN work_zpfso6pk3vf5df7625v6vawp2e 59 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 59 4 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 59 5 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 59 6 Tθk+1←θk Tθk+1←θk NNP work_zpfso6pk3vf5df7625v6vawp2e 59 7 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 59 8 uθk uθk NNP work_zpfso6pk3vf5df7625v6vawp2e 59 9 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 59 10 on on IN work_zpfso6pk3vf5df7625v6vawp2e 59 11 a a DT work_zpfso6pk3vf5df7625v6vawp2e 59 12 manifold manifold JJ work_zpfso6pk3vf5df7625v6vawp2e 59 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 59 14 roughly roughly RB work_zpfso6pk3vf5df7625v6vawp2e 59 15 speaking speak VBG work_zpfso6pk3vf5df7625v6vawp2e 59 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 59 17 specifies specify VBZ work_zpfso6pk3vf5df7625v6vawp2e 59 18 how how WRB work_zpfso6pk3vf5df7625v6vawp2e 59 19 to to TO work_zpfso6pk3vf5df7625v6vawp2e 59 20 transport transport VB work_zpfso6pk3vf5df7625v6vawp2e 59 21 a a DT work_zpfso6pk3vf5df7625v6vawp2e 59 22 tangent tangent NN work_zpfso6pk3vf5df7625v6vawp2e 59 23 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 59 24 uθk uθk NN work_zpfso6pk3vf5df7625v6vawp2e 59 25 from from IN work_zpfso6pk3vf5df7625v6vawp2e 59 26 a a DT work_zpfso6pk3vf5df7625v6vawp2e 59 27 point point NN work_zpfso6pk3vf5df7625v6vawp2e 59 28 θk θk UH work_zpfso6pk3vf5df7625v6vawp2e 59 29 to to IN work_zpfso6pk3vf5df7625v6vawp2e 59 30 another another DT work_zpfso6pk3vf5df7625v6vawp2e 59 31 point point NN work_zpfso6pk3vf5df7625v6vawp2e 59 32 θk+1 θk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 59 33 on on IN work_zpfso6pk3vf5df7625v6vawp2e 59 34 the the DT work_zpfso6pk3vf5df7625v6vawp2e 59 35 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 59 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 60 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 60 2 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 60 3 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 60 4 for for IN work_zpfso6pk3vf5df7625v6vawp2e 60 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 6 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 60 7 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 60 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 60 9 calculated calculate VBN work_zpfso6pk3vf5df7625v6vawp2e 60 10 as as IN work_zpfso6pk3vf5df7625v6vawp2e 60 11 Tθk+1←θk Tθk+1←θk NNP work_zpfso6pk3vf5df7625v6vawp2e 60 12 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 13 uθk uθk NNP work_zpfso6pk3vf5df7625v6vawp2e 60 14 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 15 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 60 16 Projθk+1 projθk+1 FW work_zpfso6pk3vf5df7625v6vawp2e 60 17 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 18 uθk uθk NNP work_zpfso6pk3vf5df7625v6vawp2e 60 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 21 8) 8) CD work_zpfso6pk3vf5df7625v6vawp2e 60 22 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 60 23 Proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 60 24 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 60 25 for for IN work_zpfso6pk3vf5df7625v6vawp2e 60 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 27 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 60 28 root root NN work_zpfso6pk3vf5df7625v6vawp2e 60 29 of of IN work_zpfso6pk3vf5df7625v6vawp2e 60 30 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 60 31 density density NN work_zpfso6pk3vf5df7625v6vawp2e 60 32 function function NN work_zpfso6pk3vf5df7625v6vawp2e 60 33 Given give VBN work_zpfso6pk3vf5df7625v6vawp2e 60 34 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 35 finite finite JJ work_zpfso6pk3vf5df7625v6vawp2e 60 36 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 60 37 set set VBN work_zpfso6pk3vf5df7625v6vawp2e 60 38 DN DN NNP work_zpfso6pk3vf5df7625v6vawp2e 60 39 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 60 40 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 41 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 60 42 j}Nj=1 j}Nj=1 NNP work_zpfso6pk3vf5df7625v6vawp2e 60 43 consisting consist VBG work_zpfso6pk3vf5df7625v6vawp2e 60 44 of of IN work_zpfso6pk3vf5df7625v6vawp2e 60 45 N N NNP work_zpfso6pk3vf5df7625v6vawp2e 60 46 data data NN work_zpfso6pk3vf5df7625v6vawp2e 60 47 samples sample NNS work_zpfso6pk3vf5df7625v6vawp2e 60 48 , , , work_zpfso6pk3vf5df7625v6vawp2e 60 49 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 60 50 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 51 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 60 52 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 60 53 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 60 54 ∈ ∈ NNP work_zpfso6pk3vf5df7625v6vawp2e 60 55 Rm Rm NNP work_zpfso6pk3vf5df7625v6vawp2e 60 56 follows follow VBZ work_zpfso6pk3vf5df7625v6vawp2e 60 57 an an DT work_zpfso6pk3vf5df7625v6vawp2e 60 58 unknown unknown JJ work_zpfso6pk3vf5df7625v6vawp2e 60 59 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 60 60 p(x p(x NNS work_zpfso6pk3vf5df7625v6vawp2e 60 61 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 62 , , , work_zpfso6pk3vf5df7625v6vawp2e 60 63 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 64 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 60 65 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 60 66 model model NN work_zpfso6pk3vf5df7625v6vawp2e 60 67 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 68 McLachlan McLachlan NNP work_zpfso6pk3vf5df7625v6vawp2e 60 69 and and CC work_zpfso6pk3vf5df7625v6vawp2e 60 70 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 60 71 , , , work_zpfso6pk3vf5df7625v6vawp2e 60 72 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 60 73 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 74 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 60 75 in in IN work_zpfso6pk3vf5df7625v6vawp2e 60 76 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 77 form form NN work_zpfso6pk3vf5df7625v6vawp2e 60 78 of of IN work_zpfso6pk3vf5df7625v6vawp2e 60 79 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 60 80 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 81 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 60 82 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 60 83 of of IN work_zpfso6pk3vf5df7625v6vawp2e 60 84 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 60 85 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 60 86 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 60 87 on on IN work_zpfso6pk3vf5df7625v6vawp2e 60 88 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 60 89 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 60 90 pGMM(x pgmm(x NN work_zpfso6pk3vf5df7625v6vawp2e 60 91 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 92 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 60 93 P p NN work_zpfso6pk3vf5df7625v6vawp2e 60 94 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 60 95 i=1 i=1 UH work_zpfso6pk3vf5df7625v6vawp2e 60 96 gi gi NN work_zpfso6pk3vf5df7625v6vawp2e 60 97 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 98 2π)m/2|Σi|m/2 2π)m/2|σi|m/2 CD work_zpfso6pk3vf5df7625v6vawp2e 60 99 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 60 100 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 101 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 60 102 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 60 103 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 60 104 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 105 x−µ x−µ NNP work_zpfso6pk3vf5df7625v6vawp2e 60 106 i i NN work_zpfso6pk3vf5df7625v6vawp2e 60 107 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 108 TΣi−1(x−µ TΣi−1(x−µ NNP work_zpfso6pk3vf5df7625v6vawp2e 60 109 i i NNP work_zpfso6pk3vf5df7625v6vawp2e 60 110 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 111 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 112 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 113 9 9 CD work_zpfso6pk3vf5df7625v6vawp2e 60 114 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 115 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 60 116 µi µi UH work_zpfso6pk3vf5df7625v6vawp2e 60 117 and and CC work_zpfso6pk3vf5df7625v6vawp2e 60 118 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 60 119 i i PRP work_zpfso6pk3vf5df7625v6vawp2e 60 120 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 60 121 called call VBN work_zpfso6pk3vf5df7625v6vawp2e 60 122 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 123 mean mean JJ work_zpfso6pk3vf5df7625v6vawp2e 60 124 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 60 125 , , , work_zpfso6pk3vf5df7625v6vawp2e 60 126 and and CC work_zpfso6pk3vf5df7625v6vawp2e 60 127 covariance covariance NN work_zpfso6pk3vf5df7625v6vawp2e 60 128 matrix matrix NNP work_zpfso6pk3vf5df7625v6vawp2e 60 129 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 60 130 positive positive JJ work_zpfso6pk3vf5df7625v6vawp2e 60 131 definite definite JJ work_zpfso6pk3vf5df7625v6vawp2e 60 132 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 60 133 of of IN work_zpfso6pk3vf5df7625v6vawp2e 60 134 the the DT work_zpfso6pk3vf5df7625v6vawp2e 60 135 ith ith NNP work_zpfso6pk3vf5df7625v6vawp2e 60 136 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 60 137 . . . work_zpfso6pk3vf5df7625v6vawp2e 61 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 61 2 mixing mix VBG work_zpfso6pk3vf5df7625v6vawp2e 61 3 coefficients coefficient NNS work_zpfso6pk3vf5df7625v6vawp2e 61 4 satisfies satisfy VBZ work_zpfso6pk3vf5df7625v6vawp2e 61 5 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 61 6 ≤ ≤ NN work_zpfso6pk3vf5df7625v6vawp2e 61 7 gi gi NNP work_zpfso6pk3vf5df7625v6vawp2e 61 8 ≤ ≤ NNP work_zpfso6pk3vf5df7625v6vawp2e 61 9 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 61 10 for for IN work_zpfso6pk3vf5df7625v6vawp2e 61 11 all all DT work_zpfso6pk3vf5df7625v6vawp2e 61 12 i i PRP work_zpfso6pk3vf5df7625v6vawp2e 61 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 61 14 and and CC work_zpfso6pk3vf5df7625v6vawp2e 61 15 P p NN work_zpfso6pk3vf5df7625v6vawp2e 61 16 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 61 17 i=1 i=1 UH work_zpfso6pk3vf5df7625v6vawp2e 61 18 gi gi NN work_zpfso6pk3vf5df7625v6vawp2e 61 19 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 61 20 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 61 21 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 61 22 10 10 CD work_zpfso6pk3vf5df7625v6vawp2e 61 23 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 61 24 In in IN work_zpfso6pk3vf5df7625v6vawp2e 61 25 this this DT work_zpfso6pk3vf5df7625v6vawp2e 61 26 work work NN work_zpfso6pk3vf5df7625v6vawp2e 61 27 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 61 28 investigate investigate VBP work_zpfso6pk3vf5df7625v6vawp2e 61 29 the the DT work_zpfso6pk3vf5df7625v6vawp2e 61 30 less less RBR work_zpfso6pk3vf5df7625v6vawp2e 61 31 studied studied JJ work_zpfso6pk3vf5df7625v6vawp2e 61 32 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 61 33 of of IN work_zpfso6pk3vf5df7625v6vawp2e 61 34 estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 61 35 the the DT work_zpfso6pk3vf5df7625v6vawp2e 61 36 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 61 37 root root NN work_zpfso6pk3vf5df7625v6vawp2e 61 38 of of IN work_zpfso6pk3vf5df7625v6vawp2e 61 39 the the DT work_zpfso6pk3vf5df7625v6vawp2e 61 40 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 61 41 density density NN work_zpfso6pk3vf5df7625v6vawp2e 61 42 function function NN work_zpfso6pk3vf5df7625v6vawp2e 61 43 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 61 44 PDF PDF NNP work_zpfso6pk3vf5df7625v6vawp2e 61 45 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 61 46 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 61 47 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 61 48 Pinheiro Pinheiro NNP work_zpfso6pk3vf5df7625v6vawp2e 61 49 and and CC work_zpfso6pk3vf5df7625v6vawp2e 61 50 Vidakovic Vidakovic NNP work_zpfso6pk3vf5df7625v6vawp2e 61 51 , , , work_zpfso6pk3vf5df7625v6vawp2e 61 52 1998 1998 CD work_zpfso6pk3vf5df7625v6vawp2e 61 53 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 61 54 . . . work_zpfso6pk3vf5df7625v6vawp2e 62 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 62 2 reason reason NN work_zpfso6pk3vf5df7625v6vawp2e 62 3 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 62 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 62 5 root root NN work_zpfso6pk3vf5df7625v6vawp2e 62 6 square square NN work_zpfso6pk3vf5df7625v6vawp2e 62 7 of of IN work_zpfso6pk3vf5df7625v6vawp2e 62 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 62 9 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 62 10 density density NN work_zpfso6pk3vf5df7625v6vawp2e 62 11 function function NN work_zpfso6pk3vf5df7625v6vawp2e 62 12 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 62 13 esti- esti- RB work_zpfso6pk3vf5df7625v6vawp2e 62 14 mated mated JJ work_zpfso6pk3vf5df7625v6vawp2e 62 15 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 62 16 that that IN work_zpfso6pk3vf5df7625v6vawp2e 62 17 the the DT work_zpfso6pk3vf5df7625v6vawp2e 62 18 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 62 19 can can MD work_zpfso6pk3vf5df7625v6vawp2e 62 20 be be VB work_zpfso6pk3vf5df7625v6vawp2e 62 21 formulated formulate VBN work_zpfso6pk3vf5df7625v6vawp2e 62 22 as as IN work_zpfso6pk3vf5df7625v6vawp2e 62 23 a a DT work_zpfso6pk3vf5df7625v6vawp2e 62 24 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 62 25 optimisation optimisation NN work_zpfso6pk3vf5df7625v6vawp2e 62 26 one one CD work_zpfso6pk3vf5df7625v6vawp2e 62 27 for for IN work_zpfso6pk3vf5df7625v6vawp2e 62 28 computational computational JJ work_zpfso6pk3vf5df7625v6vawp2e 62 29 advantage advantage NN work_zpfso6pk3vf5df7625v6vawp2e 62 30 , , , work_zpfso6pk3vf5df7625v6vawp2e 62 31 as as RB work_zpfso6pk3vf5df7625v6vawp2e 62 32 well well RB work_zpfso6pk3vf5df7625v6vawp2e 62 33 as as IN work_zpfso6pk3vf5df7625v6vawp2e 62 34 that that DT work_zpfso6pk3vf5df7625v6vawp2e 62 35 the the DT work_zpfso6pk3vf5df7625v6vawp2e 62 36 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 62 37 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 62 38 can can MD work_zpfso6pk3vf5df7625v6vawp2e 62 39 be be VB work_zpfso6pk3vf5df7625v6vawp2e 62 40 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 62 41 as as IN work_zpfso6pk3vf5df7625v6vawp2e 62 42 an an DT work_zpfso6pk3vf5df7625v6vawp2e 62 43 alternative alternative NN work_zpfso6pk3vf5df7625v6vawp2e 62 44 to to IN work_zpfso6pk3vf5df7625v6vawp2e 62 45 a a DT work_zpfso6pk3vf5df7625v6vawp2e 62 46 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 62 47 density density NN work_zpfso6pk3vf5df7625v6vawp2e 62 48 function function NN work_zpfso6pk3vf5df7625v6vawp2e 62 49 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 62 50 . . . work_zpfso6pk3vf5df7625v6vawp2e 63 1 Specifically specifically RB work_zpfso6pk3vf5df7625v6vawp2e 63 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 4 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 63 5 un- un- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 63 6 der der NN work_zpfso6pk3vf5df7625v6vawp2e 63 7 study study NN work_zpfso6pk3vf5df7625v6vawp2e 63 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 63 9 to to TO work_zpfso6pk3vf5df7625v6vawp2e 63 10 find find VB work_zpfso6pk3vf5df7625v6vawp2e 63 11 a a DT work_zpfso6pk3vf5df7625v6vawp2e 63 12 sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 63 13 approximation approximation NN work_zpfso6pk3vf5df7625v6vawp2e 63 14 of of IN work_zpfso6pk3vf5df7625v6vawp2e 63 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 16 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 63 17 root root NN work_zpfso6pk3vf5df7625v6vawp2e 63 18 of of IN work_zpfso6pk3vf5df7625v6vawp2e 63 19 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 20 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 21 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 63 22 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 63 23 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 24 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 25 > > XX work_zpfso6pk3vf5df7625v6vawp2e 63 26 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 63 27 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 63 28 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 63 29 component component NN work_zpfso6pk3vf5df7625v6vawp2e 63 30 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 63 31 kernels kernel NNS work_zpfso6pk3vf5df7625v6vawp2e 63 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 33 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 63 34 by by IN work_zpfso6pk3vf5df7625v6vawp2e 63 35 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 36 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 37 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 63 38 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 63 39 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 63 40 i=1 i=1 UH work_zpfso6pk3vf5df7625v6vawp2e 63 41 ωiKσ ωikσ XX work_zpfso6pk3vf5df7625v6vawp2e 63 42 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 43 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 44 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 45 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 63 46 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 47 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 63 48 ω ω NNP work_zpfso6pk3vf5df7625v6vawp2e 63 49 Tk(x Tk(x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 50 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 51 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 52 11 11 CD work_zpfso6pk3vf5df7625v6vawp2e 63 53 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 54 subject subject JJ work_zpfso6pk3vf5df7625v6vawp2e 63 55 to to IN work_zpfso6pk3vf5df7625v6vawp2e 63 56 ∫ ∫ CD work_zpfso6pk3vf5df7625v6vawp2e 63 57 ψ ψ NNP work_zpfso6pk3vf5df7625v6vawp2e 63 58 2(x)dx 2(x)dx NNP work_zpfso6pk3vf5df7625v6vawp2e 63 59 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 63 60 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 63 61 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 62 12 12 CD work_zpfso6pk3vf5df7625v6vawp2e 63 63 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 64 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 63 65 Kσ Kσ NNP work_zpfso6pk3vf5df7625v6vawp2e 63 66 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 67 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 63 68 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 69 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 63 70 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 71 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 63 72 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 63 73 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 74 2π 2π CD work_zpfso6pk3vf5df7625v6vawp2e 63 75 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 63 76 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 63 77 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 78 m/2 m/2 NNP work_zpfso6pk3vf5df7625v6vawp2e 63 79 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 63 80 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 81 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 63 82 ∥x−ci∥2 ∥x−ci∥2 CD work_zpfso6pk3vf5df7625v6vawp2e 63 83 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 63 84 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 63 85 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 86 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 87 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 88 13 13 CD work_zpfso6pk3vf5df7625v6vawp2e 63 89 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 90 in in IN work_zpfso6pk3vf5df7625v6vawp2e 63 91 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 63 92 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 63 93 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 63 94 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 63 95 ci,1 ci,1 NNP work_zpfso6pk3vf5df7625v6vawp2e 63 96 ci,2 ci,2 : work_zpfso6pk3vf5df7625v6vawp2e 63 97 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 63 98 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 63 99 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 63 100 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 63 101 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 102 m m LS work_zpfso6pk3vf5df7625v6vawp2e 63 103 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 63 104 T T NNP work_zpfso6pk3vf5df7625v6vawp2e 63 105 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 63 106 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 107 center center JJ work_zpfso6pk3vf5df7625v6vawp2e 63 108 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 63 109 of of IN work_zpfso6pk3vf5df7625v6vawp2e 63 110 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 111 ith ith NNP work_zpfso6pk3vf5df7625v6vawp2e 63 112 kernels kernels NNPS work_zpfso6pk3vf5df7625v6vawp2e 63 113 and and CC work_zpfso6pk3vf5df7625v6vawp2e 63 114 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 63 115 > > NNP work_zpfso6pk3vf5df7625v6vawp2e 63 116 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 63 117 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 63 118 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 119 width width JJ work_zpfso6pk3vf5df7625v6vawp2e 63 120 parameter parameter NN work_zpfso6pk3vf5df7625v6vawp2e 63 121 , , , work_zpfso6pk3vf5df7625v6vawp2e 63 122 and and CC work_zpfso6pk3vf5df7625v6vawp2e 63 123 ωi ωi NNP work_zpfso6pk3vf5df7625v6vawp2e 63 124 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 63 125 the the DT work_zpfso6pk3vf5df7625v6vawp2e 63 126 ith ith NNP work_zpfso6pk3vf5df7625v6vawp2e 63 127 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 63 128 weight weight NN work_zpfso6pk3vf5df7625v6vawp2e 63 129 . . . work_zpfso6pk3vf5df7625v6vawp2e 64 1 ω ω LS work_zpfso6pk3vf5df7625v6vawp2e 64 2 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 64 3 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 4 ω1 ω1 NNP work_zpfso6pk3vf5df7625v6vawp2e 64 5 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 6 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 7 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 8 ωM]T ωM]T NNP work_zpfso6pk3vf5df7625v6vawp2e 64 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 10 k(x k(x NNP work_zpfso6pk3vf5df7625v6vawp2e 64 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 12 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 64 13 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 14 Kσ Kσ NNP work_zpfso6pk3vf5df7625v6vawp2e 64 15 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 16 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 64 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 18 c1 c1 NN work_zpfso6pk3vf5df7625v6vawp2e 64 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 20 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 21 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 22 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 64 23 Kσ Kσ NNP work_zpfso6pk3vf5df7625v6vawp2e 64 24 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 25 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 64 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 27 cM cM . work_zpfso6pk3vf5df7625v6vawp2e 64 28 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 29 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 30 T. T. NNP work_zpfso6pk3vf5df7625v6vawp2e 64 31 Applying applying NN work_zpfso6pk3vf5df7625v6vawp2e 64 32 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 33 11 11 CD work_zpfso6pk3vf5df7625v6vawp2e 64 34 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 35 to to IN work_zpfso6pk3vf5df7625v6vawp2e 64 36 the the DT work_zpfso6pk3vf5df7625v6vawp2e 64 37 constraint constraint NN work_zpfso6pk3vf5df7625v6vawp2e 64 38 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 39 12 12 CD work_zpfso6pk3vf5df7625v6vawp2e 64 40 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 42 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 64 43 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 64 44 ∫ ∫ : work_zpfso6pk3vf5df7625v6vawp2e 64 45 ψ ψ NN work_zpfso6pk3vf5df7625v6vawp2e 64 46 2(x)dx 2(x)dx NNP work_zpfso6pk3vf5df7625v6vawp2e 64 47 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 64 48 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 64 49 ∑ ∑ NN work_zpfso6pk3vf5df7625v6vawp2e 64 50 i=1 i=1 UH work_zpfso6pk3vf5df7625v6vawp2e 64 51 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 64 52 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 64 53 j=1 j=1 NN work_zpfso6pk3vf5df7625v6vawp2e 64 54 ωiω ωiω XX work_zpfso6pk3vf5df7625v6vawp2e 64 55 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 64 56 ∫ ∫ : work_zpfso6pk3vf5df7625v6vawp2e 64 57 Kσ Kσ NNP work_zpfso6pk3vf5df7625v6vawp2e 64 58 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 59 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 64 60 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 61 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 64 62 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 63 Kσ Kσ NNP work_zpfso6pk3vf5df7625v6vawp2e 64 64 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 65 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 64 66 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 67 c c NN work_zpfso6pk3vf5df7625v6vawp2e 64 68 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 64 69 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 70 dx dx NNP work_zpfso6pk3vf5df7625v6vawp2e 64 71 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 64 72 ω ω NNP work_zpfso6pk3vf5df7625v6vawp2e 64 73 TQω TQω NNS work_zpfso6pk3vf5df7625v6vawp2e 64 74 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 64 75 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 64 76 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 77 14 14 CD work_zpfso6pk3vf5df7625v6vawp2e 64 78 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 79 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 64 80 Q q NN work_zpfso6pk3vf5df7625v6vawp2e 64 81 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 64 82 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 83 qi qi NNP work_zpfso6pk3vf5df7625v6vawp2e 64 84 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 85 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 64 86 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 87 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 88 with with IN work_zpfso6pk3vf5df7625v6vawp2e 64 89 qi qi NNP work_zpfso6pk3vf5df7625v6vawp2e 64 90 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 91 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 64 92 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 64 93 K√2σ k√2σ ADD work_zpfso6pk3vf5df7625v6vawp2e 64 94 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 64 95 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 64 96 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 97 c c NNP work_zpfso6pk3vf5df7625v6vawp2e 64 98 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 64 99 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 64 100 , , , work_zpfso6pk3vf5df7625v6vawp2e 64 101 as as IN work_zpfso6pk3vf5df7625v6vawp2e 64 102 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 64 103 in in IN work_zpfso6pk3vf5df7625v6vawp2e 64 104 Appendix Appendix NNP work_zpfso6pk3vf5df7625v6vawp2e 64 105 A. A. NNP work_zpfso6pk3vf5df7625v6vawp2e 64 106 Clustering Clustering NNP work_zpfso6pk3vf5df7625v6vawp2e 64 107 algorithms algorithm NNS work_zpfso6pk3vf5df7625v6vawp2e 64 108 can can MD work_zpfso6pk3vf5df7625v6vawp2e 64 109 be be VB work_zpfso6pk3vf5df7625v6vawp2e 64 110 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 64 111 to to TO work_zpfso6pk3vf5df7625v6vawp2e 64 112 find find VB work_zpfso6pk3vf5df7625v6vawp2e 64 113 a a DT work_zpfso6pk3vf5df7625v6vawp2e 64 114 set set NN work_zpfso6pk3vf5df7625v6vawp2e 64 115 of of IN work_zpfso6pk3vf5df7625v6vawp2e 64 116 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 64 117 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 64 118 accurately accurately RB work_zpfso6pk3vf5df7625v6vawp2e 64 119 reflects reflect VBZ work_zpfso6pk3vf5df7625v6vawp2e 64 120 the the DT work_zpfso6pk3vf5df7625v6vawp2e 64 121 distribution distribution NN work_zpfso6pk3vf5df7625v6vawp2e 64 122 of of IN work_zpfso6pk3vf5df7625v6vawp2e 64 123 the the DT work_zpfso6pk3vf5df7625v6vawp2e 64 124 data data NN work_zpfso6pk3vf5df7625v6vawp2e 64 125 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 64 126 . . . work_zpfso6pk3vf5df7625v6vawp2e 65 1 From from IN work_zpfso6pk3vf5df7625v6vawp2e 65 2 N N NNP work_zpfso6pk3vf5df7625v6vawp2e 65 3 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 65 4 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 65 5 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 65 6 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 65 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 8 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 65 9 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 65 10 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 65 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 12 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 65 13 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 65 14 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 65 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 16 N n CD work_zpfso6pk3vf5df7625v6vawp2e 65 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 65 19 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 65 20 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 65 21 means means NN work_zpfso6pk3vf5df7625v6vawp2e 65 22 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 65 23 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 65 24 Haykin Haykin NNP work_zpfso6pk3vf5df7625v6vawp2e 65 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 26 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 65 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 28 2009 2009 CD work_zpfso6pk3vf5df7625v6vawp2e 65 29 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 65 30 seeks seek VBZ work_zpfso6pk3vf5df7625v6vawp2e 65 31 to to TO work_zpfso6pk3vf5df7625v6vawp2e 65 32 partition partition VB work_zpfso6pk3vf5df7625v6vawp2e 65 33 the the DT work_zpfso6pk3vf5df7625v6vawp2e 65 34 data data NN work_zpfso6pk3vf5df7625v6vawp2e 65 35 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 65 36 in in IN work_zpfso6pk3vf5df7625v6vawp2e 65 37 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 65 38 disjoint disjoint NN work_zpfso6pk3vf5df7625v6vawp2e 65 39 subset subset NN work_zpfso6pk3vf5df7625v6vawp2e 65 40 Si Si NNP work_zpfso6pk3vf5df7625v6vawp2e 65 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 42 each each DT work_zpfso6pk3vf5df7625v6vawp2e 65 43 containing contain VBG work_zpfso6pk3vf5df7625v6vawp2e 65 44 Ni Ni NNP work_zpfso6pk3vf5df7625v6vawp2e 65 45 data data NN work_zpfso6pk3vf5df7625v6vawp2e 65 46 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 65 47 , , , work_zpfso6pk3vf5df7625v6vawp2e 65 48 so so IN work_zpfso6pk3vf5df7625v6vawp2e 65 49 as as IN work_zpfso6pk3vf5df7625v6vawp2e 65 50 to to TO work_zpfso6pk3vf5df7625v6vawp2e 65 51 minimize minimize VB work_zpfso6pk3vf5df7625v6vawp2e 65 52 the the DT work_zpfso6pk3vf5df7625v6vawp2e 65 53 sum sum NN work_zpfso6pk3vf5df7625v6vawp2e 65 54 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 65 55 of of IN work_zpfso6pk3vf5df7625v6vawp2e 65 56 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 65 57 squares square NNS work_zpfso6pk3vf5df7625v6vawp2e 65 58 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 65 59 function function NN work_zpfso6pk3vf5df7625v6vawp2e 65 60 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 65 61 by by IN work_zpfso6pk3vf5df7625v6vawp2e 65 62 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 65 63 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 65 64 and and CC work_zpfso6pk3vf5df7625v6vawp2e 65 65 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 65 66 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 65 67 J J NNP work_zpfso6pk3vf5df7625v6vawp2e 65 68 = = NNP work_zpfso6pk3vf5df7625v6vawp2e 65 69 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 65 70 ∑ ∑ NNP work_zpfso6pk3vf5df7625v6vawp2e 65 71 i=1 i=1 NNS work_zpfso6pk3vf5df7625v6vawp2e 65 72 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 65 73 x x UH work_zpfso6pk3vf5df7625v6vawp2e 65 74 j∈Si j∈Si NNP work_zpfso6pk3vf5df7625v6vawp2e 65 75 ∥x ∥x NN work_zpfso6pk3vf5df7625v6vawp2e 65 76 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 65 77 −ci∥2 −ci∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 65 78 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 65 79 15 15 CD work_zpfso6pk3vf5df7625v6vawp2e 65 80 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 65 81 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 65 82 ∈ ∈ NNP work_zpfso6pk3vf5df7625v6vawp2e 65 83 denotes denote NNS work_zpfso6pk3vf5df7625v6vawp2e 65 84 belongs belong VBZ work_zpfso6pk3vf5df7625v6vawp2e 65 85 to to TO work_zpfso6pk3vf5df7625v6vawp2e 65 86 . . . work_zpfso6pk3vf5df7625v6vawp2e 66 1 J J NNP work_zpfso6pk3vf5df7625v6vawp2e 66 2 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 66 3 minimized minimize VBN work_zpfso6pk3vf5df7625v6vawp2e 66 4 when when WRB work_zpfso6pk3vf5df7625v6vawp2e 66 5 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 66 6 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 66 7 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 66 8 Ni Ni NNP work_zpfso6pk3vf5df7625v6vawp2e 66 9 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 66 10 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 66 11 j∈Si j∈Si NNP work_zpfso6pk3vf5df7625v6vawp2e 66 12 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 66 13 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 66 14 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 66 15 16 16 CD work_zpfso6pk3vf5df7625v6vawp2e 66 16 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 66 17 The the DT work_zpfso6pk3vf5df7625v6vawp2e 66 18 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 66 19 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 66 20 means means NN work_zpfso6pk3vf5df7625v6vawp2e 66 21 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 66 22 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 66 23 detailed detail VBN work_zpfso6pk3vf5df7625v6vawp2e 66 24 in in IN work_zpfso6pk3vf5df7625v6vawp2e 66 25 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 66 26 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 66 27 . . . work_zpfso6pk3vf5df7625v6vawp2e 67 1 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 67 2 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 67 3 The the DT work_zpfso6pk3vf5df7625v6vawp2e 67 4 k k NN work_zpfso6pk3vf5df7625v6vawp2e 67 5 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 67 6 means means NN work_zpfso6pk3vf5df7625v6vawp2e 67 7 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 67 8 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 67 9 Require Require NNP work_zpfso6pk3vf5df7625v6vawp2e 67 10 : : : work_zpfso6pk3vf5df7625v6vawp2e 67 11 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 67 12 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 67 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 14 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 67 15 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 67 16 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 67 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 18 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 19 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 20 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 21 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 22 N n NN work_zpfso6pk3vf5df7625v6vawp2e 67 23 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 24 and and CC work_zpfso6pk3vf5df7625v6vawp2e 67 25 a a DT work_zpfso6pk3vf5df7625v6vawp2e 67 26 preset preset JJ work_zpfso6pk3vf5df7625v6vawp2e 67 27 number number NN work_zpfso6pk3vf5df7625v6vawp2e 67 28 of of IN work_zpfso6pk3vf5df7625v6vawp2e 67 29 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 67 30 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 67 31 Ensure Ensure NNP work_zpfso6pk3vf5df7625v6vawp2e 67 32 : : : work_zpfso6pk3vf5df7625v6vawp2e 67 33 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 67 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 35 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 67 36 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 67 37 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 67 38 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 39 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 40 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 41 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 67 42 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 43 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 67 44 , , , work_zpfso6pk3vf5df7625v6vawp2e 67 45 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 67 46 yields yield VBZ work_zpfso6pk3vf5df7625v6vawp2e 67 47 the the DT work_zpfso6pk3vf5df7625v6vawp2e 67 48 minimum minimum NN work_zpfso6pk3vf5df7625v6vawp2e 67 49 of of IN work_zpfso6pk3vf5df7625v6vawp2e 67 50 J J NNP work_zpfso6pk3vf5df7625v6vawp2e 67 51 = = NNPS work_zpfso6pk3vf5df7625v6vawp2e 67 52 ∑Mi=1 ∑Mi=1 NNP work_zpfso6pk3vf5df7625v6vawp2e 67 53 ∑x ∑x NNP work_zpfso6pk3vf5df7625v6vawp2e 67 54 j∈Si j∈Si . work_zpfso6pk3vf5df7625v6vawp2e 67 55 ∥x ∥x NN work_zpfso6pk3vf5df7625v6vawp2e 67 56 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 67 57 −ci∥ −ci∥ NNP work_zpfso6pk3vf5df7625v6vawp2e 67 58 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 67 59 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 67 60 : : : work_zpfso6pk3vf5df7625v6vawp2e 67 61 Randomly randomly VB work_zpfso6pk3vf5df7625v6vawp2e 67 62 select select VB work_zpfso6pk3vf5df7625v6vawp2e 67 63 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 67 64 data data NN work_zpfso6pk3vf5df7625v6vawp2e 67 65 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 67 66 from from IN work_zpfso6pk3vf5df7625v6vawp2e 67 67 DN DN NNP work_zpfso6pk3vf5df7625v6vawp2e 67 68 as as IN work_zpfso6pk3vf5df7625v6vawp2e 67 69 initial initial JJ work_zpfso6pk3vf5df7625v6vawp2e 67 70 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 67 71 coldi coldi VBP work_zpfso6pk3vf5df7625v6vawp2e 67 72 . . . work_zpfso6pk3vf5df7625v6vawp2e 68 1 2 2 LS work_zpfso6pk3vf5df7625v6vawp2e 68 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 68 3 Randomly randomly RB work_zpfso6pk3vf5df7625v6vawp2e 68 4 draw draw VB work_zpfso6pk3vf5df7625v6vawp2e 68 5 a a DT work_zpfso6pk3vf5df7625v6vawp2e 68 6 data data NN work_zpfso6pk3vf5df7625v6vawp2e 68 7 point point NN work_zpfso6pk3vf5df7625v6vawp2e 68 8 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 68 9 j j NN work_zpfso6pk3vf5df7625v6vawp2e 68 10 from from IN work_zpfso6pk3vf5df7625v6vawp2e 68 11 DN DN NNP work_zpfso6pk3vf5df7625v6vawp2e 68 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 69 1 3 3 LS work_zpfso6pk3vf5df7625v6vawp2e 69 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 69 3 From from IN work_zpfso6pk3vf5df7625v6vawp2e 69 4 all all DT work_zpfso6pk3vf5df7625v6vawp2e 69 5 coldi coldi NN work_zpfso6pk3vf5df7625v6vawp2e 69 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 69 7 i i PRP work_zpfso6pk3vf5df7625v6vawp2e 69 8 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 69 9 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 69 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 69 11 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 69 12 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 69 13 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 69 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 69 15 M m NN work_zpfso6pk3vf5df7625v6vawp2e 69 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 69 17 find find VB work_zpfso6pk3vf5df7625v6vawp2e 69 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 69 19 nearest near JJS work_zpfso6pk3vf5df7625v6vawp2e 69 20 center center NN work_zpfso6pk3vf5df7625v6vawp2e 69 21 to to IN work_zpfso6pk3vf5df7625v6vawp2e 69 22 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 69 23 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 69 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 69 25 denoted denote VBD work_zpfso6pk3vf5df7625v6vawp2e 69 26 as as IN work_zpfso6pk3vf5df7625v6vawp2e 69 27 c c NNP work_zpfso6pk3vf5df7625v6vawp2e 69 28 old old JJ work_zpfso6pk3vf5df7625v6vawp2e 69 29 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 69 30 . . . work_zpfso6pk3vf5df7625v6vawp2e 70 1 4 4 LS work_zpfso6pk3vf5df7625v6vawp2e 70 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 70 3 Update update NN work_zpfso6pk3vf5df7625v6vawp2e 70 4 cnewk cnewk NN work_zpfso6pk3vf5df7625v6vawp2e 70 5 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 70 6 c c NN work_zpfso6pk3vf5df7625v6vawp2e 70 7 old old JJ work_zpfso6pk3vf5df7625v6vawp2e 70 8 k k NN work_zpfso6pk3vf5df7625v6vawp2e 70 9 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 70 10 ε(x ε(x NNP work_zpfso6pk3vf5df7625v6vawp2e 70 11 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 70 12 −c −c CD work_zpfso6pk3vf5df7625v6vawp2e 70 13 old old NNP work_zpfso6pk3vf5df7625v6vawp2e 70 14 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 70 15 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 70 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 70 17 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 70 18 ε ε DT work_zpfso6pk3vf5df7625v6vawp2e 70 19 > > NN work_zpfso6pk3vf5df7625v6vawp2e 70 20 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 70 21 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 70 22 the the DT work_zpfso6pk3vf5df7625v6vawp2e 70 23 predetermined predetermine VBN work_zpfso6pk3vf5df7625v6vawp2e 70 24 learning learning NN work_zpfso6pk3vf5df7625v6vawp2e 70 25 rate rate NN work_zpfso6pk3vf5df7625v6vawp2e 70 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 71 1 5 5 LS work_zpfso6pk3vf5df7625v6vawp2e 71 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 71 3 Set set NN work_zpfso6pk3vf5df7625v6vawp2e 71 4 cnewi cnewi NNP work_zpfso6pk3vf5df7625v6vawp2e 71 5 as as IN work_zpfso6pk3vf5df7625v6vawp2e 71 6 c c NNP work_zpfso6pk3vf5df7625v6vawp2e 71 7 old old JJ work_zpfso6pk3vf5df7625v6vawp2e 71 8 i i PRP work_zpfso6pk3vf5df7625v6vawp2e 71 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 72 1 6 6 LS work_zpfso6pk3vf5df7625v6vawp2e 72 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 72 3 Goto Goto NNP work_zpfso6pk3vf5df7625v6vawp2e 72 4 Step Step NNP work_zpfso6pk3vf5df7625v6vawp2e 72 5 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 72 6 until until IN work_zpfso6pk3vf5df7625v6vawp2e 72 7 a a DT work_zpfso6pk3vf5df7625v6vawp2e 72 8 sufficient sufficient JJ work_zpfso6pk3vf5df7625v6vawp2e 72 9 large large JJ work_zpfso6pk3vf5df7625v6vawp2e 72 10 number number NN work_zpfso6pk3vf5df7625v6vawp2e 72 11 of of IN work_zpfso6pk3vf5df7625v6vawp2e 72 12 iterations iteration NNS work_zpfso6pk3vf5df7625v6vawp2e 72 13 has have VBZ work_zpfso6pk3vf5df7625v6vawp2e 72 14 reached reach VBN work_zpfso6pk3vf5df7625v6vawp2e 72 15 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 72 16 for for IN work_zpfso6pk3vf5df7625v6vawp2e 72 17 convergence convergence NN work_zpfso6pk3vf5df7625v6vawp2e 72 18 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 72 19 . . . work_zpfso6pk3vf5df7625v6vawp2e 73 1 7 7 LS work_zpfso6pk3vf5df7625v6vawp2e 73 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 73 3 Return return NN work_zpfso6pk3vf5df7625v6vawp2e 73 4 cnewi cnewi NNP work_zpfso6pk3vf5df7625v6vawp2e 73 5 as as IN work_zpfso6pk3vf5df7625v6vawp2e 73 6 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 73 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 73 8 i i NNP work_zpfso6pk3vf5df7625v6vawp2e 73 9 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 73 10 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 73 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 73 12 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 73 13 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 73 14 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 73 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 73 16 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 73 17 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 73 18 now now RB work_zpfso6pk3vf5df7625v6vawp2e 73 19 propose propose VBP work_zpfso6pk3vf5df7625v6vawp2e 73 20 a a DT work_zpfso6pk3vf5df7625v6vawp2e 73 21 new new JJ work_zpfso6pk3vf5df7625v6vawp2e 73 22 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 73 23 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 73 24 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 73 25 for for IN work_zpfso6pk3vf5df7625v6vawp2e 73 26 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 73 27 ωi ωi CD work_zpfso6pk3vf5df7625v6vawp2e 73 28 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 73 29 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 73 30 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 73 31 on on IN work_zpfso6pk3vf5df7625v6vawp2e 73 32 that that DT work_zpfso6pk3vf5df7625v6vawp2e 73 33 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 73 34 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 73 35 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 73 36 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 73 37 and and CC work_zpfso6pk3vf5df7625v6vawp2e 73 38 a a DT work_zpfso6pk3vf5df7625v6vawp2e 73 39 preset preset JJ work_zpfso6pk3vf5df7625v6vawp2e 73 40 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 73 41 width width NN work_zpfso6pk3vf5df7625v6vawp2e 73 42 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 73 43 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 73 44 . . . work_zpfso6pk3vf5df7625v6vawp2e 74 1 Initially initially RB work_zpfso6pk3vf5df7625v6vawp2e 74 2 denote denote VB work_zpfso6pk3vf5df7625v6vawp2e 74 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 74 4 eigenvalue eigenvalue NN work_zpfso6pk3vf5df7625v6vawp2e 74 5 decomposition decomposition NN work_zpfso6pk3vf5df7625v6vawp2e 74 6 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 74 7 as as IN work_zpfso6pk3vf5df7625v6vawp2e 74 8 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 74 9 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 74 10 UΣ UΣ NNP work_zpfso6pk3vf5df7625v6vawp2e 74 11 UT UT NNP work_zpfso6pk3vf5df7625v6vawp2e 74 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 74 13 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 74 14 U u NN work_zpfso6pk3vf5df7625v6vawp2e 74 15 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 74 16 an an DT work_zpfso6pk3vf5df7625v6vawp2e 74 17 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 74 18 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 74 19 consisting consist VBG work_zpfso6pk3vf5df7625v6vawp2e 74 20 of of IN work_zpfso6pk3vf5df7625v6vawp2e 74 21 the the DT work_zpfso6pk3vf5df7625v6vawp2e 74 22 eigenvectors eigenvector NNS work_zpfso6pk3vf5df7625v6vawp2e 74 23 and and CC work_zpfso6pk3vf5df7625v6vawp2e 74 24 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 74 25 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 74 26 a a DT work_zpfso6pk3vf5df7625v6vawp2e 74 27 diagonal diagonal JJ work_zpfso6pk3vf5df7625v6vawp2e 74 28 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 74 29 of of IN work_zpfso6pk3vf5df7625v6vawp2e 74 30 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 74 31 the the DT work_zpfso6pk3vf5df7625v6vawp2e 74 32 entries entry NNS work_zpfso6pk3vf5df7625v6vawp2e 74 33 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 74 34 eigenvalues eigenvalue VBZ work_zpfso6pk3vf5df7625v6vawp2e 74 35 Q. Q. NNP work_zpfso6pk3vf5df7625v6vawp2e 75 1 Let let VB work_zpfso6pk3vf5df7625v6vawp2e 75 2 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 3 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 75 4 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 5 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 6 UTω UTω NNS work_zpfso6pk3vf5df7625v6vawp2e 75 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 75 8 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 75 9 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 10 can can MD work_zpfso6pk3vf5df7625v6vawp2e 75 11 be be VB work_zpfso6pk3vf5df7625v6vawp2e 75 12 written write VBN work_zpfso6pk3vf5df7625v6vawp2e 75 13 as as IN work_zpfso6pk3vf5df7625v6vawp2e 75 14 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 75 15 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 16 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 75 17 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 18 Tk̄(x tk̄(x NN work_zpfso6pk3vf5df7625v6vawp2e 75 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 75 21 17 17 CD work_zpfso6pk3vf5df7625v6vawp2e 75 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 23 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 75 24 k̄(x k̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 75 25 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 26 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 75 27 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 28 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 75 29 −1 −1 NNP work_zpfso6pk3vf5df7625v6vawp2e 75 30 UTk(x UTk(x NNP work_zpfso6pk3vf5df7625v6vawp2e 75 31 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 75 32 . . . work_zpfso6pk3vf5df7625v6vawp2e 76 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 76 2 order order NN work_zpfso6pk3vf5df7625v6vawp2e 76 3 to to TO work_zpfso6pk3vf5df7625v6vawp2e 76 4 satisfy satisfy VB work_zpfso6pk3vf5df7625v6vawp2e 76 5 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 76 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 76 7 > > NFP work_zpfso6pk3vf5df7625v6vawp2e 76 8 0 0 NFP work_zpfso6pk3vf5df7625v6vawp2e 76 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 76 10 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 76 11 initialize initialize VBP work_zpfso6pk3vf5df7625v6vawp2e 76 12 all all DT work_zpfso6pk3vf5df7625v6vawp2e 76 13 ωi ωi RB work_zpfso6pk3vf5df7625v6vawp2e 76 14 as as IN work_zpfso6pk3vf5df7625v6vawp2e 76 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 76 16 same same JJ work_zpfso6pk3vf5df7625v6vawp2e 76 17 positive positive JJ work_zpfso6pk3vf5df7625v6vawp2e 76 18 number number NN work_zpfso6pk3vf5df7625v6vawp2e 76 19 ξ ξ NNP work_zpfso6pk3vf5df7625v6vawp2e 76 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 76 21 and and CC work_zpfso6pk3vf5df7625v6vawp2e 76 22 ωIni ωIni NNP work_zpfso6pk3vf5df7625v6vawp2e 76 23 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 76 24 ξ ξ NNP work_zpfso6pk3vf5df7625v6vawp2e 76 25 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 76 26 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 76 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 76 28 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 76 29 M m NN work_zpfso6pk3vf5df7625v6vawp2e 76 30 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 76 31 a a DT work_zpfso6pk3vf5df7625v6vawp2e 76 32 length length NN work_zpfso6pk3vf5df7625v6vawp2e 76 33 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 76 34 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 76 35 with with IN work_zpfso6pk3vf5df7625v6vawp2e 76 36 all all DT work_zpfso6pk3vf5df7625v6vawp2e 76 37 elements element NNS work_zpfso6pk3vf5df7625v6vawp2e 76 38 as as IN work_zpfso6pk3vf5df7625v6vawp2e 76 39 ones one NNS work_zpfso6pk3vf5df7625v6vawp2e 76 40 . . . work_zpfso6pk3vf5df7625v6vawp2e 77 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 77 2 correspond- correspond- JJ work_zpfso6pk3vf5df7625v6vawp2e 77 3 ing ing NN work_zpfso6pk3vf5df7625v6vawp2e 77 4 θ0 θ0 NN work_zpfso6pk3vf5df7625v6vawp2e 77 5 can can MD work_zpfso6pk3vf5df7625v6vawp2e 77 6 be be VB work_zpfso6pk3vf5df7625v6vawp2e 77 7 calculated calculate VBN work_zpfso6pk3vf5df7625v6vawp2e 77 8 as as IN work_zpfso6pk3vf5df7625v6vawp2e 77 9 θ0 θ0 NNP work_zpfso6pk3vf5df7625v6vawp2e 77 10 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 77 11 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 77 12 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 77 13 UT1 UT1 NNP work_zpfso6pk3vf5df7625v6vawp2e 77 14 M m NN work_zpfso6pk3vf5df7625v6vawp2e 77 15 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 77 16 18 18 CD work_zpfso6pk3vf5df7625v6vawp2e 77 17 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 77 18 followed follow VBN work_zpfso6pk3vf5df7625v6vawp2e 77 19 by by IN work_zpfso6pk3vf5df7625v6vawp2e 77 20 a a DT work_zpfso6pk3vf5df7625v6vawp2e 77 21 normalization normalization NN work_zpfso6pk3vf5df7625v6vawp2e 77 22 step step NN work_zpfso6pk3vf5df7625v6vawp2e 77 23 θ0 θ0 NNP work_zpfso6pk3vf5df7625v6vawp2e 77 24 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 77 25 θ0/∥θ0∥ θ0/∥θ0∥ XX work_zpfso6pk3vf5df7625v6vawp2e 77 26 so so RB work_zpfso6pk3vf5df7625v6vawp2e 77 27 that that IN work_zpfso6pk3vf5df7625v6vawp2e 77 28 θ0 θ0 NNP work_zpfso6pk3vf5df7625v6vawp2e 77 29 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 77 30 on on IN work_zpfso6pk3vf5df7625v6vawp2e 77 31 the the DT work_zpfso6pk3vf5df7625v6vawp2e 77 32 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 77 33 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 77 34 . . . work_zpfso6pk3vf5df7625v6vawp2e 78 1 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 78 2 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 78 3 now now RB work_zpfso6pk3vf5df7625v6vawp2e 78 4 ready ready JJ work_zpfso6pk3vf5df7625v6vawp2e 78 5 to to TO work_zpfso6pk3vf5df7625v6vawp2e 78 6 formulate formulate VB work_zpfso6pk3vf5df7625v6vawp2e 78 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 78 8 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 78 9 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 78 10 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 78 11 as as IN work_zpfso6pk3vf5df7625v6vawp2e 78 12 the the DT work_zpfso6pk3vf5df7625v6vawp2e 78 13 following follow VBG work_zpfso6pk3vf5df7625v6vawp2e 78 14 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 78 15 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 78 16 problem problem NN work_zpfso6pk3vf5df7625v6vawp2e 78 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 78 18 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 78 19 as as IN work_zpfso6pk3vf5df7625v6vawp2e 78 20 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 78 21 opt opt NNP work_zpfso6pk3vf5df7625v6vawp2e 78 22 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 78 23 min min NNP work_zpfso6pk3vf5df7625v6vawp2e 78 24 θ∈SM−1 θ∈SM−1 NNP work_zpfso6pk3vf5df7625v6vawp2e 78 25 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 78 26 F(θ f(θ NN work_zpfso6pk3vf5df7625v6vawp2e 78 27 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 78 28 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 78 29 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 78 30 N n CD work_zpfso6pk3vf5df7625v6vawp2e 78 31 ∑ ∑ NNP work_zpfso6pk3vf5df7625v6vawp2e 78 32 j=1 j=1 NNS work_zpfso6pk3vf5df7625v6vawp2e 78 33 log(θ log(θ . work_zpfso6pk3vf5df7625v6vawp2e 78 34 Tk̄(x Tk̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 78 35 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 78 36 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 78 37 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 78 38 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 78 39 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 78 40 19 19 CD work_zpfso6pk3vf5df7625v6vawp2e 78 41 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 78 42 followed follow VBN work_zpfso6pk3vf5df7625v6vawp2e 78 43 by by IN work_zpfso6pk3vf5df7625v6vawp2e 78 44 setting set VBG work_zpfso6pk3vf5df7625v6vawp2e 78 45 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 78 46 opt opt NNP work_zpfso6pk3vf5df7625v6vawp2e 78 47 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 78 48 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 78 49 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 78 50 UTω UTω NNP work_zpfso6pk3vf5df7625v6vawp2e 78 51 opt opt NNP work_zpfso6pk3vf5df7625v6vawp2e 78 52 . . . work_zpfso6pk3vf5df7625v6vawp2e 79 1 For for IN work_zpfso6pk3vf5df7625v6vawp2e 79 2 our -PRON- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 79 3 objective objective JJ work_zpfso6pk3vf5df7625v6vawp2e 79 4 function function NN work_zpfso6pk3vf5df7625v6vawp2e 79 5 F(θ F(θ VBN work_zpfso6pk3vf5df7625v6vawp2e 79 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 79 8 it -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 79 9 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 79 10 easy easy JJ work_zpfso6pk3vf5df7625v6vawp2e 79 11 to to TO work_zpfso6pk3vf5df7625v6vawp2e 79 12 check check VB work_zpfso6pk3vf5df7625v6vawp2e 79 13 that that IN work_zpfso6pk3vf5df7625v6vawp2e 79 14 Euclidean Euclidean NNP work_zpfso6pk3vf5df7625v6vawp2e 79 15 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 79 16 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 79 17 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 18 can can MD work_zpfso6pk3vf5df7625v6vawp2e 79 19 be be VB work_zpfso6pk3vf5df7625v6vawp2e 79 20 calculated calculate VBN work_zpfso6pk3vf5df7625v6vawp2e 79 21 respectively respectively RB work_zpfso6pk3vf5df7625v6vawp2e 79 22 as as IN work_zpfso6pk3vf5df7625v6vawp2e 79 23 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 79 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 79 25 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 79 26 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 79 27 of of IN work_zpfso6pk3vf5df7625v6vawp2e 79 28 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 79 29 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 79 30 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 79 31 on on IN work_zpfso6pk3vf5df7625v6vawp2e 79 32 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 79 33 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 79 34 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 79 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 36 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 79 37 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 79 38 N n CD work_zpfso6pk3vf5df7625v6vawp2e 79 39 ∑ ∑ NNP work_zpfso6pk3vf5df7625v6vawp2e 79 40 j=1 j=1 NN work_zpfso6pk3vf5df7625v6vawp2e 79 41 k̄(x k̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 79 42 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 79 43 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 44 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 79 45 Tk̄(x Tk̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 79 46 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 79 47 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 48 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 79 49 20 20 CD work_zpfso6pk3vf5df7625v6vawp2e 79 50 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 51 Based base VBN work_zpfso6pk3vf5df7625v6vawp2e 79 52 on on IN work_zpfso6pk3vf5df7625v6vawp2e 79 53 GradF(θ GradF(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 79 54 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 55 , , , work_zpfso6pk3vf5df7625v6vawp2e 79 56 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 79 57 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 79 58 of of IN work_zpfso6pk3vf5df7625v6vawp2e 79 59 the the DT work_zpfso6pk3vf5df7625v6vawp2e 79 60 objective objective JJ work_zpfso6pk3vf5df7625v6vawp2e 79 61 function function NN work_zpfso6pk3vf5df7625v6vawp2e 79 62 F(θ F(θ VBN work_zpfso6pk3vf5df7625v6vawp2e 79 63 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 64 on on IN work_zpfso6pk3vf5df7625v6vawp2e 79 65 the the DT work_zpfso6pk3vf5df7625v6vawp2e 79 66 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 79 67 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 79 68 can can MD work_zpfso6pk3vf5df7625v6vawp2e 79 69 be be VB work_zpfso6pk3vf5df7625v6vawp2e 79 70 calculated calculate VBN work_zpfso6pk3vf5df7625v6vawp2e 79 71 according accord VBG work_zpfso6pk3vf5df7625v6vawp2e 79 72 to to IN work_zpfso6pk3vf5df7625v6vawp2e 79 73 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 79 74 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 79 75 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 76 , , , work_zpfso6pk3vf5df7625v6vawp2e 79 77 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 79 78 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 79 79 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 79 80 . . . work_zpfso6pk3vf5df7625v6vawp2e 80 1 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 80 2 opt opt VBP work_zpfso6pk3vf5df7625v6vawp2e 80 3 to to IN work_zpfso6pk3vf5df7625v6vawp2e 80 4 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 80 5 con- con- NN work_zpfso6pk3vf5df7625v6vawp2e 80 6 jugate jugate NN work_zpfso6pk3vf5df7625v6vawp2e 80 7 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 80 8 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 80 9 to to TO work_zpfso6pk3vf5df7625v6vawp2e 80 10 solve solve VB work_zpfso6pk3vf5df7625v6vawp2e 80 11 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 80 12 19 19 CD work_zpfso6pk3vf5df7625v6vawp2e 80 13 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 80 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 80 15 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 80 16 generalizes generalize VBZ work_zpfso6pk3vf5df7625v6vawp2e 80 17 the the DT work_zpfso6pk3vf5df7625v6vawp2e 80 18 classical classical JJ work_zpfso6pk3vf5df7625v6vawp2e 80 19 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 80 20 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 80 21 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 80 22 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 80 23 Hager Hager NNP work_zpfso6pk3vf5df7625v6vawp2e 80 24 and and CC work_zpfso6pk3vf5df7625v6vawp2e 80 25 Zhang Zhang NNP work_zpfso6pk3vf5df7625v6vawp2e 80 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 80 27 2006 2006 CD work_zpfso6pk3vf5df7625v6vawp2e 80 28 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 80 29 to to TO work_zpfso6pk3vf5df7625v6vawp2e 80 30 optimization optimization VB work_zpfso6pk3vf5df7625v6vawp2e 80 31 problems problem NNS work_zpfso6pk3vf5df7625v6vawp2e 80 32 over over IN work_zpfso6pk3vf5df7625v6vawp2e 80 33 Rie- Rie- NNP work_zpfso6pk3vf5df7625v6vawp2e 80 34 mannian mannian NN work_zpfso6pk3vf5df7625v6vawp2e 80 35 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 80 36 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 80 37 Boumal Boumal NNP work_zpfso6pk3vf5df7625v6vawp2e 80 38 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 80 39 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 80 40 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 80 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 80 42 2014 2014 CD work_zpfso6pk3vf5df7625v6vawp2e 80 43 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 80 44 . . . work_zpfso6pk3vf5df7625v6vawp2e 81 1 Since since IN work_zpfso6pk3vf5df7625v6vawp2e 81 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 81 3 logarithm logarithm NNP work_zpfso6pk3vf5df7625v6vawp2e 81 4 function function NN work_zpfso6pk3vf5df7625v6vawp2e 81 5 acts act VBZ work_zpfso6pk3vf5df7625v6vawp2e 81 6 as as IN work_zpfso6pk3vf5df7625v6vawp2e 81 7 a a DT work_zpfso6pk3vf5df7625v6vawp2e 81 8 natural natural JJ work_zpfso6pk3vf5df7625v6vawp2e 81 9 barrier barrier NN work_zpfso6pk3vf5df7625v6vawp2e 81 10 at at IN work_zpfso6pk3vf5df7625v6vawp2e 81 11 zero zero CD work_zpfso6pk3vf5df7625v6vawp2e 81 12 and and CC work_zpfso6pk3vf5df7625v6vawp2e 81 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 81 14 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 81 15 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 81 16 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 81 17 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 81 18 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 81 19 a a DT work_zpfso6pk3vf5df7625v6vawp2e 81 20 local local JJ work_zpfso6pk3vf5df7625v6vawp2e 81 21 minimization minimization NN work_zpfso6pk3vf5df7625v6vawp2e 81 22 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 81 23 , , , work_zpfso6pk3vf5df7625v6vawp2e 81 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 81 25 constraint constraint NN work_zpfso6pk3vf5df7625v6vawp2e 81 26 ψ(x ψ(x NN work_zpfso6pk3vf5df7625v6vawp2e 81 27 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 81 28 > > NFP work_zpfso6pk3vf5df7625v6vawp2e 81 29 0 0 NFP work_zpfso6pk3vf5df7625v6vawp2e 81 30 can can MD work_zpfso6pk3vf5df7625v6vawp2e 81 31 be be VB work_zpfso6pk3vf5df7625v6vawp2e 81 32 met meet VBN work_zpfso6pk3vf5df7625v6vawp2e 81 33 . . . work_zpfso6pk3vf5df7625v6vawp2e 82 1 With with IN work_zpfso6pk3vf5df7625v6vawp2e 82 2 all all PDT work_zpfso6pk3vf5df7625v6vawp2e 82 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 82 4 ingredients ingredient NNS work_zpfso6pk3vf5df7625v6vawp2e 82 5 available available JJ work_zpfso6pk3vf5df7625v6vawp2e 82 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 82 7 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 82 8 form form VBP work_zpfso6pk3vf5df7625v6vawp2e 82 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 82 10 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 82 11 for for IN work_zpfso6pk3vf5df7625v6vawp2e 82 12 solving solve VBG work_zpfso6pk3vf5df7625v6vawp2e 82 13 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 82 14 19 19 CD work_zpfso6pk3vf5df7625v6vawp2e 82 15 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 82 16 in in IN work_zpfso6pk3vf5df7625v6vawp2e 82 17 Algo- Algo- NNP work_zpfso6pk3vf5df7625v6vawp2e 82 18 rithm rithm NNP work_zpfso6pk3vf5df7625v6vawp2e 82 19 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 82 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 82 21 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 82 22 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 82 23 well well RB work_zpfso6pk3vf5df7625v6vawp2e 82 24 implemented implement VBN work_zpfso6pk3vf5df7625v6vawp2e 82 25 in in IN work_zpfso6pk3vf5df7625v6vawp2e 82 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 82 27 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 82 28 Optimization Optimization NNP work_zpfso6pk3vf5df7625v6vawp2e 82 29 Toolbox Toolbox NNP work_zpfso6pk3vf5df7625v6vawp2e 82 30 Manopt Manopt NNP work_zpfso6pk3vf5df7625v6vawp2e 82 31 http://www.manopt.org http://www.manopt.org ADD work_zpfso6pk3vf5df7625v6vawp2e 82 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 82 33 see see VB work_zpfso6pk3vf5df7625v6vawp2e 82 34 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 82 35 Boumal Boumal NNP work_zpfso6pk3vf5df7625v6vawp2e 82 36 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 82 37 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 82 38 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 82 39 , , , work_zpfso6pk3vf5df7625v6vawp2e 82 40 2014 2014 CD work_zpfso6pk3vf5df7625v6vawp2e 82 41 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 82 42 . . . work_zpfso6pk3vf5df7625v6vawp2e 83 1 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 83 2 used use VBD work_zpfso6pk3vf5df7625v6vawp2e 83 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 83 4 default default NN work_zpfso6pk3vf5df7625v6vawp2e 83 5 pa- pa- NN work_zpfso6pk3vf5df7625v6vawp2e 83 6 rameter rameter NN work_zpfso6pk3vf5df7625v6vawp2e 83 7 settings setting NNS work_zpfso6pk3vf5df7625v6vawp2e 83 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 83 9 Manopt Manopt NNP work_zpfso6pk3vf5df7625v6vawp2e 83 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 83 11 so so IN work_zpfso6pk3vf5df7625v6vawp2e 83 12 that that IN work_zpfso6pk3vf5df7625v6vawp2e 83 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 83 14 Step step NN work_zpfso6pk3vf5df7625v6vawp2e 83 15 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 83 16 of of IN work_zpfso6pk3vf5df7625v6vawp2e 83 17 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 83 18 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 83 19 αk αk NN work_zpfso6pk3vf5df7625v6vawp2e 83 20 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 83 21 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 83 22 on on IN work_zpfso6pk3vf5df7625v6vawp2e 83 23 line line NN work_zpfso6pk3vf5df7625v6vawp2e 83 24 search search NN work_zpfso6pk3vf5df7625v6vawp2e 83 25 backtracking backtrack VBG work_zpfso6pk3vf5df7625v6vawp2e 83 26 procedure procedure NN work_zpfso6pk3vf5df7625v6vawp2e 83 27 as as IN work_zpfso6pk3vf5df7625v6vawp2e 83 28 described describe VBN work_zpfso6pk3vf5df7625v6vawp2e 83 29 in in IN work_zpfso6pk3vf5df7625v6vawp2e 83 30 Chapter chapter NN work_zpfso6pk3vf5df7625v6vawp2e 83 31 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 83 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 83 33 p63 p63 CD work_zpfso6pk3vf5df7625v6vawp2e 83 34 of of IN work_zpfso6pk3vf5df7625v6vawp2e 83 35 Section section NN work_zpfso6pk3vf5df7625v6vawp2e 83 36 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 83 37 of of IN work_zpfso6pk3vf5df7625v6vawp2e 83 38 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 83 39 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 83 40 et et NNP work_zpfso6pk3vf5df7625v6vawp2e 83 41 al al NNP work_zpfso6pk3vf5df7625v6vawp2e 83 42 . . NNP work_zpfso6pk3vf5df7625v6vawp2e 83 43 , , , work_zpfso6pk3vf5df7625v6vawp2e 83 44 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 83 45 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 83 46 . . . work_zpfso6pk3vf5df7625v6vawp2e 84 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 84 2 Step step NN work_zpfso6pk3vf5df7625v6vawp2e 84 3 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 84 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 84 5 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 84 6 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 84 7 ωk+1 ωk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 84 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 84 9 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 84 10 on on IN work_zpfso6pk3vf5df7625v6vawp2e 84 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 84 12 default default NN work_zpfso6pk3vf5df7625v6vawp2e 84 13 option option NN work_zpfso6pk3vf5df7625v6vawp2e 84 14 “ " `` work_zpfso6pk3vf5df7625v6vawp2e 84 15 Hestenes- Hestenes- NNP work_zpfso6pk3vf5df7625v6vawp2e 84 16 Stiefel Stiefel NNP work_zpfso6pk3vf5df7625v6vawp2e 84 17 ’s ’s POS work_zpfso6pk3vf5df7625v6vawp2e 84 18 modified modify VBN work_zpfso6pk3vf5df7625v6vawp2e 84 19 rule rule NN work_zpfso6pk3vf5df7625v6vawp2e 84 20 ” " '' work_zpfso6pk3vf5df7625v6vawp2e 84 21 . . . work_zpfso6pk3vf5df7625v6vawp2e 85 1 Specifically specifically RB work_zpfso6pk3vf5df7625v6vawp2e 85 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 3 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 85 4 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 85 5 βk+1 βk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 85 6 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 85 7 max max NNP work_zpfso6pk3vf5df7625v6vawp2e 85 8 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 9 0 0 NFP work_zpfso6pk3vf5df7625v6vawp2e 85 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 11 < < XX work_zpfso6pk3vf5df7625v6vawp2e 85 12 gradF(θk+1),γk+1 gradf(θk+1),γk+1 ADD work_zpfso6pk3vf5df7625v6vawp2e 85 13 > > XX work_zpfso6pk3vf5df7625v6vawp2e 85 14 < < XX work_zpfso6pk3vf5df7625v6vawp2e 85 15 Tθk+1←θk Tθk+1←θk NNP work_zpfso6pk3vf5df7625v6vawp2e 85 16 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 17 ηk),γk+1 ηk),γk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 85 18 > > XX work_zpfso6pk3vf5df7625v6vawp2e 85 19 } } -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 21 21 21 CD work_zpfso6pk3vf5df7625v6vawp2e 85 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 23 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 85 24 < < XX work_zpfso6pk3vf5df7625v6vawp2e 85 25 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 85 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 27 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 85 28 > > XX work_zpfso6pk3vf5df7625v6vawp2e 85 29 denotes denote VBZ work_zpfso6pk3vf5df7625v6vawp2e 85 30 inner inner JJ work_zpfso6pk3vf5df7625v6vawp2e 85 31 product product NN work_zpfso6pk3vf5df7625v6vawp2e 85 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 33 and and CC work_zpfso6pk3vf5df7625v6vawp2e 85 34 γk+1 γk+1 NNP work_zpfso6pk3vf5df7625v6vawp2e 85 35 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 85 36 gradF(θk+1)−Tθk+1←θk gradF(θk+1)−Tθk+1←θk NNP work_zpfso6pk3vf5df7625v6vawp2e 85 37 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 38 gradF(θk gradF(θk NNP work_zpfso6pk3vf5df7625v6vawp2e 85 39 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 40 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 41 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 42 22 22 CD work_zpfso6pk3vf5df7625v6vawp2e 85 43 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 44 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 85 45 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 85 46 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 85 47 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 85 48 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 85 49 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 85 50 for for IN work_zpfso6pk3vf5df7625v6vawp2e 85 51 solving solve VBG work_zpfso6pk3vf5df7625v6vawp2e 85 52 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 53 19 19 CD work_zpfso6pk3vf5df7625v6vawp2e 85 54 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 55 Require require VB work_zpfso6pk3vf5df7625v6vawp2e 85 56 : : : work_zpfso6pk3vf5df7625v6vawp2e 85 57 k̄(x k̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 85 58 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 85 59 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 60 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 61 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 85 62 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 85 63 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 85 64 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 65 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 85 66 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 85 67 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 85 68 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 69 N. N. NNP work_zpfso6pk3vf5df7625v6vawp2e 85 70 Initial Initial NNP work_zpfso6pk3vf5df7625v6vawp2e 85 71 point point NN work_zpfso6pk3vf5df7625v6vawp2e 85 72 θ0 θ0 NN work_zpfso6pk3vf5df7625v6vawp2e 85 73 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 85 74 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 85 75 on on IN work_zpfso6pk3vf5df7625v6vawp2e 85 76 the the DT work_zpfso6pk3vf5df7625v6vawp2e 85 77 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 85 78 manifold manifold JJ work_zpfso6pk3vf5df7625v6vawp2e 85 79 SM−1 sm−1 NN work_zpfso6pk3vf5df7625v6vawp2e 85 80 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 81 and and CC work_zpfso6pk3vf5df7625v6vawp2e 85 82 default default NN work_zpfso6pk3vf5df7625v6vawp2e 85 83 threshold threshold NN work_zpfso6pk3vf5df7625v6vawp2e 85 84 ϖ ϖ NN work_zpfso6pk3vf5df7625v6vawp2e 85 85 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 86 e.g. e.g. RB work_zpfso6pk3vf5df7625v6vawp2e 85 87 , , , work_zpfso6pk3vf5df7625v6vawp2e 85 88 ϖ ϖ NN work_zpfso6pk3vf5df7625v6vawp2e 85 89 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 85 90 10−6 10−6 CD work_zpfso6pk3vf5df7625v6vawp2e 85 91 or or CC work_zpfso6pk3vf5df7625v6vawp2e 85 92 ϖ ϖ NN work_zpfso6pk3vf5df7625v6vawp2e 85 93 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 85 94 10−5 10−5 CD work_zpfso6pk3vf5df7625v6vawp2e 85 95 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 85 96 Ensure ensure VB work_zpfso6pk3vf5df7625v6vawp2e 85 97 : : : work_zpfso6pk3vf5df7625v6vawp2e 85 98 θ θ LS work_zpfso6pk3vf5df7625v6vawp2e 85 99 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 85 100 yields yield VBZ work_zpfso6pk3vf5df7625v6vawp2e 85 101 the the DT work_zpfso6pk3vf5df7625v6vawp2e 85 102 minimum minimum NN work_zpfso6pk3vf5df7625v6vawp2e 85 103 F F NNP work_zpfso6pk3vf5df7625v6vawp2e 85 104 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 85 105 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 85 106 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 85 107 . . . work_zpfso6pk3vf5df7625v6vawp2e 86 1 1 1 LS work_zpfso6pk3vf5df7625v6vawp2e 86 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 3 Set set NN work_zpfso6pk3vf5df7625v6vawp2e 86 4 η0 η0 NNP work_zpfso6pk3vf5df7625v6vawp2e 86 5 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 86 6 −gradF(θ0 −gradf(θ0 ADD work_zpfso6pk3vf5df7625v6vawp2e 86 7 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 8 and and CC work_zpfso6pk3vf5df7625v6vawp2e 86 9 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 86 10 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 86 11 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 86 12 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 86 13 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 86 14 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 15 while while IN work_zpfso6pk3vf5df7625v6vawp2e 86 16 ∥gradF(θk)∥2 ∥gradF(θk)∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 86 17 < < XX work_zpfso6pk3vf5df7625v6vawp2e 86 18 ϖ ϖ NNP work_zpfso6pk3vf5df7625v6vawp2e 86 19 do do VB work_zpfso6pk3vf5df7625v6vawp2e 86 20 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 86 21 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 22 k k NN work_zpfso6pk3vf5df7625v6vawp2e 86 23 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 86 24 k k NN work_zpfso6pk3vf5df7625v6vawp2e 86 25 + + CC work_zpfso6pk3vf5df7625v6vawp2e 86 26 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 86 27 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 86 28 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 86 29 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 30 Compute compute VB work_zpfso6pk3vf5df7625v6vawp2e 86 31 a a DT work_zpfso6pk3vf5df7625v6vawp2e 86 32 step step NN work_zpfso6pk3vf5df7625v6vawp2e 86 33 size size NN work_zpfso6pk3vf5df7625v6vawp2e 86 34 αk αk VBN work_zpfso6pk3vf5df7625v6vawp2e 86 35 and and CC work_zpfso6pk3vf5df7625v6vawp2e 86 36 set set VBN work_zpfso6pk3vf5df7625v6vawp2e 86 37 θk θk NNP work_zpfso6pk3vf5df7625v6vawp2e 86 38 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 86 39 Expθk−1 expθk−1 NN work_zpfso6pk3vf5df7625v6vawp2e 86 40 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 86 41 αk αk IN work_zpfso6pk3vf5df7625v6vawp2e 86 42 ηk−1 ηk−1 NNP work_zpfso6pk3vf5df7625v6vawp2e 86 43 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 44 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 86 45 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 86 46 23 23 CD work_zpfso6pk3vf5df7625v6vawp2e 86 47 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 48 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 86 49 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 50 Compute compute NN work_zpfso6pk3vf5df7625v6vawp2e 86 51 βk βk PRP work_zpfso6pk3vf5df7625v6vawp2e 86 52 and and CC work_zpfso6pk3vf5df7625v6vawp2e 86 53 set set VB work_zpfso6pk3vf5df7625v6vawp2e 86 54 ηk ηk PRP work_zpfso6pk3vf5df7625v6vawp2e 86 55 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 86 56 −gradF(θk)+ −gradF(θk)+ NNP work_zpfso6pk3vf5df7625v6vawp2e 86 57 βkTθk←θk−1 βktθk←θk−1 JJ work_zpfso6pk3vf5df7625v6vawp2e 86 58 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 86 59 ηk−1 ηk−1 NN work_zpfso6pk3vf5df7625v6vawp2e 86 60 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 61 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 86 62 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 86 63 24 24 CD work_zpfso6pk3vf5df7625v6vawp2e 86 64 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 65 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 86 66 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 67 end end NN work_zpfso6pk3vf5df7625v6vawp2e 86 68 while while IN work_zpfso6pk3vf5df7625v6vawp2e 86 69 7 7 CD work_zpfso6pk3vf5df7625v6vawp2e 86 70 : : : work_zpfso6pk3vf5df7625v6vawp2e 86 71 Return return NN work_zpfso6pk3vf5df7625v6vawp2e 86 72 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 86 73 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 86 74 θk θk UH work_zpfso6pk3vf5df7625v6vawp2e 86 75 , , , work_zpfso6pk3vf5df7625v6vawp2e 86 76 F(θ f(θ UH work_zpfso6pk3vf5df7625v6vawp2e 86 77 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 86 78 , , , work_zpfso6pk3vf5df7625v6vawp2e 86 79 and and CC work_zpfso6pk3vf5df7625v6vawp2e 86 80 the the DT work_zpfso6pk3vf5df7625v6vawp2e 86 81 associated associated JJ work_zpfso6pk3vf5df7625v6vawp2e 86 82 U U NNP work_zpfso6pk3vf5df7625v6vawp2e 86 83 , , , work_zpfso6pk3vf5df7625v6vawp2e 86 84 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 86 85 . . . work_zpfso6pk3vf5df7625v6vawp2e 87 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 87 2 summary summary NN work_zpfso6pk3vf5df7625v6vawp2e 87 3 our -PRON- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 87 4 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 87 5 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 87 6 consists consist VBZ work_zpfso6pk3vf5df7625v6vawp2e 87 7 of of IN work_zpfso6pk3vf5df7625v6vawp2e 87 8 two two CD work_zpfso6pk3vf5df7625v6vawp2e 87 9 consecutive consecutive JJ work_zpfso6pk3vf5df7625v6vawp2e 87 10 steps step NNS work_zpfso6pk3vf5df7625v6vawp2e 87 11 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 87 12 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 87 13 i i NN work_zpfso6pk3vf5df7625v6vawp2e 87 14 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 87 15 at at IN work_zpfso6pk3vf5df7625v6vawp2e 87 16 the the DT work_zpfso6pk3vf5df7625v6vawp2e 87 17 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 87 18 stage stage NN work_zpfso6pk3vf5df7625v6vawp2e 87 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 20 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 87 21 determine determine VBP work_zpfso6pk3vf5df7625v6vawp2e 87 22 M m CD work_zpfso6pk3vf5df7625v6vawp2e 87 23 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 87 24 centres centre NNS work_zpfso6pk3vf5df7625v6vawp2e 87 25 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 87 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 87 27 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 87 28 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 87 29 means means NN work_zpfso6pk3vf5df7625v6vawp2e 87 30 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 87 31 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 87 32 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 33 as as IN work_zpfso6pk3vf5df7625v6vawp2e 87 34 presented present VBN work_zpfso6pk3vf5df7625v6vawp2e 87 35 in in IN work_zpfso6pk3vf5df7625v6vawp2e 87 36 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 87 37 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 87 38 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 87 39 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 87 40 ii ii NN work_zpfso6pk3vf5df7625v6vawp2e 87 41 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 87 42 for for IN work_zpfso6pk3vf5df7625v6vawp2e 87 43 a a DT work_zpfso6pk3vf5df7625v6vawp2e 87 44 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 87 45 search search NN work_zpfso6pk3vf5df7625v6vawp2e 87 46 of of IN work_zpfso6pk3vf5df7625v6vawp2e 87 47 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 87 48 width width NN work_zpfso6pk3vf5df7625v6vawp2e 87 49 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 50 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 87 51 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 87 52 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 87 53 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 87 54 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 87 55 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 87 56 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 87 57 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 87 58 ω ω XX work_zpfso6pk3vf5df7625v6vawp2e 87 59 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 87 60 on on IN work_zpfso6pk3vf5df7625v6vawp2e 87 61 the the DT work_zpfso6pk3vf5df7625v6vawp2e 87 62 maxi- maxi- NN work_zpfso6pk3vf5df7625v6vawp2e 87 63 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 87 64 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 87 65 and and CC work_zpfso6pk3vf5df7625v6vawp2e 87 66 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 87 67 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 87 68 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 87 69 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 87 70 Proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 87 71 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 87 72 for for IN work_zpfso6pk3vf5df7625v6vawp2e 87 73 the the DT work_zpfso6pk3vf5df7625v6vawp2e 87 74 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 87 75 root root NN work_zpfso6pk3vf5df7625v6vawp2e 87 76 of of IN work_zpfso6pk3vf5df7625v6vawp2e 87 77 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 87 78 density density NN work_zpfso6pk3vf5df7625v6vawp2e 87 79 function function NN work_zpfso6pk3vf5df7625v6vawp2e 87 80 Require Require NNP work_zpfso6pk3vf5df7625v6vawp2e 87 81 : : : work_zpfso6pk3vf5df7625v6vawp2e 87 82 x x NNP work_zpfso6pk3vf5df7625v6vawp2e 87 83 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 87 84 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 85 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 87 86 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 87 87 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 87 88 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 89 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 87 90 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 87 91 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 87 92 , , , work_zpfso6pk3vf5df7625v6vawp2e 87 93 N. N. NNP work_zpfso6pk3vf5df7625v6vawp2e 87 94 Preset preset JJ work_zpfso6pk3vf5df7625v6vawp2e 87 95 number number NN work_zpfso6pk3vf5df7625v6vawp2e 87 96 of of IN work_zpfso6pk3vf5df7625v6vawp2e 87 97 kernels kernel NNS work_zpfso6pk3vf5df7625v6vawp2e 87 98 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 87 99 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 87 100 Ensure Ensure NNP work_zpfso6pk3vf5df7625v6vawp2e 87 101 : : : work_zpfso6pk3vf5df7625v6vawp2e 87 102 ψ(x ψ(x NN work_zpfso6pk3vf5df7625v6vawp2e 87 103 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 87 104 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 87 105 maximizes maximize VBZ work_zpfso6pk3vf5df7625v6vawp2e 87 106 the the DT work_zpfso6pk3vf5df7625v6vawp2e 87 107 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 87 108 . . . work_zpfso6pk3vf5df7625v6vawp2e 88 1 1 1 LS work_zpfso6pk3vf5df7625v6vawp2e 88 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 88 3 Use use VB work_zpfso6pk3vf5df7625v6vawp2e 88 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 88 5 k k NN work_zpfso6pk3vf5df7625v6vawp2e 88 6 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 88 7 means means NN work_zpfso6pk3vf5df7625v6vawp2e 88 8 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 88 9 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 88 10 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 88 11 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 88 12 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 88 13 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 88 14 to to TO work_zpfso6pk3vf5df7625v6vawp2e 88 15 find find VB work_zpfso6pk3vf5df7625v6vawp2e 88 16 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 88 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 88 18 i i PRP work_zpfso6pk3vf5df7625v6vawp2e 88 19 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 88 20 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 88 21 , , , work_zpfso6pk3vf5df7625v6vawp2e 88 22 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 88 23 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 88 24 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 88 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 88 26 M m NN work_zpfso6pk3vf5df7625v6vawp2e 88 27 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 88 28 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 88 29 : : : work_zpfso6pk3vf5df7625v6vawp2e 88 30 for for IN work_zpfso6pk3vf5df7625v6vawp2e 88 31 i i NN work_zpfso6pk3vf5df7625v6vawp2e 88 32 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 88 33 1,2, 1,2, CD work_zpfso6pk3vf5df7625v6vawp2e 88 34 ... ... NFP work_zpfso6pk3vf5df7625v6vawp2e 88 35 ,(Iter ,(Iter , work_zpfso6pk3vf5df7625v6vawp2e 88 36 + + CC work_zpfso6pk3vf5df7625v6vawp2e 88 37 1 1 LS work_zpfso6pk3vf5df7625v6vawp2e 88 38 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 88 39 do do VB work_zpfso6pk3vf5df7625v6vawp2e 88 40 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 88 41 : : SYM work_zpfso6pk3vf5df7625v6vawp2e 88 42 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 88 43 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 88 44 σmin σmin NN work_zpfso6pk3vf5df7625v6vawp2e 88 45 + + CC work_zpfso6pk3vf5df7625v6vawp2e 88 46 i−1n i−1n NNP work_zpfso6pk3vf5df7625v6vawp2e 88 47 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 88 48 σmax σmax NNP work_zpfso6pk3vf5df7625v6vawp2e 88 49 −σmin −σmin NNP work_zpfso6pk3vf5df7625v6vawp2e 88 50 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 88 51 . . . work_zpfso6pk3vf5df7625v6vawp2e 89 1 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 89 2 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 89 3 Iter iter NN work_zpfso6pk3vf5df7625v6vawp2e 89 4 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 89 5 1),σmin 1),σmin NNP work_zpfso6pk3vf5df7625v6vawp2e 89 6 and and CC work_zpfso6pk3vf5df7625v6vawp2e 89 7 σmax σmax NNP work_zpfso6pk3vf5df7625v6vawp2e 89 8 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 89 9 preset preset JJ work_zpfso6pk3vf5df7625v6vawp2e 89 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 89 11 and and CC work_zpfso6pk3vf5df7625v6vawp2e 89 12 they -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 89 13 denote denote VBP work_zpfso6pk3vf5df7625v6vawp2e 89 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 89 15 minimum minimum JJ work_zpfso6pk3vf5df7625v6vawp2e 89 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 89 17 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 89 18 value value NN work_zpfso6pk3vf5df7625v6vawp2e 89 19 and and CC work_zpfso6pk3vf5df7625v6vawp2e 89 20 the the DT work_zpfso6pk3vf5df7625v6vawp2e 89 21 total total JJ work_zpfso6pk3vf5df7625v6vawp2e 89 22 number number NN work_zpfso6pk3vf5df7625v6vawp2e 89 23 of of IN work_zpfso6pk3vf5df7625v6vawp2e 89 24 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 89 25 width width NN work_zpfso6pk3vf5df7625v6vawp2e 89 26 on on IN work_zpfso6pk3vf5df7625v6vawp2e 89 27 a a DT work_zpfso6pk3vf5df7625v6vawp2e 89 28 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 89 29 search search NN work_zpfso6pk3vf5df7625v6vawp2e 89 30 . . . work_zpfso6pk3vf5df7625v6vawp2e 90 1 4 4 LS work_zpfso6pk3vf5df7625v6vawp2e 90 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 90 3 Form Form NNP work_zpfso6pk3vf5df7625v6vawp2e 90 4 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 90 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 90 6 its -PRON- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 90 7 eigen eigen NN work_zpfso6pk3vf5df7625v6vawp2e 90 8 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 90 9 decomposition decomposition NN work_zpfso6pk3vf5df7625v6vawp2e 90 10 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 90 11 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 90 12 UΣ UΣ NNP work_zpfso6pk3vf5df7625v6vawp2e 90 13 UT UT NNP work_zpfso6pk3vf5df7625v6vawp2e 90 14 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 90 15 : : : work_zpfso6pk3vf5df7625v6vawp2e 90 16 Obtain obtain VB work_zpfso6pk3vf5df7625v6vawp2e 90 17 k̄(x k̄(x NNP work_zpfso6pk3vf5df7625v6vawp2e 90 18 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 90 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 90 20 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 90 21 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 90 22 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 90 23 −1 −1 NNP work_zpfso6pk3vf5df7625v6vawp2e 90 24 UTk(x UTk(x NNP work_zpfso6pk3vf5df7625v6vawp2e 90 25 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 90 26 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 90 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 90 28 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 90 29 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 90 30 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 90 31 , , , work_zpfso6pk3vf5df7625v6vawp2e 90 32 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 90 33 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 90 34 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 90 35 , , , work_zpfso6pk3vf5df7625v6vawp2e 90 36 N n NN work_zpfso6pk3vf5df7625v6vawp2e 90 37 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 90 38 : : : work_zpfso6pk3vf5df7625v6vawp2e 90 39 Find find VB work_zpfso6pk3vf5df7625v6vawp2e 90 40 θ θ NN work_zpfso6pk3vf5df7625v6vawp2e 90 41 0 0 NFP work_zpfso6pk3vf5df7625v6vawp2e 90 42 according accord VBG work_zpfso6pk3vf5df7625v6vawp2e 90 43 to to IN work_zpfso6pk3vf5df7625v6vawp2e 90 44 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 90 45 18 18 CD work_zpfso6pk3vf5df7625v6vawp2e 90 46 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 90 47 and and CC work_zpfso6pk3vf5df7625v6vawp2e 90 48 normalize normalize VB work_zpfso6pk3vf5df7625v6vawp2e 90 49 it -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 90 50 . . . work_zpfso6pk3vf5df7625v6vawp2e 91 1 7 7 LS work_zpfso6pk3vf5df7625v6vawp2e 91 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 91 3 Apply apply VB work_zpfso6pk3vf5df7625v6vawp2e 91 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 91 5 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 91 6 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 91 7 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 91 8 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 91 9 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 91 10 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 91 11 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 91 12 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 91 13 to to TO work_zpfso6pk3vf5df7625v6vawp2e 91 14 return return VB work_zpfso6pk3vf5df7625v6vawp2e 91 15 F(θ F(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 91 16 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 91 17 . . . work_zpfso6pk3vf5df7625v6vawp2e 92 1 8 8 LS work_zpfso6pk3vf5df7625v6vawp2e 92 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 92 3 end end VB work_zpfso6pk3vf5df7625v6vawp2e 92 4 for for IN work_zpfso6pk3vf5df7625v6vawp2e 92 5 9 9 CD work_zpfso6pk3vf5df7625v6vawp2e 92 6 : : : work_zpfso6pk3vf5df7625v6vawp2e 92 7 Find find VB work_zpfso6pk3vf5df7625v6vawp2e 92 8 σ σ NN work_zpfso6pk3vf5df7625v6vawp2e 92 9 opt opt NN work_zpfso6pk3vf5df7625v6vawp2e 92 10 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 92 11 minimizes minimize VBZ work_zpfso6pk3vf5df7625v6vawp2e 92 12 F(θ F(θ VBN work_zpfso6pk3vf5df7625v6vawp2e 92 13 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 92 14 over over IN work_zpfso6pk3vf5df7625v6vawp2e 92 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 92 16 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 92 17 search search NN work_zpfso6pk3vf5df7625v6vawp2e 92 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 93 1 Return return VB work_zpfso6pk3vf5df7625v6vawp2e 93 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 93 3 associated associated NNP work_zpfso6pk3vf5df7625v6vawp2e 93 4 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 93 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 93 6 U U NNP work_zpfso6pk3vf5df7625v6vawp2e 93 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 93 8 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 93 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 94 1 10 10 LS work_zpfso6pk3vf5df7625v6vawp2e 94 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 94 3 Return Return NNP work_zpfso6pk3vf5df7625v6vawp2e 94 4 ω ω NNP work_zpfso6pk3vf5df7625v6vawp2e 94 5 opt opt NN work_zpfso6pk3vf5df7625v6vawp2e 94 6 = = -RRB- work_zpfso6pk3vf5df7625v6vawp2e 94 7 U U NNP work_zpfso6pk3vf5df7625v6vawp2e 94 8 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 94 9 Σ Σ NNP work_zpfso6pk3vf5df7625v6vawp2e 94 10 −1 −1 NNP work_zpfso6pk3vf5df7625v6vawp2e 94 11 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 94 12 opt opt NNP work_zpfso6pk3vf5df7625v6vawp2e 94 13 . . . work_zpfso6pk3vf5df7625v6vawp2e 95 1 mum mum NNP work_zpfso6pk3vf5df7625v6vawp2e 95 2 likelihood likelihood NNP work_zpfso6pk3vf5df7625v6vawp2e 95 3 criterion criterion NN work_zpfso6pk3vf5df7625v6vawp2e 95 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 96 1 For for IN work_zpfso6pk3vf5df7625v6vawp2e 96 2 completeness completeness JJ work_zpfso6pk3vf5df7625v6vawp2e 96 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 96 4 the the DT work_zpfso6pk3vf5df7625v6vawp2e 96 5 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 96 6 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 96 7 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 96 8 detailed detail VBN work_zpfso6pk3vf5df7625v6vawp2e 96 9 in in IN work_zpfso6pk3vf5df7625v6vawp2e 96 10 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 96 11 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 96 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 97 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 97 2 computational computational JJ work_zpfso6pk3vf5df7625v6vawp2e 97 3 complexity complexity NN work_zpfso6pk3vf5df7625v6vawp2e 97 4 consists consist VBZ work_zpfso6pk3vf5df7625v6vawp2e 97 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 97 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 97 7 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 97 8 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 97 9 means means NN work_zpfso6pk3vf5df7625v6vawp2e 97 10 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 97 11 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 97 12 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 97 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 97 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 97 15 order order NN work_zpfso6pk3vf5df7625v6vawp2e 97 16 Iterkmeans Iterkmeans NNPS work_zpfso6pk3vf5df7625v6vawp2e 97 17 ∗O(N ∗o(n NN work_zpfso6pk3vf5df7625v6vawp2e 97 18 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 97 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 97 20 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 97 21 Iterkmeans Iterkmeans NNPS work_zpfso6pk3vf5df7625v6vawp2e 97 22 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 97 23 the the DT work_zpfso6pk3vf5df7625v6vawp2e 97 24 number number NN work_zpfso6pk3vf5df7625v6vawp2e 97 25 of of IN work_zpfso6pk3vf5df7625v6vawp2e 97 26 iterations iteration NNS work_zpfso6pk3vf5df7625v6vawp2e 97 27 of of IN work_zpfso6pk3vf5df7625v6vawp2e 97 28 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 97 29 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 97 30 means means NN work_zpfso6pk3vf5df7625v6vawp2e 97 31 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 97 32 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 97 33 , , , work_zpfso6pk3vf5df7625v6vawp2e 97 34 and and CC work_zpfso6pk3vf5df7625v6vawp2e 97 35 that that DT work_zpfso6pk3vf5df7625v6vawp2e 97 36 of of IN work_zpfso6pk3vf5df7625v6vawp2e 97 37 the the DT work_zpfso6pk3vf5df7625v6vawp2e 97 38 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 97 39 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 97 40 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 97 41 , , , work_zpfso6pk3vf5df7625v6vawp2e 97 42 scaled scale VBN work_zpfso6pk3vf5df7625v6vawp2e 97 43 by by IN work_zpfso6pk3vf5df7625v6vawp2e 97 44 the the DT work_zpfso6pk3vf5df7625v6vawp2e 97 45 number number NN work_zpfso6pk3vf5df7625v6vawp2e 97 46 of of IN work_zpfso6pk3vf5df7625v6vawp2e 97 47 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 97 48 search search NN work_zpfso6pk3vf5df7625v6vawp2e 97 49 Iter Iter NNP work_zpfso6pk3vf5df7625v6vawp2e 97 50 . . . work_zpfso6pk3vf5df7625v6vawp2e 98 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 98 2 main main JJ work_zpfso6pk3vf5df7625v6vawp2e 98 3 cost cost NN work_zpfso6pk3vf5df7625v6vawp2e 98 4 in in IN work_zpfso6pk3vf5df7625v6vawp2e 98 5 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 98 6 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 98 7 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 98 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 98 9 function function NN work_zpfso6pk3vf5df7625v6vawp2e 98 10 and and CC work_zpfso6pk3vf5df7625v6vawp2e 98 11 derivative derivative JJ work_zpfso6pk3vf5df7625v6vawp2e 98 12 evaluation evaluation NN work_zpfso6pk3vf5df7625v6vawp2e 98 13 of of IN work_zpfso6pk3vf5df7625v6vawp2e 98 14 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 98 15 19 19 CD work_zpfso6pk3vf5df7625v6vawp2e 98 16 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 98 17 & & CC work_zpfso6pk3vf5df7625v6vawp2e 98 18 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 98 19 20 20 CD work_zpfso6pk3vf5df7625v6vawp2e 98 20 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 98 21 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 98 22 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 98 23 in in IN work_zpfso6pk3vf5df7625v6vawp2e 98 24 the the DT work_zpfso6pk3vf5df7625v6vawp2e 98 25 order order NN work_zpfso6pk3vf5df7625v6vawp2e 98 26 of of IN work_zpfso6pk3vf5df7625v6vawp2e 98 27 O(MN O(MN NNP work_zpfso6pk3vf5df7625v6vawp2e 98 28 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 98 29 . . . work_zpfso6pk3vf5df7625v6vawp2e 99 1 Hence hence RB work_zpfso6pk3vf5df7625v6vawp2e 99 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 99 3 total total JJ work_zpfso6pk3vf5df7625v6vawp2e 99 4 cost cost NN work_zpfso6pk3vf5df7625v6vawp2e 99 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 99 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 99 7 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 99 8 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 99 9 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 99 10 evaluated evaluate VBN work_zpfso6pk3vf5df7625v6vawp2e 99 11 as as IN work_zpfso6pk3vf5df7625v6vawp2e 99 12 Iterkmeans Iterkmeans NNPS work_zpfso6pk3vf5df7625v6vawp2e 99 13 ∗O(N ∗o(n NN work_zpfso6pk3vf5df7625v6vawp2e 99 14 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 99 15 + + NFP work_zpfso6pk3vf5df7625v6vawp2e 99 16 Iter∗O(MN Iter∗O(MN NNP work_zpfso6pk3vf5df7625v6vawp2e 99 17 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 99 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 100 1 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 100 2 Illustrative illustrative JJ work_zpfso6pk3vf5df7625v6vawp2e 100 3 examples example NNS work_zpfso6pk3vf5df7625v6vawp2e 100 4 Example example NN work_zpfso6pk3vf5df7625v6vawp2e 100 5 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 100 6 : : : work_zpfso6pk3vf5df7625v6vawp2e 100 7 A a DT work_zpfso6pk3vf5df7625v6vawp2e 100 8 data data NN work_zpfso6pk3vf5df7625v6vawp2e 100 9 set set NN work_zpfso6pk3vf5df7625v6vawp2e 100 10 of of IN work_zpfso6pk3vf5df7625v6vawp2e 100 11 N n NN work_zpfso6pk3vf5df7625v6vawp2e 100 12 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 100 13 600 600 CD work_zpfso6pk3vf5df7625v6vawp2e 100 14 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 100 15 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 100 16 randomly randomly RB work_zpfso6pk3vf5df7625v6vawp2e 100 17 drawn draw VBN work_zpfso6pk3vf5df7625v6vawp2e 100 18 from from IN work_zpfso6pk3vf5df7625v6vawp2e 100 19 a a DT work_zpfso6pk3vf5df7625v6vawp2e 100 20 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 100 21 dis- dis- IN work_zpfso6pk3vf5df7625v6vawp2e 100 22 tribution tribution NN work_zpfso6pk3vf5df7625v6vawp2e 100 23 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 100 24 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 100 25 and and CC work_zpfso6pk3vf5df7625v6vawp2e 100 26 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 100 27 to to TO work_zpfso6pk3vf5df7625v6vawp2e 100 28 construct construct VB work_zpfso6pk3vf5df7625v6vawp2e 100 29 the the DT work_zpfso6pk3vf5df7625v6vawp2e 100 30 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 100 31 of of IN work_zpfso6pk3vf5df7625v6vawp2e 100 32 the the DT work_zpfso6pk3vf5df7625v6vawp2e 100 33 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 100 34 root root NN work_zpfso6pk3vf5df7625v6vawp2e 100 35 of of IN work_zpfso6pk3vf5df7625v6vawp2e 100 36 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 100 37 density density NN work_zpfso6pk3vf5df7625v6vawp2e 100 38 function function NN work_zpfso6pk3vf5df7625v6vawp2e 100 39 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 100 40 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 100 41 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 100 42 the the DT work_zpfso6pk3vf5df7625v6vawp2e 100 43 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 100 44 approach approach NN work_zpfso6pk3vf5df7625v6vawp2e 100 45 . . . work_zpfso6pk3vf5df7625v6vawp2e 101 1 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 101 2 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 3 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 101 4 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 101 5 as as IN work_zpfso6pk3vf5df7625v6vawp2e 101 6 a a DT work_zpfso6pk3vf5df7625v6vawp2e 101 7 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 101 8 of of IN work_zpfso6pk3vf5df7625v6vawp2e 101 9 one one CD work_zpfso6pk3vf5df7625v6vawp2e 101 10 Gaussian Gaussian NNP work_zpfso6pk3vf5df7625v6vawp2e 101 11 and and CC work_zpfso6pk3vf5df7625v6vawp2e 101 12 one one CD work_zpfso6pk3vf5df7625v6vawp2e 101 13 Laplacian Laplacian NNP work_zpfso6pk3vf5df7625v6vawp2e 101 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 15 as as IN work_zpfso6pk3vf5df7625v6vawp2e 101 16 defined define VBN work_zpfso6pk3vf5df7625v6vawp2e 101 17 by by IN work_zpfso6pk3vf5df7625v6vawp2e 101 18 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 101 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 20 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 101 21 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 101 22 3π 3π CD work_zpfso6pk3vf5df7625v6vawp2e 101 23 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 101 24 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 101 25 −2(x1 −2(x1 NNS work_zpfso6pk3vf5df7625v6vawp2e 101 26 −1)2 −1)2 CD work_zpfso6pk3vf5df7625v6vawp2e 101 27 + + CC work_zpfso6pk3vf5df7625v6vawp2e 101 28 2(x2 2(x2 CD work_zpfso6pk3vf5df7625v6vawp2e 101 29 −1)2 −1)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 101 30 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 31 + + CC work_zpfso6pk3vf5df7625v6vawp2e 101 32 0.35 0.35 CD work_zpfso6pk3vf5df7625v6vawp2e 101 33 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 101 34 exp(−0.7|x1 exp(−0.7|x1 NNP work_zpfso6pk3vf5df7625v6vawp2e 101 35 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 101 36 1|−0.5|x2 1|−0.5|x2 CD work_zpfso6pk3vf5df7625v6vawp2e 101 37 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 101 38 1| 1| CD work_zpfso6pk3vf5df7625v6vawp2e 101 39 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 40 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 101 41 25 25 CD work_zpfso6pk3vf5df7625v6vawp2e 101 42 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 43 We -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 101 44 preset preset VBP work_zpfso6pk3vf5df7625v6vawp2e 101 45 M m NN work_zpfso6pk3vf5df7625v6vawp2e 101 46 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 101 47 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 101 48 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 49 the the DT work_zpfso6pk3vf5df7625v6vawp2e 101 50 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 101 51 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 101 52 means means NNP work_zpfso6pk3vf5df7625v6vawp2e 101 53 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 101 54 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 101 55 applied apply VBN work_zpfso6pk3vf5df7625v6vawp2e 101 56 to to TO work_zpfso6pk3vf5df7625v6vawp2e 101 57 find find VB work_zpfso6pk3vf5df7625v6vawp2e 101 58 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 101 59 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 101 60 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 101 61 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 101 62 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 101 63 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 64 i i NNP work_zpfso6pk3vf5df7625v6vawp2e 101 65 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 101 66 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 101 67 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 68 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 101 69 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 101 70 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 101 71 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 72 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 101 73 The the DT work_zpfso6pk3vf5df7625v6vawp2e 101 74 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 101 75 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 101 76 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 101 77 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 101 78 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 101 79 applied apply VBN work_zpfso6pk3vf5df7625v6vawp2e 101 80 to to IN work_zpfso6pk3vf5df7625v6vawp2e 101 81 mini- mini- NNP work_zpfso6pk3vf5df7625v6vawp2e 101 82 mize mize VB work_zpfso6pk3vf5df7625v6vawp2e 101 83 the the DT work_zpfso6pk3vf5df7625v6vawp2e 101 84 negative negative JJ work_zpfso6pk3vf5df7625v6vawp2e 101 85 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 101 86 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 101 87 on on IN work_zpfso6pk3vf5df7625v6vawp2e 101 88 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 101 89 obtained obtain VBD work_zpfso6pk3vf5df7625v6vawp2e 101 90 a a DT work_zpfso6pk3vf5df7625v6vawp2e 101 91 range range NN work_zpfso6pk3vf5df7625v6vawp2e 101 92 of of IN work_zpfso6pk3vf5df7625v6vawp2e 101 93 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 101 94 widths width NNS work_zpfso6pk3vf5df7625v6vawp2e 101 95 of of IN work_zpfso6pk3vf5df7625v6vawp2e 101 96 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 101 97 0.5,2 0.5,2 NN work_zpfso6pk3vf5df7625v6vawp2e 101 98 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 101 99 , , , work_zpfso6pk3vf5df7625v6vawp2e 101 100 with with IN work_zpfso6pk3vf5df7625v6vawp2e 101 101 a a DT work_zpfso6pk3vf5df7625v6vawp2e 101 102 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 101 103 width width NN work_zpfso6pk3vf5df7625v6vawp2e 101 104 of of IN work_zpfso6pk3vf5df7625v6vawp2e 101 105 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 101 106 . . . work_zpfso6pk3vf5df7625v6vawp2e 102 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 102 2 result result NN work_zpfso6pk3vf5df7625v6vawp2e 102 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 102 4 log log NN work_zpfso6pk3vf5df7625v6vawp2e 102 5 F(θ f(θ NN work_zpfso6pk3vf5df7625v6vawp2e 102 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 102 7 versus versus IN work_zpfso6pk3vf5df7625v6vawp2e 102 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 102 9 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 102 10 width width NN work_zpfso6pk3vf5df7625v6vawp2e 102 11 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 102 12 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 102 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 102 14 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 102 15 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 102 16 . . . work_zpfso6pk3vf5df7625v6vawp2e 103 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 103 2 convergence convergence NN work_zpfso6pk3vf5df7625v6vawp2e 103 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 103 4 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 103 5 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 103 6 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 103 7 algorithm algorithm VBP work_zpfso6pk3vf5df7625v6vawp2e 103 8 on on IN work_zpfso6pk3vf5df7625v6vawp2e 103 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 103 10 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 103 11 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 103 12 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 103 13 on on IN work_zpfso6pk3vf5df7625v6vawp2e 103 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 103 15 optimal optimal JJ work_zpfso6pk3vf5df7625v6vawp2e 103 16 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 103 17 width width NN work_zpfso6pk3vf5df7625v6vawp2e 103 18 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 103 19 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 103 20 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 103 21 in in IN work_zpfso6pk3vf5df7625v6vawp2e 103 22 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 103 23 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 103 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 103 25 showing show VBG work_zpfso6pk3vf5df7625v6vawp2e 103 26 that that IN work_zpfso6pk3vf5df7625v6vawp2e 103 27 the the DT work_zpfso6pk3vf5df7625v6vawp2e 103 28 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 103 29 can can MD work_zpfso6pk3vf5df7625v6vawp2e 103 30 converge converge VB work_zpfso6pk3vf5df7625v6vawp2e 103 31 rapidly rapidly RB work_zpfso6pk3vf5df7625v6vawp2e 103 32 . . . work_zpfso6pk3vf5df7625v6vawp2e 104 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 104 2 performance performance NN work_zpfso6pk3vf5df7625v6vawp2e 104 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 104 4 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 104 5 es- es- NN work_zpfso6pk3vf5df7625v6vawp2e 104 6 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 104 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 104 8 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 104 9 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 104 10 of of IN work_zpfso6pk3vf5df7625v6vawp2e 104 11 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 104 12 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 104 13 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 104 14 on on IN work_zpfso6pk3vf5df7625v6vawp2e 104 15 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 104 16 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 104 17 timator timator NN work_zpfso6pk3vf5df7625v6vawp2e 104 18 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 104 19 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 104 20 in in IN work_zpfso6pk3vf5df7625v6vawp2e 104 21 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 104 22 3(a),(b)&(c 3(a),(b)&(c CD work_zpfso6pk3vf5df7625v6vawp2e 104 23 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 104 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 104 25 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 104 26 plots plot VBZ work_zpfso6pk3vf5df7625v6vawp2e 104 27 ψ ψ CD work_zpfso6pk3vf5df7625v6vawp2e 104 28 2(x 2(x CD work_zpfso6pk3vf5df7625v6vawp2e 104 29 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 104 30 , , , work_zpfso6pk3vf5df7625v6vawp2e 104 31 the the DT work_zpfso6pk3vf5df7625v6vawp2e 104 32 true true JJ work_zpfso6pk3vf5df7625v6vawp2e 104 33 density density NN work_zpfso6pk3vf5df7625v6vawp2e 104 34 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 104 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 104 36 , , , work_zpfso6pk3vf5df7625v6vawp2e 104 37 and and CC work_zpfso6pk3vf5df7625v6vawp2e 104 38 the the DT work_zpfso6pk3vf5df7625v6vawp2e 104 39 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 104 40 error error NN work_zpfso6pk3vf5df7625v6vawp2e 104 41 e(x e(x NNP work_zpfso6pk3vf5df7625v6vawp2e 104 42 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 104 43 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 104 44 ψ(x)2 ψ(x)2 NN work_zpfso6pk3vf5df7625v6vawp2e 104 45 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 104 46 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 104 47 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 104 48 respectively respectively RB work_zpfso6pk3vf5df7625v6vawp2e 104 49 over over IN work_zpfso6pk3vf5df7625v6vawp2e 104 50 a a DT work_zpfso6pk3vf5df7625v6vawp2e 104 51 41×41 41×41 CD work_zpfso6pk3vf5df7625v6vawp2e 104 52 meshed mesh VBN work_zpfso6pk3vf5df7625v6vawp2e 104 53 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 104 54 , , , work_zpfso6pk3vf5df7625v6vawp2e 104 55 with with IN work_zpfso6pk3vf5df7625v6vawp2e 104 56 a a DT work_zpfso6pk3vf5df7625v6vawp2e 104 57 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 104 58 size size NN work_zpfso6pk3vf5df7625v6vawp2e 104 59 of of IN work_zpfso6pk3vf5df7625v6vawp2e 104 60 0.2 0.2 CD work_zpfso6pk3vf5df7625v6vawp2e 104 61 , , , work_zpfso6pk3vf5df7625v6vawp2e 104 62 ranging range VBG work_zpfso6pk3vf5df7625v6vawp2e 104 63 from from IN work_zpfso6pk3vf5df7625v6vawp2e 104 64 -4 -4 NNP work_zpfso6pk3vf5df7625v6vawp2e 104 65 to to IN work_zpfso6pk3vf5df7625v6vawp2e 104 66 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 104 67 for for IN work_zpfso6pk3vf5df7625v6vawp2e 104 68 both both CC work_zpfso6pk3vf5df7625v6vawp2e 104 69 x1 x1 NN work_zpfso6pk3vf5df7625v6vawp2e 104 70 and and CC work_zpfso6pk3vf5df7625v6vawp2e 104 71 x2 x2 NNP work_zpfso6pk3vf5df7625v6vawp2e 104 72 . . . work_zpfso6pk3vf5df7625v6vawp2e 105 1 0.5 0.5 CD work_zpfso6pk3vf5df7625v6vawp2e 105 2 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 105 3 1.5 1.5 CD work_zpfso6pk3vf5df7625v6vawp2e 105 4 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 105 5 1220 1220 CD work_zpfso6pk3vf5df7625v6vawp2e 105 6 1240 1240 CD work_zpfso6pk3vf5df7625v6vawp2e 105 7 1260 1260 CD work_zpfso6pk3vf5df7625v6vawp2e 105 8 1280 1280 CD work_zpfso6pk3vf5df7625v6vawp2e 105 9 1300 1300 CD work_zpfso6pk3vf5df7625v6vawp2e 105 10 1320 1320 CD work_zpfso6pk3vf5df7625v6vawp2e 105 11 1340 1340 CD work_zpfso6pk3vf5df7625v6vawp2e 105 12 1360 1360 CD work_zpfso6pk3vf5df7625v6vawp2e 105 13 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 105 14 V V NNP work_zpfso6pk3vf5df7625v6vawp2e 105 15 a a NN work_zpfso6pk3vf5df7625v6vawp2e 105 16 lu lu NN work_zpfso6pk3vf5df7625v6vawp2e 105 17 e e NNP work_zpfso6pk3vf5df7625v6vawp2e 105 18 o o NNP work_zpfso6pk3vf5df7625v6vawp2e 105 19 f f NNP work_zpfso6pk3vf5df7625v6vawp2e 105 20 m m NNP work_zpfso6pk3vf5df7625v6vawp2e 105 21 in in IN work_zpfso6pk3vf5df7625v6vawp2e 105 22 i -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 105 23 m be VBP work_zpfso6pk3vf5df7625v6vawp2e 105 24 a a DT work_zpfso6pk3vf5df7625v6vawp2e 105 25 l l NN work_zpfso6pk3vf5df7625v6vawp2e 105 26 o o NN work_zpfso6pk3vf5df7625v6vawp2e 105 27 f f NNP work_zpfso6pk3vf5df7625v6vawp2e 105 28 F F NNP work_zpfso6pk3vf5df7625v6vawp2e 105 29 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 105 30 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 105 31 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 105 32 Fig Fig NNP work_zpfso6pk3vf5df7625v6vawp2e 105 33 . . . work_zpfso6pk3vf5df7625v6vawp2e 106 1 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 106 2 log(F(θ log(F(θ NNP work_zpfso6pk3vf5df7625v6vawp2e 106 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 106 4 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 106 5 versus versus IN work_zpfso6pk3vf5df7625v6vawp2e 106 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 106 7 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 106 8 width width NN work_zpfso6pk3vf5df7625v6vawp2e 106 9 for for IN work_zpfso6pk3vf5df7625v6vawp2e 106 10 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 106 11 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 106 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 107 1 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 107 2 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 107 3 10 10 CD work_zpfso6pk3vf5df7625v6vawp2e 107 4 15 15 CD work_zpfso6pk3vf5df7625v6vawp2e 107 5 20 20 CD work_zpfso6pk3vf5df7625v6vawp2e 107 6 600 600 CD work_zpfso6pk3vf5df7625v6vawp2e 107 7 605 605 CD work_zpfso6pk3vf5df7625v6vawp2e 107 8 610 610 CD work_zpfso6pk3vf5df7625v6vawp2e 107 9 615 615 CD work_zpfso6pk3vf5df7625v6vawp2e 107 10 620 620 CD work_zpfso6pk3vf5df7625v6vawp2e 107 11 625 625 CD work_zpfso6pk3vf5df7625v6vawp2e 107 12 630 630 CD work_zpfso6pk3vf5df7625v6vawp2e 107 13 635 635 CD work_zpfso6pk3vf5df7625v6vawp2e 107 14 640 640 CD work_zpfso6pk3vf5df7625v6vawp2e 107 15 645 645 CD work_zpfso6pk3vf5df7625v6vawp2e 107 16 Iterations Iterations NNPS work_zpfso6pk3vf5df7625v6vawp2e 107 17 lo lo IN work_zpfso6pk3vf5df7625v6vawp2e 107 18 g g NNP work_zpfso6pk3vf5df7625v6vawp2e 107 19 F F NNP work_zpfso6pk3vf5df7625v6vawp2e 107 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 107 21 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 107 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 107 23 Fig Fig NNP work_zpfso6pk3vf5df7625v6vawp2e 107 24 . . . work_zpfso6pk3vf5df7625v6vawp2e 108 1 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 108 2 Convergence Convergence NNP work_zpfso6pk3vf5df7625v6vawp2e 108 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 108 4 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 108 5 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 108 6 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 108 7 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 108 8 for for IN work_zpfso6pk3vf5df7625v6vawp2e 108 9 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 108 10 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 108 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 109 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 109 2 experiment experiment NN work_zpfso6pk3vf5df7625v6vawp2e 109 3 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 109 4 repeated repeat VBN work_zpfso6pk3vf5df7625v6vawp2e 109 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 109 6 100 100 CD work_zpfso6pk3vf5df7625v6vawp2e 109 7 different different JJ work_zpfso6pk3vf5df7625v6vawp2e 109 8 random random JJ work_zpfso6pk3vf5df7625v6vawp2e 109 9 runs run NNS work_zpfso6pk3vf5df7625v6vawp2e 109 10 in in IN work_zpfso6pk3vf5df7625v6vawp2e 109 11 order order NN work_zpfso6pk3vf5df7625v6vawp2e 109 12 to to IN work_zpfso6pk3vf5df7625v6vawp2e 109 13 com- com- NN work_zpfso6pk3vf5df7625v6vawp2e 109 14 pare pare VB work_zpfso6pk3vf5df7625v6vawp2e 109 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 109 16 performance performance NN work_zpfso6pk3vf5df7625v6vawp2e 109 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 109 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 109 19 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 109 20 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 109 21 with with IN work_zpfso6pk3vf5df7625v6vawp2e 109 22 the the DT work_zpfso6pk3vf5df7625v6vawp2e 109 23 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 109 24 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 109 25 model model NN work_zpfso6pk3vf5df7625v6vawp2e 109 26 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 109 27 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 109 28 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 109 29 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 109 30 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 109 31 fitted fit VBN work_zpfso6pk3vf5df7625v6vawp2e 109 32 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 109 33 the the DT work_zpfso6pk3vf5df7625v6vawp2e 109 34 EM em NN work_zpfso6pk3vf5df7625v6vawp2e 109 35 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 109 36 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 109 37 McLachlan McLachlan NNP work_zpfso6pk3vf5df7625v6vawp2e 109 38 and and CC work_zpfso6pk3vf5df7625v6vawp2e 109 39 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 109 40 , , , work_zpfso6pk3vf5df7625v6vawp2e 109 41 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 109 42 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 109 43 . . . work_zpfso6pk3vf5df7625v6vawp2e 110 1 A a DT work_zpfso6pk3vf5df7625v6vawp2e 110 2 sepa- sepa- NN work_zpfso6pk3vf5df7625v6vawp2e 110 3 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 110 4 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 110 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 110 6 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 110 7 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 110 8 −4 −4 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 9 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 10 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 11 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 12 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 13 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 14 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 15 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 16 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 17 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 18 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 19 0.02 0.02 CD work_zpfso6pk3vf5df7625v6vawp2e 110 20 0.04 0.04 CD work_zpfso6pk3vf5df7625v6vawp2e 110 21 0.06 0.06 CD work_zpfso6pk3vf5df7625v6vawp2e 110 22 0.08 0.08 CD work_zpfso6pk3vf5df7625v6vawp2e 110 23 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 24 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 25 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 26 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 27 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 28 ψ ψ NNS work_zpfso6pk3vf5df7625v6vawp2e 110 29 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 30 x x NN work_zpfso6pk3vf5df7625v6vawp2e 110 31 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 32 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 33 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 34 a a DT work_zpfso6pk3vf5df7625v6vawp2e 110 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 36 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 37 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 38 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 39 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 40 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 41 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 42 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 43 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 44 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 45 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 46 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 47 0.02 0.02 CD work_zpfso6pk3vf5df7625v6vawp2e 110 48 0.04 0.04 CD work_zpfso6pk3vf5df7625v6vawp2e 110 49 0.06 0.06 CD work_zpfso6pk3vf5df7625v6vawp2e 110 50 0.08 0.08 CD work_zpfso6pk3vf5df7625v6vawp2e 110 51 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 52 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 53 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 54 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 55 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 56 p p NN work_zpfso6pk3vf5df7625v6vawp2e 110 57 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 58 x x NN work_zpfso6pk3vf5df7625v6vawp2e 110 59 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 60 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 61 b b NN work_zpfso6pk3vf5df7625v6vawp2e 110 62 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 63 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 64 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 65 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 66 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 67 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 68 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 69 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 110 70 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 71 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 72 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 110 73 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 110 74 0.02 0.02 CD work_zpfso6pk3vf5df7625v6vawp2e 110 75 0.04 0.04 CD work_zpfso6pk3vf5df7625v6vawp2e 110 76 0.06 0.06 CD work_zpfso6pk3vf5df7625v6vawp2e 110 77 0.08 0.08 CD work_zpfso6pk3vf5df7625v6vawp2e 110 78 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 79 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 80 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 110 81 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 110 82 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 110 83 e e NNS work_zpfso6pk3vf5df7625v6vawp2e 110 84 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 85 x x NN work_zpfso6pk3vf5df7625v6vawp2e 110 86 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 87 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 110 88 c c NN work_zpfso6pk3vf5df7625v6vawp2e 110 89 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 110 90 Fig fig NN work_zpfso6pk3vf5df7625v6vawp2e 110 91 . . . work_zpfso6pk3vf5df7625v6vawp2e 111 1 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 111 2 The the DT work_zpfso6pk3vf5df7625v6vawp2e 111 3 result result NN work_zpfso6pk3vf5df7625v6vawp2e 111 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 111 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 111 6 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 111 7 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 111 8 for for IN work_zpfso6pk3vf5df7625v6vawp2e 111 9 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 111 10 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 111 11 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 111 12 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 111 13 a a LS work_zpfso6pk3vf5df7625v6vawp2e 111 14 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 111 15 The the DT work_zpfso6pk3vf5df7625v6vawp2e 111 16 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 111 17 pdf pdf NN work_zpfso6pk3vf5df7625v6vawp2e 111 18 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 111 19 ψ(x)2 ψ(x)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 111 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 111 21 b b NNP work_zpfso6pk3vf5df7625v6vawp2e 111 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 111 23 The the DT work_zpfso6pk3vf5df7625v6vawp2e 111 24 true true JJ work_zpfso6pk3vf5df7625v6vawp2e 111 25 pdf pdf NN work_zpfso6pk3vf5df7625v6vawp2e 111 26 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 111 27 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 111 28 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 111 29 and and CC work_zpfso6pk3vf5df7625v6vawp2e 111 30 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 111 31 c)The c)the JJ work_zpfso6pk3vf5df7625v6vawp2e 111 32 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 111 33 error error NN work_zpfso6pk3vf5df7625v6vawp2e 111 34 e(x e(x NNP work_zpfso6pk3vf5df7625v6vawp2e 111 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 111 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 112 1 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 112 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 112 3 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 112 4 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 112 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 112 6 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 112 7 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 112 8 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 112 9 on on IN work_zpfso6pk3vf5df7625v6vawp2e 112 10 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 112 11 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 112 12 rate rate NN work_zpfso6pk3vf5df7625v6vawp2e 112 13 test test NN work_zpfso6pk3vf5df7625v6vawp2e 112 14 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 112 15 set set NN work_zpfso6pk3vf5df7625v6vawp2e 112 16 of of IN work_zpfso6pk3vf5df7625v6vawp2e 112 17 Ntest Ntest NNP work_zpfso6pk3vf5df7625v6vawp2e 112 18 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 112 19 1681 1681 CD work_zpfso6pk3vf5df7625v6vawp2e 112 20 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 112 21 generated generate VBN work_zpfso6pk3vf5df7625v6vawp2e 112 22 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 112 23 a a DT work_zpfso6pk3vf5df7625v6vawp2e 112 24 41×41 41×41 CD work_zpfso6pk3vf5df7625v6vawp2e 112 25 meshed mesh VBN work_zpfso6pk3vf5df7625v6vawp2e 112 26 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 112 27 , , , work_zpfso6pk3vf5df7625v6vawp2e 112 28 with with IN work_zpfso6pk3vf5df7625v6vawp2e 112 29 a a DT work_zpfso6pk3vf5df7625v6vawp2e 112 30 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 112 31 size size NN work_zpfso6pk3vf5df7625v6vawp2e 112 32 of of IN work_zpfso6pk3vf5df7625v6vawp2e 112 33 0.2 0.2 CD work_zpfso6pk3vf5df7625v6vawp2e 112 34 , , , work_zpfso6pk3vf5df7625v6vawp2e 112 35 ranging range VBG work_zpfso6pk3vf5df7625v6vawp2e 112 36 from from IN work_zpfso6pk3vf5df7625v6vawp2e 112 37 -4 -4 NNP work_zpfso6pk3vf5df7625v6vawp2e 112 38 to to IN work_zpfso6pk3vf5df7625v6vawp2e 112 39 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 112 40 for for IN work_zpfso6pk3vf5df7625v6vawp2e 112 41 both both CC work_zpfso6pk3vf5df7625v6vawp2e 112 42 x1 x1 NN work_zpfso6pk3vf5df7625v6vawp2e 112 43 and and CC work_zpfso6pk3vf5df7625v6vawp2e 112 44 x2 x2 NNP work_zpfso6pk3vf5df7625v6vawp2e 112 45 . . . work_zpfso6pk3vf5df7625v6vawp2e 113 1 These these DT work_zpfso6pk3vf5df7625v6vawp2e 113 2 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 113 3 were be VBD work_zpfso6pk3vf5df7625v6vawp2e 113 4 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 113 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 113 6 evaluation evaluation NN work_zpfso6pk3vf5df7625v6vawp2e 113 7 according accord VBG work_zpfso6pk3vf5df7625v6vawp2e 113 8 to to IN work_zpfso6pk3vf5df7625v6vawp2e 113 9 L1 L1 NNP work_zpfso6pk3vf5df7625v6vawp2e 113 10 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 113 11 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 113 12 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 113 13 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 113 14 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 113 15 Ntest Ntest NNP work_zpfso6pk3vf5df7625v6vawp2e 113 16 k=1 k=1 VBD work_zpfso6pk3vf5df7625v6vawp2e 113 17 |p(xk)−ψ |p(xk)−ψ , work_zpfso6pk3vf5df7625v6vawp2e 113 18 2(xk)| 2(xk)| CD work_zpfso6pk3vf5df7625v6vawp2e 113 19 Proposed propose VBD work_zpfso6pk3vf5df7625v6vawp2e 113 20 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 113 21 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 113 22 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 113 23 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 113 24 k=1 k=1 VBN work_zpfso6pk3vf5df7625v6vawp2e 113 25 |p(xk)− |p(xk)− DT work_zpfso6pk3vf5df7625v6vawp2e 113 26 pGMM(xk)| pgmm(xk)| NN work_zpfso6pk3vf5df7625v6vawp2e 113 27 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 113 28 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 113 29 26 26 CD work_zpfso6pk3vf5df7625v6vawp2e 113 30 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 113 31 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 113 32 pGMM pgmm NN work_zpfso6pk3vf5df7625v6vawp2e 113 33 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 113 34 the the DT work_zpfso6pk3vf5df7625v6vawp2e 113 35 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 113 36 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 113 37 model model NN work_zpfso6pk3vf5df7625v6vawp2e 113 38 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 113 39 on on IN work_zpfso6pk3vf5df7625v6vawp2e 113 40 two two CD work_zpfso6pk3vf5df7625v6vawp2e 113 41 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 113 42 mixtures mixture NNS work_zpfso6pk3vf5df7625v6vawp2e 113 43 , , , work_zpfso6pk3vf5df7625v6vawp2e 113 44 with with IN work_zpfso6pk3vf5df7625v6vawp2e 113 45 the the DT work_zpfso6pk3vf5df7625v6vawp2e 113 46 constraint constraint NN work_zpfso6pk3vf5df7625v6vawp2e 113 47 that that IN work_zpfso6pk3vf5df7625v6vawp2e 113 48 the the DT work_zpfso6pk3vf5df7625v6vawp2e 113 49 covariance covariance NN work_zpfso6pk3vf5df7625v6vawp2e 113 50 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 113 51 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 113 52 diagonal diagonal JJ work_zpfso6pk3vf5df7625v6vawp2e 113 53 . . . work_zpfso6pk3vf5df7625v6vawp2e 114 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 114 2 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 114 3 model model NN work_zpfso6pk3vf5df7625v6vawp2e 114 4 fitting fitting NN work_zpfso6pk3vf5df7625v6vawp2e 114 5 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 114 6 im- im- RB work_zpfso6pk3vf5df7625v6vawp2e 114 7 plemented plemente VBN work_zpfso6pk3vf5df7625v6vawp2e 114 8 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 114 9 Matlab Matlab NNP work_zpfso6pk3vf5df7625v6vawp2e 114 10 command command NN work_zpfso6pk3vf5df7625v6vawp2e 114 11 gmdistribution gmdistribution NN work_zpfso6pk3vf5df7625v6vawp2e 114 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 115 1 f f NNP work_zpfso6pk3vf5df7625v6vawp2e 115 2 it.m it.m NNP work_zpfso6pk3vf5df7625v6vawp2e 115 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 116 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 116 2 results result NNS work_zpfso6pk3vf5df7625v6vawp2e 116 3 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 116 4 as as IN work_zpfso6pk3vf5df7625v6vawp2e 116 5 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 116 6 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 116 7 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 116 8 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 116 9 demonstrate demonstrate VBP work_zpfso6pk3vf5df7625v6vawp2e 116 10 that that IN work_zpfso6pk3vf5df7625v6vawp2e 116 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 116 12 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 116 13 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 116 14 outperforms outperform VBZ work_zpfso6pk3vf5df7625v6vawp2e 116 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 116 16 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 116 17 fitted fit VBD work_zpfso6pk3vf5df7625v6vawp2e 116 18 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 116 19 EM EM NNP work_zpfso6pk3vf5df7625v6vawp2e 116 20 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 116 21 with with IN work_zpfso6pk3vf5df7625v6vawp2e 116 22 two two CD work_zpfso6pk3vf5df7625v6vawp2e 116 23 mixtures mixture NNS work_zpfso6pk3vf5df7625v6vawp2e 116 24 . . . work_zpfso6pk3vf5df7625v6vawp2e 117 1 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 117 2 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 117 3 Performance Performance NNP work_zpfso6pk3vf5df7625v6vawp2e 117 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 117 5 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 117 6 density density NN work_zpfso6pk3vf5df7625v6vawp2e 117 7 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 117 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 117 9 comparison comparison NN work_zpfso6pk3vf5df7625v6vawp2e 117 10 with with IN work_zpfso6pk3vf5df7625v6vawp2e 117 11 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 117 12 model model NN work_zpfso6pk3vf5df7625v6vawp2e 117 13 for for IN work_zpfso6pk3vf5df7625v6vawp2e 117 14 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 117 15 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 117 16 . . . work_zpfso6pk3vf5df7625v6vawp2e 118 1 Method Method NNP work_zpfso6pk3vf5df7625v6vawp2e 118 2 L1 L1 NNP work_zpfso6pk3vf5df7625v6vawp2e 118 3 test test NN work_zpfso6pk3vf5df7625v6vawp2e 118 4 error error NN work_zpfso6pk3vf5df7625v6vawp2e 118 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 118 6 mean mean NNP work_zpfso6pk3vf5df7625v6vawp2e 118 7 ± ± NNP work_zpfso6pk3vf5df7625v6vawp2e 118 8 STD STD NNP work_zpfso6pk3vf5df7625v6vawp2e 118 9 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 10 Proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 118 11 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 118 12 2.2±0.3)×10−4 2.2±0.3)×10−4 CD work_zpfso6pk3vf5df7625v6vawp2e 118 13 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 118 14 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 118 15 3.2±0.6)×10−4 3.2±0.6)×10−4 CD work_zpfso6pk3vf5df7625v6vawp2e 118 16 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 118 17 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 118 18 : : : work_zpfso6pk3vf5df7625v6vawp2e 118 19 A a DT work_zpfso6pk3vf5df7625v6vawp2e 118 20 data data NN work_zpfso6pk3vf5df7625v6vawp2e 118 21 set set NN work_zpfso6pk3vf5df7625v6vawp2e 118 22 of of IN work_zpfso6pk3vf5df7625v6vawp2e 118 23 N n NN work_zpfso6pk3vf5df7625v6vawp2e 118 24 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 118 25 1500 1500 CD work_zpfso6pk3vf5df7625v6vawp2e 118 26 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 118 27 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 118 28 randomly randomly RB work_zpfso6pk3vf5df7625v6vawp2e 118 29 drawn draw VBN work_zpfso6pk3vf5df7625v6vawp2e 118 30 from from IN work_zpfso6pk3vf5df7625v6vawp2e 118 31 a a DT work_zpfso6pk3vf5df7625v6vawp2e 118 32 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 118 33 distribution distribution NN work_zpfso6pk3vf5df7625v6vawp2e 118 34 p(x p(x NN work_zpfso6pk3vf5df7625v6vawp2e 118 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 36 given give VBN work_zpfso6pk3vf5df7625v6vawp2e 118 37 as as IN work_zpfso6pk3vf5df7625v6vawp2e 118 38 a a DT work_zpfso6pk3vf5df7625v6vawp2e 118 39 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 118 40 of of IN work_zpfso6pk3vf5df7625v6vawp2e 118 41 one one CD work_zpfso6pk3vf5df7625v6vawp2e 118 42 Gaussian Gaussian NNP work_zpfso6pk3vf5df7625v6vawp2e 118 43 and and CC work_zpfso6pk3vf5df7625v6vawp2e 118 44 one one CD work_zpfso6pk3vf5df7625v6vawp2e 118 45 Laplacian Laplacian NNP work_zpfso6pk3vf5df7625v6vawp2e 118 46 , , , work_zpfso6pk3vf5df7625v6vawp2e 118 47 as as IN work_zpfso6pk3vf5df7625v6vawp2e 118 48 defined define VBN work_zpfso6pk3vf5df7625v6vawp2e 118 49 by by IN work_zpfso6pk3vf5df7625v6vawp2e 118 50 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 118 51 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 52 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 118 53 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 118 54 2.1π 2.1π CD work_zpfso6pk3vf5df7625v6vawp2e 118 55 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 118 56 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 118 57 −2(x1 −2(x1 NNS work_zpfso6pk3vf5df7625v6vawp2e 118 58 −2)2 −2)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 118 59 −(x2 −(x2 NNP work_zpfso6pk3vf5df7625v6vawp2e 118 60 −2)2/0.98 −2)2/0.98 ADD work_zpfso6pk3vf5df7625v6vawp2e 118 61 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 62 + + CC work_zpfso6pk3vf5df7625v6vawp2e 118 63 0.35 0.35 CD work_zpfso6pk3vf5df7625v6vawp2e 118 64 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 118 65 exp(−0.7|x1 exp(−0.7|x1 NNP work_zpfso6pk3vf5df7625v6vawp2e 118 66 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 118 67 1|−0.5|x2 1|−0.5|x2 CD work_zpfso6pk3vf5df7625v6vawp2e 118 68 + + SYM work_zpfso6pk3vf5df7625v6vawp2e 118 69 1| 1| CD work_zpfso6pk3vf5df7625v6vawp2e 118 70 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 71 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 118 72 27 27 CD work_zpfso6pk3vf5df7625v6vawp2e 118 73 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 74 and and CC work_zpfso6pk3vf5df7625v6vawp2e 118 75 the the DT work_zpfso6pk3vf5df7625v6vawp2e 118 76 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 118 77 approach approach NN work_zpfso6pk3vf5df7625v6vawp2e 118 78 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 118 79 experimented experiment VBN work_zpfso6pk3vf5df7625v6vawp2e 118 80 to to TO work_zpfso6pk3vf5df7625v6vawp2e 118 81 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 118 82 ψ(x ψ(x NNP work_zpfso6pk3vf5df7625v6vawp2e 118 83 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 84 , , , work_zpfso6pk3vf5df7625v6vawp2e 118 85 the the DT work_zpfso6pk3vf5df7625v6vawp2e 118 86 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 118 87 root root NN work_zpfso6pk3vf5df7625v6vawp2e 118 88 of of IN work_zpfso6pk3vf5df7625v6vawp2e 118 89 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 118 90 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 118 91 . . . work_zpfso6pk3vf5df7625v6vawp2e 119 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 119 2 number number NN work_zpfso6pk3vf5df7625v6vawp2e 119 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 119 4 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 119 5 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 119 6 empirically empirically RB work_zpfso6pk3vf5df7625v6vawp2e 119 7 set set VBN work_zpfso6pk3vf5df7625v6vawp2e 119 8 as as IN work_zpfso6pk3vf5df7625v6vawp2e 119 9 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 119 10 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 119 11 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 119 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 119 14 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 119 15 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 119 16 means means NNP work_zpfso6pk3vf5df7625v6vawp2e 119 17 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 119 18 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 119 19 implemented implement VBN work_zpfso6pk3vf5df7625v6vawp2e 119 20 according accord VBG work_zpfso6pk3vf5df7625v6vawp2e 119 21 to to IN work_zpfso6pk3vf5df7625v6vawp2e 119 22 Algorithm Algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 119 23 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 119 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 25 producing produce VBG work_zpfso6pk3vf5df7625v6vawp2e 119 26 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 119 27 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 119 28 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 119 29 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 30 i i NNP work_zpfso6pk3vf5df7625v6vawp2e 119 31 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 119 32 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 119 33 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 34 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 119 35 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 119 36 · · NFP work_zpfso6pk3vf5df7625v6vawp2e 119 37 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 38 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 119 39 Based Based NNP work_zpfso6pk3vf5df7625v6vawp2e 119 40 on on IN work_zpfso6pk3vf5df7625v6vawp2e 119 41 the the DT work_zpfso6pk3vf5df7625v6vawp2e 119 42 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 119 43 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 44 the the DT work_zpfso6pk3vf5df7625v6vawp2e 119 45 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 119 46 matrices matrix NNS work_zpfso6pk3vf5df7625v6vawp2e 119 47 Q Q NNP work_zpfso6pk3vf5df7625v6vawp2e 119 48 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 119 49 generated generate VBN work_zpfso6pk3vf5df7625v6vawp2e 119 50 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 119 51 any any DT work_zpfso6pk3vf5df7625v6vawp2e 119 52 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 119 53 width width NN work_zpfso6pk3vf5df7625v6vawp2e 119 54 on on IN work_zpfso6pk3vf5df7625v6vawp2e 119 55 the the DT work_zpfso6pk3vf5df7625v6vawp2e 119 56 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 119 57 point point NN work_zpfso6pk3vf5df7625v6vawp2e 119 58 on on IN work_zpfso6pk3vf5df7625v6vawp2e 119 59 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 119 60 0.2,2 0.2,2 NN work_zpfso6pk3vf5df7625v6vawp2e 119 61 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 119 62 , , , work_zpfso6pk3vf5df7625v6vawp2e 119 63 with with IN work_zpfso6pk3vf5df7625v6vawp2e 119 64 a a DT work_zpfso6pk3vf5df7625v6vawp2e 119 65 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 119 66 width width NN work_zpfso6pk3vf5df7625v6vawp2e 119 67 of of IN work_zpfso6pk3vf5df7625v6vawp2e 119 68 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 119 69 . . . work_zpfso6pk3vf5df7625v6vawp2e 120 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 120 2 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 120 3 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 120 4 gradi- gradi- FW work_zpfso6pk3vf5df7625v6vawp2e 120 5 ent ent NNP work_zpfso6pk3vf5df7625v6vawp2e 120 6 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 120 7 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 120 8 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 120 9 to to TO work_zpfso6pk3vf5df7625v6vawp2e 120 10 minimize minimize VB work_zpfso6pk3vf5df7625v6vawp2e 120 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 120 12 negative negative JJ work_zpfso6pk3vf5df7625v6vawp2e 120 13 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 120 14 for for IN work_zpfso6pk3vf5df7625v6vawp2e 120 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 120 16 range range NN work_zpfso6pk3vf5df7625v6vawp2e 120 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 120 18 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 120 19 widths width NNS work_zpfso6pk3vf5df7625v6vawp2e 120 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 121 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 121 2 result result NN work_zpfso6pk3vf5df7625v6vawp2e 121 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 121 4 log log NN work_zpfso6pk3vf5df7625v6vawp2e 121 5 F(θ f(θ NN work_zpfso6pk3vf5df7625v6vawp2e 121 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 121 7 versus versus IN work_zpfso6pk3vf5df7625v6vawp2e 121 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 121 9 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 121 10 width width NN work_zpfso6pk3vf5df7625v6vawp2e 121 11 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 121 12 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 121 13 in in IN work_zpfso6pk3vf5df7625v6vawp2e 121 14 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 121 15 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 121 16 . . . work_zpfso6pk3vf5df7625v6vawp2e 122 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 122 2 convergence convergence NN work_zpfso6pk3vf5df7625v6vawp2e 122 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 122 4 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 122 5 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 122 6 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 122 7 algorithm algorithm VBP work_zpfso6pk3vf5df7625v6vawp2e 122 8 on on IN work_zpfso6pk3vf5df7625v6vawp2e 122 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 122 10 sphere sphere JJ work_zpfso6pk3vf5df7625v6vawp2e 122 11 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 122 12 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 122 13 on on IN work_zpfso6pk3vf5df7625v6vawp2e 122 14 the the DT work_zpfso6pk3vf5df7625v6vawp2e 122 15 optimal optimal JJ work_zpfso6pk3vf5df7625v6vawp2e 122 16 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 122 17 width width NN work_zpfso6pk3vf5df7625v6vawp2e 122 18 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 122 19 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 122 20 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 122 21 in in IN work_zpfso6pk3vf5df7625v6vawp2e 122 22 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 122 23 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 122 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 122 25 showing show VBG work_zpfso6pk3vf5df7625v6vawp2e 122 26 that that IN work_zpfso6pk3vf5df7625v6vawp2e 122 27 the the DT work_zpfso6pk3vf5df7625v6vawp2e 122 28 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 122 29 can can MD work_zpfso6pk3vf5df7625v6vawp2e 122 30 converge converge VB work_zpfso6pk3vf5df7625v6vawp2e 122 31 rapidly rapidly RB work_zpfso6pk3vf5df7625v6vawp2e 122 32 . . . work_zpfso6pk3vf5df7625v6vawp2e 123 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 123 2 performance performance NN work_zpfso6pk3vf5df7625v6vawp2e 123 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 123 4 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 123 5 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 123 6 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 123 7 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 123 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 123 9 Figure Figure NNP work_zpfso6pk3vf5df7625v6vawp2e 123 10 6(a),(b)&(c 6(a),(b)&(c CD work_zpfso6pk3vf5df7625v6vawp2e 123 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 123 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 123 13 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 123 14 plots plot VBZ work_zpfso6pk3vf5df7625v6vawp2e 123 15 ψ ψ CD work_zpfso6pk3vf5df7625v6vawp2e 123 16 2(x 2(x CD work_zpfso6pk3vf5df7625v6vawp2e 123 17 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 123 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 123 19 the the DT work_zpfso6pk3vf5df7625v6vawp2e 123 20 true true JJ work_zpfso6pk3vf5df7625v6vawp2e 123 21 density density NN work_zpfso6pk3vf5df7625v6vawp2e 123 22 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 123 23 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 123 24 , , , work_zpfso6pk3vf5df7625v6vawp2e 123 25 and and CC work_zpfso6pk3vf5df7625v6vawp2e 123 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 123 27 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 123 28 error error NN work_zpfso6pk3vf5df7625v6vawp2e 123 29 e(x e(x NNP work_zpfso6pk3vf5df7625v6vawp2e 123 30 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 123 31 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 123 32 ψ(x)2 ψ(x)2 NN work_zpfso6pk3vf5df7625v6vawp2e 123 33 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 123 34 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 123 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 123 36 respectively respectively RB work_zpfso6pk3vf5df7625v6vawp2e 123 37 over over IN work_zpfso6pk3vf5df7625v6vawp2e 123 38 a a DT work_zpfso6pk3vf5df7625v6vawp2e 123 39 41×41 41×41 CD work_zpfso6pk3vf5df7625v6vawp2e 123 40 meshed mesh VBN work_zpfso6pk3vf5df7625v6vawp2e 123 41 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 123 42 , , , work_zpfso6pk3vf5df7625v6vawp2e 123 43 with with IN work_zpfso6pk3vf5df7625v6vawp2e 123 44 a a DT work_zpfso6pk3vf5df7625v6vawp2e 123 45 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 123 46 size size NN work_zpfso6pk3vf5df7625v6vawp2e 123 47 of of IN work_zpfso6pk3vf5df7625v6vawp2e 123 48 0.2 0.2 CD work_zpfso6pk3vf5df7625v6vawp2e 123 49 , , , work_zpfso6pk3vf5df7625v6vawp2e 123 50 ranging range VBG work_zpfso6pk3vf5df7625v6vawp2e 123 51 from from IN work_zpfso6pk3vf5df7625v6vawp2e 123 52 -4 -4 NNP work_zpfso6pk3vf5df7625v6vawp2e 123 53 to to IN work_zpfso6pk3vf5df7625v6vawp2e 123 54 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 123 55 for for IN work_zpfso6pk3vf5df7625v6vawp2e 123 56 both both CC work_zpfso6pk3vf5df7625v6vawp2e 123 57 x1 x1 NN work_zpfso6pk3vf5df7625v6vawp2e 123 58 and and CC work_zpfso6pk3vf5df7625v6vawp2e 123 59 x2 x2 NNP work_zpfso6pk3vf5df7625v6vawp2e 123 60 . . . work_zpfso6pk3vf5df7625v6vawp2e 124 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 124 2 experiment experiment NN work_zpfso6pk3vf5df7625v6vawp2e 124 3 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 124 4 repeated repeat VBN work_zpfso6pk3vf5df7625v6vawp2e 124 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 124 6 100 100 CD work_zpfso6pk3vf5df7625v6vawp2e 124 7 different different JJ work_zpfso6pk3vf5df7625v6vawp2e 124 8 random random JJ work_zpfso6pk3vf5df7625v6vawp2e 124 9 runs run NNS work_zpfso6pk3vf5df7625v6vawp2e 124 10 in in IN work_zpfso6pk3vf5df7625v6vawp2e 124 11 order order NN work_zpfso6pk3vf5df7625v6vawp2e 124 12 to to IN work_zpfso6pk3vf5df7625v6vawp2e 124 13 com- com- NN work_zpfso6pk3vf5df7625v6vawp2e 124 14 pare pare VB work_zpfso6pk3vf5df7625v6vawp2e 124 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 124 16 performance performance NN work_zpfso6pk3vf5df7625v6vawp2e 124 17 of of IN work_zpfso6pk3vf5df7625v6vawp2e 124 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 124 19 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 124 20 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 124 21 with with IN work_zpfso6pk3vf5df7625v6vawp2e 124 22 the the DT work_zpfso6pk3vf5df7625v6vawp2e 124 23 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 124 24 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 124 25 model model NN work_zpfso6pk3vf5df7625v6vawp2e 124 26 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 124 27 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 124 28 and and CC work_zpfso6pk3vf5df7625v6vawp2e 124 29 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 124 30 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 124 31 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 124 32 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 124 33 10 10 CD work_zpfso6pk3vf5df7625v6vawp2e 124 34 15 15 CD work_zpfso6pk3vf5df7625v6vawp2e 124 35 20 20 CD work_zpfso6pk3vf5df7625v6vawp2e 124 36 25 25 CD work_zpfso6pk3vf5df7625v6vawp2e 124 37 30 30 CD work_zpfso6pk3vf5df7625v6vawp2e 124 38 1500 1500 CD work_zpfso6pk3vf5df7625v6vawp2e 124 39 1550 1550 CD work_zpfso6pk3vf5df7625v6vawp2e 124 40 1600 1600 CD work_zpfso6pk3vf5df7625v6vawp2e 124 41 1650 1650 CD work_zpfso6pk3vf5df7625v6vawp2e 124 42 1700 1700 CD work_zpfso6pk3vf5df7625v6vawp2e 124 43 1750 1750 CD work_zpfso6pk3vf5df7625v6vawp2e 124 44 Iterations Iterations NNPS work_zpfso6pk3vf5df7625v6vawp2e 124 45 lo lo NNP work_zpfso6pk3vf5df7625v6vawp2e 124 46 g g NNP work_zpfso6pk3vf5df7625v6vawp2e 124 47 F F NNP work_zpfso6pk3vf5df7625v6vawp2e 124 48 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 124 49 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 124 50 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 124 51 Fig Fig NNP work_zpfso6pk3vf5df7625v6vawp2e 124 52 . . . work_zpfso6pk3vf5df7625v6vawp2e 125 1 4 4 LS work_zpfso6pk3vf5df7625v6vawp2e 125 2 log(F(θ log(f(θ XX work_zpfso6pk3vf5df7625v6vawp2e 125 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 125 4 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 125 5 versus versus IN work_zpfso6pk3vf5df7625v6vawp2e 125 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 125 7 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 125 8 width width NN work_zpfso6pk3vf5df7625v6vawp2e 125 9 for for IN work_zpfso6pk3vf5df7625v6vawp2e 125 10 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 125 11 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 125 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 126 1 0.2 0.2 CD work_zpfso6pk3vf5df7625v6vawp2e 126 2 0.4 0.4 CD work_zpfso6pk3vf5df7625v6vawp2e 126 3 0.6 0.6 CD work_zpfso6pk3vf5df7625v6vawp2e 126 4 0.8 0.8 CD work_zpfso6pk3vf5df7625v6vawp2e 126 5 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 126 6 1.2 1.2 CD work_zpfso6pk3vf5df7625v6vawp2e 126 7 1.4 1.4 CD work_zpfso6pk3vf5df7625v6vawp2e 126 8 1.6 1.6 CD work_zpfso6pk3vf5df7625v6vawp2e 126 9 1.8 1.8 CD work_zpfso6pk3vf5df7625v6vawp2e 126 10 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 126 11 3000 3000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 12 4000 4000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 13 5000 5000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 14 6000 6000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 15 7000 7000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 16 8000 8000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 17 9000 9000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 18 10000 10000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 19 11000 11000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 20 12000 12000 CD work_zpfso6pk3vf5df7625v6vawp2e 126 21 σ σ NN work_zpfso6pk3vf5df7625v6vawp2e 126 22 V V NNP work_zpfso6pk3vf5df7625v6vawp2e 126 23 a a NN work_zpfso6pk3vf5df7625v6vawp2e 126 24 lu lu NN work_zpfso6pk3vf5df7625v6vawp2e 126 25 e e NNP work_zpfso6pk3vf5df7625v6vawp2e 126 26 o o NNP work_zpfso6pk3vf5df7625v6vawp2e 126 27 f f NNP work_zpfso6pk3vf5df7625v6vawp2e 126 28 m m NNP work_zpfso6pk3vf5df7625v6vawp2e 126 29 in in IN work_zpfso6pk3vf5df7625v6vawp2e 126 30 i -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 126 31 m be VBP work_zpfso6pk3vf5df7625v6vawp2e 126 32 a a DT work_zpfso6pk3vf5df7625v6vawp2e 126 33 l l NN work_zpfso6pk3vf5df7625v6vawp2e 126 34 o o NN work_zpfso6pk3vf5df7625v6vawp2e 126 35 f f NNP work_zpfso6pk3vf5df7625v6vawp2e 126 36 F F NNP work_zpfso6pk3vf5df7625v6vawp2e 126 37 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 126 38 θ θ NNP work_zpfso6pk3vf5df7625v6vawp2e 126 39 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 126 40 Fig Fig NNP work_zpfso6pk3vf5df7625v6vawp2e 126 41 . . . work_zpfso6pk3vf5df7625v6vawp2e 127 1 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 127 2 Convergence Convergence NNP work_zpfso6pk3vf5df7625v6vawp2e 127 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 127 4 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 127 5 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 127 6 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 127 7 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 127 8 for for IN work_zpfso6pk3vf5df7625v6vawp2e 127 9 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 127 10 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 127 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 128 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 128 2 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 128 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 128 4 that that WDT work_zpfso6pk3vf5df7625v6vawp2e 128 5 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 128 6 fitted fit VBN work_zpfso6pk3vf5df7625v6vawp2e 128 7 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 128 8 the the DT work_zpfso6pk3vf5df7625v6vawp2e 128 9 EM em NN work_zpfso6pk3vf5df7625v6vawp2e 128 10 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 128 11 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 128 12 McLachlan McLachlan NNP work_zpfso6pk3vf5df7625v6vawp2e 128 13 and and CC work_zpfso6pk3vf5df7625v6vawp2e 128 14 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 128 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 128 16 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 128 17 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 128 18 . . . work_zpfso6pk3vf5df7625v6vawp2e 129 1 A a DT work_zpfso6pk3vf5df7625v6vawp2e 129 2 sepa- sepa- NN work_zpfso6pk3vf5df7625v6vawp2e 129 3 rate rate NN work_zpfso6pk3vf5df7625v6vawp2e 129 4 test test NN work_zpfso6pk3vf5df7625v6vawp2e 129 5 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 129 6 set set NN work_zpfso6pk3vf5df7625v6vawp2e 129 7 of of IN work_zpfso6pk3vf5df7625v6vawp2e 129 8 Ntest Ntest NNP work_zpfso6pk3vf5df7625v6vawp2e 129 9 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 129 10 1681 1681 CD work_zpfso6pk3vf5df7625v6vawp2e 129 11 was be VBD work_zpfso6pk3vf5df7625v6vawp2e 129 12 generated generate VBN work_zpfso6pk3vf5df7625v6vawp2e 129 13 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 129 14 a a DT work_zpfso6pk3vf5df7625v6vawp2e 129 15 41×41 41×41 CD work_zpfso6pk3vf5df7625v6vawp2e 129 16 meshed mesh VBN work_zpfso6pk3vf5df7625v6vawp2e 129 17 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 129 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 129 19 with with IN work_zpfso6pk3vf5df7625v6vawp2e 129 20 a a DT work_zpfso6pk3vf5df7625v6vawp2e 129 21 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 129 22 size size NN work_zpfso6pk3vf5df7625v6vawp2e 129 23 of of IN work_zpfso6pk3vf5df7625v6vawp2e 129 24 0.2 0.2 CD work_zpfso6pk3vf5df7625v6vawp2e 129 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 129 26 ranging range VBG work_zpfso6pk3vf5df7625v6vawp2e 129 27 from from IN work_zpfso6pk3vf5df7625v6vawp2e 129 28 -4 -4 NNP work_zpfso6pk3vf5df7625v6vawp2e 129 29 to to IN work_zpfso6pk3vf5df7625v6vawp2e 129 30 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 129 31 for for IN work_zpfso6pk3vf5df7625v6vawp2e 129 32 both both CC work_zpfso6pk3vf5df7625v6vawp2e 129 33 x1 x1 NN work_zpfso6pk3vf5df7625v6vawp2e 129 34 and and CC work_zpfso6pk3vf5df7625v6vawp2e 129 35 x2 x2 NNP work_zpfso6pk3vf5df7625v6vawp2e 129 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 130 1 These these DT work_zpfso6pk3vf5df7625v6vawp2e 130 2 points point NNS work_zpfso6pk3vf5df7625v6vawp2e 130 3 were be VBD work_zpfso6pk3vf5df7625v6vawp2e 130 4 used use VBN work_zpfso6pk3vf5df7625v6vawp2e 130 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 130 6 evaluation evaluation NN work_zpfso6pk3vf5df7625v6vawp2e 130 7 according accord VBG work_zpfso6pk3vf5df7625v6vawp2e 130 8 to to IN work_zpfso6pk3vf5df7625v6vawp2e 130 9 L1 L1 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 10 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 130 11 { { -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 12 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 13 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 130 14 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 130 15 Ntest Ntest NNP work_zpfso6pk3vf5df7625v6vawp2e 130 16 k=1 k=1 VBD work_zpfso6pk3vf5df7625v6vawp2e 130 17 |p(xk)−ψ |p(xk)−ψ , work_zpfso6pk3vf5df7625v6vawp2e 130 18 2(xk)| 2(xk)| CD work_zpfso6pk3vf5df7625v6vawp2e 130 19 Proposed propose VBD work_zpfso6pk3vf5df7625v6vawp2e 130 20 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 21 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 130 22 ∑ ∑ . work_zpfso6pk3vf5df7625v6vawp2e 130 23 Ntest ntest RBS work_zpfso6pk3vf5df7625v6vawp2e 130 24 k=1 k=1 VBN work_zpfso6pk3vf5df7625v6vawp2e 130 25 |p(xk)− |p(xk)− DT work_zpfso6pk3vf5df7625v6vawp2e 130 26 pGMM(xk)| pgmm(xk)| NN work_zpfso6pk3vf5df7625v6vawp2e 130 27 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 130 28 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 29 28 28 CD work_zpfso6pk3vf5df7625v6vawp2e 130 30 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 31 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 130 32 the the DT work_zpfso6pk3vf5df7625v6vawp2e 130 33 Square Square NNP work_zpfso6pk3vf5df7625v6vawp2e 130 34 Root Root NNP work_zpfso6pk3vf5df7625v6vawp2e 130 35 of of IN work_zpfso6pk3vf5df7625v6vawp2e 130 36 Probability Probability NNP work_zpfso6pk3vf5df7625v6vawp2e 130 37 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 130 38 Function Function NNP work_zpfso6pk3vf5df7625v6vawp2e 130 39 on on IN work_zpfso6pk3vf5df7625v6vawp2e 130 40 Riemannian Riemannian NNP work_zpfso6pk3vf5df7625v6vawp2e 130 41 Manifold Manifold NNP work_zpfso6pk3vf5df7625v6vawp2e 130 42 −4 −4 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 43 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 44 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 45 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 46 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 47 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 48 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 49 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 50 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 51 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 130 52 0.02 0.02 CD work_zpfso6pk3vf5df7625v6vawp2e 130 53 0.04 0.04 CD work_zpfso6pk3vf5df7625v6vawp2e 130 54 0.06 0.06 CD work_zpfso6pk3vf5df7625v6vawp2e 130 55 0.08 0.08 CD work_zpfso6pk3vf5df7625v6vawp2e 130 56 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 57 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 130 58 2x 2x CD work_zpfso6pk3vf5df7625v6vawp2e 130 59 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 60 p p NN work_zpfso6pk3vf5df7625v6vawp2e 130 61 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 62 x x NN work_zpfso6pk3vf5df7625v6vawp2e 130 63 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 64 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 65 a a DT work_zpfso6pk3vf5df7625v6vawp2e 130 66 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 67 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 68 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 69 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 70 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 71 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 72 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 73 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 74 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 75 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 76 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 130 77 0.05 0.05 CD work_zpfso6pk3vf5df7625v6vawp2e 130 78 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 79 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 130 80 2x 2x CD work_zpfso6pk3vf5df7625v6vawp2e 130 81 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 82 ψ ψ NNS work_zpfso6pk3vf5df7625v6vawp2e 130 83 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 84 x x NN work_zpfso6pk3vf5df7625v6vawp2e 130 85 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 86 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 87 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 88 b b NN work_zpfso6pk3vf5df7625v6vawp2e 130 89 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 90 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 91 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 92 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 93 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 94 4 4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 95 −4 −4 CD work_zpfso6pk3vf5df7625v6vawp2e 130 96 −2 −2 NNP work_zpfso6pk3vf5df7625v6vawp2e 130 97 0 0 CD work_zpfso6pk3vf5df7625v6vawp2e 130 98 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 130 99 40 40 CD work_zpfso6pk3vf5df7625v6vawp2e 130 100 0.05 0.05 CD work_zpfso6pk3vf5df7625v6vawp2e 130 101 0.1 0.1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 102 x x SYM work_zpfso6pk3vf5df7625v6vawp2e 130 103 2x 2x CD work_zpfso6pk3vf5df7625v6vawp2e 130 104 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 130 105 e e NNS work_zpfso6pk3vf5df7625v6vawp2e 130 106 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 107 x x NN work_zpfso6pk3vf5df7625v6vawp2e 130 108 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 109 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 130 110 c c NN work_zpfso6pk3vf5df7625v6vawp2e 130 111 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 130 112 Fig fig NN work_zpfso6pk3vf5df7625v6vawp2e 130 113 . . . work_zpfso6pk3vf5df7625v6vawp2e 131 1 6 6 CD work_zpfso6pk3vf5df7625v6vawp2e 131 2 The the DT work_zpfso6pk3vf5df7625v6vawp2e 131 3 result result NN work_zpfso6pk3vf5df7625v6vawp2e 131 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 131 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 131 6 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 131 7 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 131 8 for for IN work_zpfso6pk3vf5df7625v6vawp2e 131 9 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 131 10 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 131 11 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 131 12 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 131 13 a a LS work_zpfso6pk3vf5df7625v6vawp2e 131 14 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 131 15 The the DT work_zpfso6pk3vf5df7625v6vawp2e 131 16 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 131 17 pdf pdf NN work_zpfso6pk3vf5df7625v6vawp2e 131 18 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 131 19 ψ(x)2 ψ(x)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 131 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 131 21 b b NNP work_zpfso6pk3vf5df7625v6vawp2e 131 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 131 23 The the DT work_zpfso6pk3vf5df7625v6vawp2e 131 24 true true JJ work_zpfso6pk3vf5df7625v6vawp2e 131 25 pdf pdf NN work_zpfso6pk3vf5df7625v6vawp2e 131 26 p(x p(x NNP work_zpfso6pk3vf5df7625v6vawp2e 131 27 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 131 28 ; ; : work_zpfso6pk3vf5df7625v6vawp2e 131 29 and and CC work_zpfso6pk3vf5df7625v6vawp2e 131 30 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 131 31 c)The c)the JJ work_zpfso6pk3vf5df7625v6vawp2e 131 32 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 131 33 error error NN work_zpfso6pk3vf5df7625v6vawp2e 131 34 e(x e(x NNP work_zpfso6pk3vf5df7625v6vawp2e 131 35 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 131 36 . . . work_zpfso6pk3vf5df7625v6vawp2e 132 1 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 132 2 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 132 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 132 4 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 132 5 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 132 6 where where WRB work_zpfso6pk3vf5df7625v6vawp2e 132 7 p̂GMM p̂GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 132 8 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 132 9 the the DT work_zpfso6pk3vf5df7625v6vawp2e 132 10 resultant resultant JJ work_zpfso6pk3vf5df7625v6vawp2e 132 11 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 132 12 model model NN work_zpfso6pk3vf5df7625v6vawp2e 132 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 132 14 with with IN work_zpfso6pk3vf5df7625v6vawp2e 132 15 the the DT work_zpfso6pk3vf5df7625v6vawp2e 132 16 constraint constraint NN work_zpfso6pk3vf5df7625v6vawp2e 132 17 that that IN work_zpfso6pk3vf5df7625v6vawp2e 132 18 the the DT work_zpfso6pk3vf5df7625v6vawp2e 132 19 covariance covariance NN work_zpfso6pk3vf5df7625v6vawp2e 132 20 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 132 21 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 132 22 diagonal diagonal JJ work_zpfso6pk3vf5df7625v6vawp2e 132 23 . . . work_zpfso6pk3vf5df7625v6vawp2e 133 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 133 2 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 133 3 model model NN work_zpfso6pk3vf5df7625v6vawp2e 133 4 fitting fitting NN work_zpfso6pk3vf5df7625v6vawp2e 133 5 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 133 6 implemented implement VBN work_zpfso6pk3vf5df7625v6vawp2e 133 7 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 133 8 Matlab Matlab NNP work_zpfso6pk3vf5df7625v6vawp2e 133 9 command command NN work_zpfso6pk3vf5df7625v6vawp2e 133 10 gmdistribution gmdistribution NN work_zpfso6pk3vf5df7625v6vawp2e 133 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 134 1 f f LS work_zpfso6pk3vf5df7625v6vawp2e 134 2 it.m it.m XX work_zpfso6pk3vf5df7625v6vawp2e 134 3 with with IN work_zpfso6pk3vf5df7625v6vawp2e 134 4 two two CD work_zpfso6pk3vf5df7625v6vawp2e 134 5 mixtures mixture NNS work_zpfso6pk3vf5df7625v6vawp2e 134 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 135 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 135 2 results result NNS work_zpfso6pk3vf5df7625v6vawp2e 135 3 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 135 4 as as IN work_zpfso6pk3vf5df7625v6vawp2e 135 5 shown show VBN work_zpfso6pk3vf5df7625v6vawp2e 135 6 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 135 7 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 135 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 135 9 showing show VBG work_zpfso6pk3vf5df7625v6vawp2e 135 10 that that IN work_zpfso6pk3vf5df7625v6vawp2e 135 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 135 12 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 135 13 method method NN work_zpfso6pk3vf5df7625v6vawp2e 135 14 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 135 15 better well JJR work_zpfso6pk3vf5df7625v6vawp2e 135 16 than than IN work_zpfso6pk3vf5df7625v6vawp2e 135 17 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 135 18 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 135 19 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 135 20 with with IN work_zpfso6pk3vf5df7625v6vawp2e 135 21 two two CD work_zpfso6pk3vf5df7625v6vawp2e 135 22 mixtures mixture NNS work_zpfso6pk3vf5df7625v6vawp2e 135 23 . . . work_zpfso6pk3vf5df7625v6vawp2e 136 1 Table table NN work_zpfso6pk3vf5df7625v6vawp2e 136 2 3 3 CD work_zpfso6pk3vf5df7625v6vawp2e 136 3 Performance Performance NNP work_zpfso6pk3vf5df7625v6vawp2e 136 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 136 5 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 136 6 density density NN work_zpfso6pk3vf5df7625v6vawp2e 136 7 estimator estimator NN work_zpfso6pk3vf5df7625v6vawp2e 136 8 in in IN work_zpfso6pk3vf5df7625v6vawp2e 136 9 comparison comparison NN work_zpfso6pk3vf5df7625v6vawp2e 136 10 with with IN work_zpfso6pk3vf5df7625v6vawp2e 136 11 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 136 12 model model NN work_zpfso6pk3vf5df7625v6vawp2e 136 13 for for IN work_zpfso6pk3vf5df7625v6vawp2e 136 14 Example Example NNP work_zpfso6pk3vf5df7625v6vawp2e 136 15 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 136 16 . . . work_zpfso6pk3vf5df7625v6vawp2e 137 1 Method Method NNP work_zpfso6pk3vf5df7625v6vawp2e 137 2 L1 L1 NNP work_zpfso6pk3vf5df7625v6vawp2e 137 3 test test NN work_zpfso6pk3vf5df7625v6vawp2e 137 4 error error NN work_zpfso6pk3vf5df7625v6vawp2e 137 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 137 6 mean mean NNP work_zpfso6pk3vf5df7625v6vawp2e 137 7 ± ± NNP work_zpfso6pk3vf5df7625v6vawp2e 137 8 STD STD NNP work_zpfso6pk3vf5df7625v6vawp2e 137 9 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 137 10 Proposed Proposed NNP work_zpfso6pk3vf5df7625v6vawp2e 137 11 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 137 12 1.7±0.2)×10−3 1.7±0.2)×10−3 CD work_zpfso6pk3vf5df7625v6vawp2e 137 13 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 137 14 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 137 15 2.9±0.1)×10−3 2.9±0.1)×10−3 CD work_zpfso6pk3vf5df7625v6vawp2e 137 16 5 5 CD work_zpfso6pk3vf5df7625v6vawp2e 137 17 Conclusions Conclusions NNPS work_zpfso6pk3vf5df7625v6vawp2e 137 18 In in IN work_zpfso6pk3vf5df7625v6vawp2e 137 19 this this DT work_zpfso6pk3vf5df7625v6vawp2e 137 20 paper paper NN work_zpfso6pk3vf5df7625v6vawp2e 137 21 a a DT work_zpfso6pk3vf5df7625v6vawp2e 137 22 new new JJ work_zpfso6pk3vf5df7625v6vawp2e 137 23 method method NN work_zpfso6pk3vf5df7625v6vawp2e 137 24 has have VBZ work_zpfso6pk3vf5df7625v6vawp2e 137 25 been be VBN work_zpfso6pk3vf5df7625v6vawp2e 137 26 introduced introduce VBN work_zpfso6pk3vf5df7625v6vawp2e 137 27 to to TO work_zpfso6pk3vf5df7625v6vawp2e 137 28 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 137 29 the the DT work_zpfso6pk3vf5df7625v6vawp2e 137 30 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 137 31 root root NN work_zpfso6pk3vf5df7625v6vawp2e 137 32 of of IN work_zpfso6pk3vf5df7625v6vawp2e 137 33 prob- prob- JJ work_zpfso6pk3vf5df7625v6vawp2e 137 34 ability ability NN work_zpfso6pk3vf5df7625v6vawp2e 137 35 density density NN work_zpfso6pk3vf5df7625v6vawp2e 137 36 function function NN work_zpfso6pk3vf5df7625v6vawp2e 137 37 from from IN work_zpfso6pk3vf5df7625v6vawp2e 137 38 observational observational JJ work_zpfso6pk3vf5df7625v6vawp2e 137 39 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 137 40 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 137 41 maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 137 42 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 137 43 . . . work_zpfso6pk3vf5df7625v6vawp2e 138 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 138 2 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 138 3 model model NN work_zpfso6pk3vf5df7625v6vawp2e 138 4 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 138 5 in in IN work_zpfso6pk3vf5df7625v6vawp2e 138 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 138 7 form form NN work_zpfso6pk3vf5df7625v6vawp2e 138 8 of of IN work_zpfso6pk3vf5df7625v6vawp2e 138 9 a a DT work_zpfso6pk3vf5df7625v6vawp2e 138 10 linear linear JJ work_zpfso6pk3vf5df7625v6vawp2e 138 11 combination combination NN work_zpfso6pk3vf5df7625v6vawp2e 138 12 of of IN work_zpfso6pk3vf5df7625v6vawp2e 138 13 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 138 14 kernels kernel NNS work_zpfso6pk3vf5df7625v6vawp2e 138 15 . . . work_zpfso6pk3vf5df7625v6vawp2e 139 1 Incor- incor- RB work_zpfso6pk3vf5df7625v6vawp2e 139 2 porating porate VBG work_zpfso6pk3vf5df7625v6vawp2e 139 3 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 4 k k NNP work_zpfso6pk3vf5df7625v6vawp2e 139 5 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 139 6 means means NN work_zpfso6pk3vf5df7625v6vawp2e 139 7 clustering cluster VBG work_zpfso6pk3vf5df7625v6vawp2e 139 8 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 139 9 to to TO work_zpfso6pk3vf5df7625v6vawp2e 139 10 determine determine VB work_zpfso6pk3vf5df7625v6vawp2e 139 11 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 12 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 139 13 center center NN work_zpfso6pk3vf5df7625v6vawp2e 139 14 as as RB work_zpfso6pk3vf5df7625v6vawp2e 139 15 well well RB work_zpfso6pk3vf5df7625v6vawp2e 139 16 as as IN work_zpfso6pk3vf5df7625v6vawp2e 139 17 a a DT work_zpfso6pk3vf5df7625v6vawp2e 139 18 grid grid NN work_zpfso6pk3vf5df7625v6vawp2e 139 19 search search NN work_zpfso6pk3vf5df7625v6vawp2e 139 20 to to TO work_zpfso6pk3vf5df7625v6vawp2e 139 21 determine determine VB work_zpfso6pk3vf5df7625v6vawp2e 139 22 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 23 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 139 24 width width NN work_zpfso6pk3vf5df7625v6vawp2e 139 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 139 26 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 27 model model NN work_zpfso6pk3vf5df7625v6vawp2e 139 28 parameters parameter NNS work_zpfso6pk3vf5df7625v6vawp2e 139 29 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 139 30 then then RB work_zpfso6pk3vf5df7625v6vawp2e 139 31 esti- esti- RB work_zpfso6pk3vf5df7625v6vawp2e 139 32 mated mate VBN work_zpfso6pk3vf5df7625v6vawp2e 139 33 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 139 34 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 35 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 139 36 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 139 37 on on IN work_zpfso6pk3vf5df7625v6vawp2e 139 38 the the DT work_zpfso6pk3vf5df7625v6vawp2e 139 39 sphere sphere NN work_zpfso6pk3vf5df7625v6vawp2e 139 40 . . . work_zpfso6pk3vf5df7625v6vawp2e 140 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 140 2 first first JJ work_zpfso6pk3vf5df7625v6vawp2e 140 3 order order NN work_zpfso6pk3vf5df7625v6vawp2e 140 4 Riemannian riemannian JJ work_zpfso6pk3vf5df7625v6vawp2e 140 5 geometry geometry NN work_zpfso6pk3vf5df7625v6vawp2e 140 6 of of IN work_zpfso6pk3vf5df7625v6vawp2e 140 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 140 8 sphere sphere NNP work_zpfso6pk3vf5df7625v6vawp2e 140 9 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 140 10 and and CC work_zpfso6pk3vf5df7625v6vawp2e 140 11 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 140 12 transport transport NN work_zpfso6pk3vf5df7625v6vawp2e 140 13 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 140 14 explored explore VBN work_zpfso6pk3vf5df7625v6vawp2e 140 15 . . . work_zpfso6pk3vf5df7625v6vawp2e 141 1 Two two CD work_zpfso6pk3vf5df7625v6vawp2e 141 2 illustra- illustra- NN work_zpfso6pk3vf5df7625v6vawp2e 141 3 tive tive JJ work_zpfso6pk3vf5df7625v6vawp2e 141 4 examples example NNS work_zpfso6pk3vf5df7625v6vawp2e 141 5 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 141 6 employed employ VBN work_zpfso6pk3vf5df7625v6vawp2e 141 7 to to TO work_zpfso6pk3vf5df7625v6vawp2e 141 8 demonstrate demonstrate VB work_zpfso6pk3vf5df7625v6vawp2e 141 9 that that IN work_zpfso6pk3vf5df7625v6vawp2e 141 10 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 141 11 obtained obtain VBN work_zpfso6pk3vf5df7625v6vawp2e 141 12 by by IN work_zpfso6pk3vf5df7625v6vawp2e 141 13 the the DT work_zpfso6pk3vf5df7625v6vawp2e 141 14 proposed propose VBN work_zpfso6pk3vf5df7625v6vawp2e 141 15 approach approach NN work_zpfso6pk3vf5df7625v6vawp2e 141 16 are be VBP work_zpfso6pk3vf5df7625v6vawp2e 141 17 comparable comparable JJ work_zpfso6pk3vf5df7625v6vawp2e 141 18 with with IN work_zpfso6pk3vf5df7625v6vawp2e 141 19 the the DT work_zpfso6pk3vf5df7625v6vawp2e 141 20 GMM GMM NNP work_zpfso6pk3vf5df7625v6vawp2e 141 21 model model NN work_zpfso6pk3vf5df7625v6vawp2e 141 22 fitted fit VBD work_zpfso6pk3vf5df7625v6vawp2e 141 23 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 141 24 EM EM NNP work_zpfso6pk3vf5df7625v6vawp2e 141 25 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 141 26 . . . work_zpfso6pk3vf5df7625v6vawp2e 142 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 142 2 this this DT work_zpfso6pk3vf5df7625v6vawp2e 142 3 research research NN work_zpfso6pk3vf5df7625v6vawp2e 142 4 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 142 5 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 142 6 included include VBN work_zpfso6pk3vf5df7625v6vawp2e 142 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 142 8 well well RB work_zpfso6pk3vf5df7625v6vawp2e 142 9 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 142 10 known know VBN work_zpfso6pk3vf5df7625v6vawp2e 142 11 k k NN work_zpfso6pk3vf5df7625v6vawp2e 142 12 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 142 13 means means NN work_zpfso6pk3vf5df7625v6vawp2e 142 14 clustering clustering NN work_zpfso6pk3vf5df7625v6vawp2e 142 15 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 142 16 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 142 17 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 142 18 based base VBN work_zpfso6pk3vf5df7625v6vawp2e 142 19 on on IN work_zpfso6pk3vf5df7625v6vawp2e 142 20 a a DT work_zpfso6pk3vf5df7625v6vawp2e 142 21 predetermined predetermined JJ work_zpfso6pk3vf5df7625v6vawp2e 142 22 number number NN work_zpfso6pk3vf5df7625v6vawp2e 142 23 M m NN work_zpfso6pk3vf5df7625v6vawp2e 142 24 centers center NNS work_zpfso6pk3vf5df7625v6vawp2e 142 25 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 142 26 may may MD work_zpfso6pk3vf5df7625v6vawp2e 142 27 not not RB work_zpfso6pk3vf5df7625v6vawp2e 142 28 optimal optimal VB work_zpfso6pk3vf5df7625v6vawp2e 142 29 . . . work_zpfso6pk3vf5df7625v6vawp2e 143 1 The the DT work_zpfso6pk3vf5df7625v6vawp2e 143 2 choice choice NN work_zpfso6pk3vf5df7625v6vawp2e 143 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 143 4 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 143 5 is be VBZ work_zpfso6pk3vf5df7625v6vawp2e 143 6 generally generally RB work_zpfso6pk3vf5df7625v6vawp2e 143 7 dependent dependent JJ work_zpfso6pk3vf5df7625v6vawp2e 143 8 on on IN work_zpfso6pk3vf5df7625v6vawp2e 143 9 applications application NNS work_zpfso6pk3vf5df7625v6vawp2e 143 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 143 11 and and CC work_zpfso6pk3vf5df7625v6vawp2e 143 12 for for IN work_zpfso6pk3vf5df7625v6vawp2e 143 13 k k NN work_zpfso6pk3vf5df7625v6vawp2e 143 14 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 143 15 means mean NNS work_zpfso6pk3vf5df7625v6vawp2e 143 16 clustering cluster VBG work_zpfso6pk3vf5df7625v6vawp2e 143 17 al- al- JJ work_zpfso6pk3vf5df7625v6vawp2e 143 18 gorithm gorithm NN work_zpfso6pk3vf5df7625v6vawp2e 143 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 143 20 M M NNP work_zpfso6pk3vf5df7625v6vawp2e 143 21 should should MD work_zpfso6pk3vf5df7625v6vawp2e 143 22 be be VB work_zpfso6pk3vf5df7625v6vawp2e 143 23 set set VBN work_zpfso6pk3vf5df7625v6vawp2e 143 24 sufficiently sufficiently RB work_zpfso6pk3vf5df7625v6vawp2e 143 25 large large JJ work_zpfso6pk3vf5df7625v6vawp2e 143 26 to to TO work_zpfso6pk3vf5df7625v6vawp2e 143 27 perform perform VB work_zpfso6pk3vf5df7625v6vawp2e 143 28 well well RB work_zpfso6pk3vf5df7625v6vawp2e 143 29 . . . work_zpfso6pk3vf5df7625v6vawp2e 144 1 Future future JJ work_zpfso6pk3vf5df7625v6vawp2e 144 2 research research NN work_zpfso6pk3vf5df7625v6vawp2e 144 3 will will MD work_zpfso6pk3vf5df7625v6vawp2e 144 4 be be VB work_zpfso6pk3vf5df7625v6vawp2e 144 5 focused focus VBN work_zpfso6pk3vf5df7625v6vawp2e 144 6 on on IN work_zpfso6pk3vf5df7625v6vawp2e 144 7 model model NN work_zpfso6pk3vf5df7625v6vawp2e 144 8 structure structure NN work_zpfso6pk3vf5df7625v6vawp2e 144 9 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 144 10 so so IN work_zpfso6pk3vf5df7625v6vawp2e 144 11 that that IN work_zpfso6pk3vf5df7625v6vawp2e 144 12 the the DT work_zpfso6pk3vf5df7625v6vawp2e 144 13 model model NN work_zpfso6pk3vf5df7625v6vawp2e 144 14 size size NN work_zpfso6pk3vf5df7625v6vawp2e 144 15 can can MD work_zpfso6pk3vf5df7625v6vawp2e 144 16 be be VB work_zpfso6pk3vf5df7625v6vawp2e 144 17 learnt learn VBN work_zpfso6pk3vf5df7625v6vawp2e 144 18 from from IN work_zpfso6pk3vf5df7625v6vawp2e 144 19 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 144 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 145 1 Appendix Appendix NNP work_zpfso6pk3vf5df7625v6vawp2e 145 2 A a DT work_zpfso6pk3vf5df7625v6vawp2e 145 3 Let let NN work_zpfso6pk3vf5df7625v6vawp2e 145 4 x x NN work_zpfso6pk3vf5df7625v6vawp2e 145 5 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 145 6 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 7 x1, x1, NNP work_zpfso6pk3vf5df7625v6vawp2e 145 8 ... ... : work_zpfso6pk3vf5df7625v6vawp2e 145 9 xm]T xm]T NNP work_zpfso6pk3vf5df7625v6vawp2e 145 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 11 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 145 12 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 145 13 References References NNPS work_zpfso6pk3vf5df7625v6vawp2e 145 14 qi qi NNP work_zpfso6pk3vf5df7625v6vawp2e 145 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 16 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 17 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 145 18 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 145 19 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 20 2π 2π CD work_zpfso6pk3vf5df7625v6vawp2e 145 21 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 145 22 2)m 2)m CD work_zpfso6pk3vf5df7625v6vawp2e 145 23 ∫ ∫ CD work_zpfso6pk3vf5df7625v6vawp2e 145 24 ... ... NFP work_zpfso6pk3vf5df7625v6vawp2e 145 25 ∫ ∫ NFP work_zpfso6pk3vf5df7625v6vawp2e 145 26 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 27 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 28 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 29 ∥x−ci∥2 ∥x−ci∥2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 30 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 31 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 32 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 33 ∥x−c ∥x−c IN work_zpfso6pk3vf5df7625v6vawp2e 145 34 j∥2 j∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 145 35 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 36 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 37 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 38 dx1 dx1 NN work_zpfso6pk3vf5df7625v6vawp2e 145 39 ... ... : work_zpfso6pk3vf5df7625v6vawp2e 145 40 dxm dxm NN work_zpfso6pk3vf5df7625v6vawp2e 145 41 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 145 42 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 145 43 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 44 2π 2π CD work_zpfso6pk3vf5df7625v6vawp2e 145 45 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 145 46 2)m 2)m CD work_zpfso6pk3vf5df7625v6vawp2e 145 47 m m NNP work_zpfso6pk3vf5df7625v6vawp2e 145 48 ∏ ∏ NNP work_zpfso6pk3vf5df7625v6vawp2e 145 49 l=1 l=1 JJ work_zpfso6pk3vf5df7625v6vawp2e 145 50 ∫ ∫ : work_zpfso6pk3vf5df7625v6vawp2e 145 51 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 52 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 53 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 54 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 55 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 56 −ci −ci CD work_zpfso6pk3vf5df7625v6vawp2e 145 57 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 58 l)2 l)2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 59 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 60 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 61 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 62 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 63 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 64 −c −c NNP work_zpfso6pk3vf5df7625v6vawp2e 145 65 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 66 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 67 l)2 l)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 145 68 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 69 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 70 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 71 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 72 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 73 29 29 CD work_zpfso6pk3vf5df7625v6vawp2e 145 74 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 75 in in IN work_zpfso6pk3vf5df7625v6vawp2e 145 76 which which WDT work_zpfso6pk3vf5df7625v6vawp2e 145 77 ∫ ∫ CD work_zpfso6pk3vf5df7625v6vawp2e 145 78 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 79 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 80 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 81 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 82 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 83 −ci −ci CD work_zpfso6pk3vf5df7625v6vawp2e 145 84 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 85 l)2 l)2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 86 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 87 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 88 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 89 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 90 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 91 −c −c NNP work_zpfso6pk3vf5df7625v6vawp2e 145 92 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 93 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 94 l)2 l)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 145 95 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 96 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 97 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 98 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 99 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 145 100 ∫ ∫ NFP work_zpfso6pk3vf5df7625v6vawp2e 145 101 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 102 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 103 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 104 x2l x2l NNP work_zpfso6pk3vf5df7625v6vawp2e 145 105 −(ci −(ci NN work_zpfso6pk3vf5df7625v6vawp2e 145 106 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 107 l l NN work_zpfso6pk3vf5df7625v6vawp2e 145 108 + + CC work_zpfso6pk3vf5df7625v6vawp2e 145 109 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 110 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 111 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 112 l)xl l)xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 113 + + NFP work_zpfso6pk3vf5df7625v6vawp2e 145 114 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 115 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 116 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 117 i i NN work_zpfso6pk3vf5df7625v6vawp2e 145 118 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 119 l l NN work_zpfso6pk3vf5df7625v6vawp2e 145 120 + + CC work_zpfso6pk3vf5df7625v6vawp2e 145 121 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 122 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 123 j j CD work_zpfso6pk3vf5df7625v6vawp2e 145 124 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 125 l)/2 l)/2 NNP work_zpfso6pk3vf5df7625v6vawp2e 145 126 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 145 127 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 128 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 129 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 130 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 145 131 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 132 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 133 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 134 c2j c2j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 135 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 136 l l NN work_zpfso6pk3vf5df7625v6vawp2e 145 137 + + CC work_zpfso6pk3vf5df7625v6vawp2e 145 138 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 139 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 140 i i NN work_zpfso6pk3vf5df7625v6vawp2e 145 141 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 142 l l NN work_zpfso6pk3vf5df7625v6vawp2e 145 143 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 144 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 145 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 146 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 145 147 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 148 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 145 149 + + CC work_zpfso6pk3vf5df7625v6vawp2e 145 150 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 151 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 152 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 153 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 145 154 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 155 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 156 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 157 σ σ SYM work_zpfso6pk3vf5df7625v6vawp2e 145 158 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 159 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 160 × × NFP work_zpfso6pk3vf5df7625v6vawp2e 145 161 ∫ ∫ NFP work_zpfso6pk3vf5df7625v6vawp2e 145 162 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 163 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 164 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 165 [ [ -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 166 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 167 −(ci −(ci NNP work_zpfso6pk3vf5df7625v6vawp2e 145 168 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 169 l l NN work_zpfso6pk3vf5df7625v6vawp2e 145 170 + + CC work_zpfso6pk3vf5df7625v6vawp2e 145 171 c c NN work_zpfso6pk3vf5df7625v6vawp2e 145 172 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 145 173 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 174 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 145 175 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 176 ] ] -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 177 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 178 σ σ SYM work_zpfso6pk3vf5df7625v6vawp2e 145 179 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 180 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 181 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 182 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 183 30 30 CD work_zpfso6pk3vf5df7625v6vawp2e 145 184 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 185 By by IN work_zpfso6pk3vf5df7625v6vawp2e 145 186 making make VBG work_zpfso6pk3vf5df7625v6vawp2e 145 187 use use NN work_zpfso6pk3vf5df7625v6vawp2e 145 188 of of IN work_zpfso6pk3vf5df7625v6vawp2e 145 189 ∫ ∫ CD work_zpfso6pk3vf5df7625v6vawp2e 145 190 1√ 1√ CD work_zpfso6pk3vf5df7625v6vawp2e 145 191 2π 2π CD work_zpfso6pk3vf5df7625v6vawp2e 145 192 σ σ NN work_zpfso6pk3vf5df7625v6vawp2e 145 193 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 194 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 145 195 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 196 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 145 197 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 145 198 xl−c xl−c NNP work_zpfso6pk3vf5df7625v6vawp2e 145 199 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 200 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 201 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 145 202 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 145 203 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 145 204 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 145 205 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 145 206 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 145 207 , , , work_zpfso6pk3vf5df7625v6vawp2e 145 208 i.e. i.e. FW work_zpfso6pk3vf5df7625v6vawp2e 146 1 Gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 146 2 density density NN work_zpfso6pk3vf5df7625v6vawp2e 146 3 integrates integrate VBZ work_zpfso6pk3vf5df7625v6vawp2e 146 4 to to IN work_zpfso6pk3vf5df7625v6vawp2e 146 5 one one CD work_zpfso6pk3vf5df7625v6vawp2e 146 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 7 we -PRON- PRP work_zpfso6pk3vf5df7625v6vawp2e 146 8 have have VBP work_zpfso6pk3vf5df7625v6vawp2e 146 9 ∫ ∫ NFP work_zpfso6pk3vf5df7625v6vawp2e 146 10 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 146 11 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 12 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 13 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 14 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 146 15 −ci −ci CD work_zpfso6pk3vf5df7625v6vawp2e 146 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 17 l)2 l)2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 18 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 146 19 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 20 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 21 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 22 xl xl NNP work_zpfso6pk3vf5df7625v6vawp2e 146 23 −c −c NNP work_zpfso6pk3vf5df7625v6vawp2e 146 24 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 25 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 26 l)2 l)2 NNP work_zpfso6pk3vf5df7625v6vawp2e 146 27 2σ 2σ CD work_zpfso6pk3vf5df7625v6vawp2e 146 28 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 29 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 30 dxl dxl NNP work_zpfso6pk3vf5df7625v6vawp2e 146 31 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 146 32 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 146 33 π π NN work_zpfso6pk3vf5df7625v6vawp2e 146 34 σ σ NN work_zpfso6pk3vf5df7625v6vawp2e 146 35 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 36 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 146 37 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 38 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 39 c2j c2j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 40 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 41 l l NN work_zpfso6pk3vf5df7625v6vawp2e 146 42 + + CC work_zpfso6pk3vf5df7625v6vawp2e 146 43 c c NN work_zpfso6pk3vf5df7625v6vawp2e 146 44 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 45 i i NN work_zpfso6pk3vf5df7625v6vawp2e 146 46 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 47 l l NN work_zpfso6pk3vf5df7625v6vawp2e 146 48 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 49 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 50 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 51 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 146 52 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 53 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 146 54 + + CC work_zpfso6pk3vf5df7625v6vawp2e 146 55 c c NN work_zpfso6pk3vf5df7625v6vawp2e 146 56 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 57 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 58 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 146 59 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 60 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 61 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 62 σ σ SYM work_zpfso6pk3vf5df7625v6vawp2e 146 63 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 64 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 65 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 146 66 √ √ NNP work_zpfso6pk3vf5df7625v6vawp2e 146 67 π π NN work_zpfso6pk3vf5df7625v6vawp2e 146 68 σ σ NN work_zpfso6pk3vf5df7625v6vawp2e 146 69 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 70 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 146 71 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 72 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 73 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 74 c c NNP work_zpfso6pk3vf5df7625v6vawp2e 146 75 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 76 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 77 l l NNP work_zpfso6pk3vf5df7625v6vawp2e 146 78 −ci −ci CD work_zpfso6pk3vf5df7625v6vawp2e 146 79 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 80 l)2 l)2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 81 4σ 4σ NN work_zpfso6pk3vf5df7625v6vawp2e 146 82 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 83 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 84 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 85 31 31 LS work_zpfso6pk3vf5df7625v6vawp2e 146 86 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 87 Hence hence RB work_zpfso6pk3vf5df7625v6vawp2e 146 88 qi qi NNP work_zpfso6pk3vf5df7625v6vawp2e 146 89 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 90 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 91 = = SYM work_zpfso6pk3vf5df7625v6vawp2e 146 92 1 1 CD work_zpfso6pk3vf5df7625v6vawp2e 146 93 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 94 4π 4π NNP work_zpfso6pk3vf5df7625v6vawp2e 146 95 σ σ NNP work_zpfso6pk3vf5df7625v6vawp2e 146 96 2)m 2)m CD work_zpfso6pk3vf5df7625v6vawp2e 146 97 exp exp NN work_zpfso6pk3vf5df7625v6vawp2e 146 98 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 99 − − NNP work_zpfso6pk3vf5df7625v6vawp2e 146 100 ∥ci ∥ci RB work_zpfso6pk3vf5df7625v6vawp2e 146 101 −c −c NNP work_zpfso6pk3vf5df7625v6vawp2e 146 102 j∥2 j∥2 NNP work_zpfso6pk3vf5df7625v6vawp2e 146 103 4σ 4σ NNP work_zpfso6pk3vf5df7625v6vawp2e 146 104 2 2 CD work_zpfso6pk3vf5df7625v6vawp2e 146 105 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 106 = = NFP work_zpfso6pk3vf5df7625v6vawp2e 146 107 K√2σ k√2σ ADD work_zpfso6pk3vf5df7625v6vawp2e 146 108 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 109 ci ci NNP work_zpfso6pk3vf5df7625v6vawp2e 146 110 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 111 c c NNP work_zpfso6pk3vf5df7625v6vawp2e 146 112 j j NNP work_zpfso6pk3vf5df7625v6vawp2e 146 113 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 114 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 115 32 32 CD work_zpfso6pk3vf5df7625v6vawp2e 146 116 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 117 References References NNPS work_zpfso6pk3vf5df7625v6vawp2e 146 118 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 146 119 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 120 P.-A. P.-A. NNP work_zpfso6pk3vf5df7625v6vawp2e 146 121 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 122 Mahony Mahony NNP work_zpfso6pk3vf5df7625v6vawp2e 146 123 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 124 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 146 125 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 126 and and CC work_zpfso6pk3vf5df7625v6vawp2e 146 127 Sepulchre Sepulchre NNP work_zpfso6pk3vf5df7625v6vawp2e 146 128 , , , work_zpfso6pk3vf5df7625v6vawp2e 146 129 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 146 130 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 146 131 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 146 132 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 146 133 . . . work_zpfso6pk3vf5df7625v6vawp2e 147 1 Optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 147 2 Algorithms Algorithms NNP work_zpfso6pk3vf5df7625v6vawp2e 147 3 on on IN work_zpfso6pk3vf5df7625v6vawp2e 147 4 Matrix Matrix NNP work_zpfso6pk3vf5df7625v6vawp2e 147 5 Manifolds Manifolds NNP work_zpfso6pk3vf5df7625v6vawp2e 147 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 148 1 Princeton Princeton NNP work_zpfso6pk3vf5df7625v6vawp2e 148 2 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 148 3 Press Press NNP work_zpfso6pk3vf5df7625v6vawp2e 148 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 149 1 Bilmes Bilmes NNP work_zpfso6pk3vf5df7625v6vawp2e 149 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 149 3 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 150 1 A. A. NNP work_zpfso6pk3vf5df7625v6vawp2e 151 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 151 2 1998 1998 CD work_zpfso6pk3vf5df7625v6vawp2e 151 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 151 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 152 1 A a DT work_zpfso6pk3vf5df7625v6vawp2e 152 2 gentle gentle JJ work_zpfso6pk3vf5df7625v6vawp2e 152 3 tutorial tutorial NN work_zpfso6pk3vf5df7625v6vawp2e 152 4 of of IN work_zpfso6pk3vf5df7625v6vawp2e 152 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 152 6 em -PRON- NNP work_zpfso6pk3vf5df7625v6vawp2e 152 7 algorithm algorithm NNP work_zpfso6pk3vf5df7625v6vawp2e 152 8 and and CC work_zpfso6pk3vf5df7625v6vawp2e 152 9 its -PRON- PRP$ work_zpfso6pk3vf5df7625v6vawp2e 152 10 application application NN work_zpfso6pk3vf5df7625v6vawp2e 152 11 to to TO work_zpfso6pk3vf5df7625v6vawp2e 152 12 parameter parameter VB work_zpfso6pk3vf5df7625v6vawp2e 152 13 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 152 14 for for IN work_zpfso6pk3vf5df7625v6vawp2e 152 15 gaussian gaussian JJ work_zpfso6pk3vf5df7625v6vawp2e 152 16 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 152 17 and and CC work_zpfso6pk3vf5df7625v6vawp2e 152 18 hidden hide VBN work_zpfso6pk3vf5df7625v6vawp2e 152 19 markov markov NN work_zpfso6pk3vf5df7625v6vawp2e 152 20 models model NNS work_zpfso6pk3vf5df7625v6vawp2e 152 21 . . . work_zpfso6pk3vf5df7625v6vawp2e 153 1 Tech- Tech- NNP work_zpfso6pk3vf5df7625v6vawp2e 153 2 nical nical JJ work_zpfso6pk3vf5df7625v6vawp2e 153 3 Report Report NNP work_zpfso6pk3vf5df7625v6vawp2e 153 4 ICSI ICSI NNP work_zpfso6pk3vf5df7625v6vawp2e 153 5 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 153 6 TR-97 TR-97 NNP work_zpfso6pk3vf5df7625v6vawp2e 153 7 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 153 8 021 021 NNP work_zpfso6pk3vf5df7625v6vawp2e 153 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 153 10 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 153 11 of of IN work_zpfso6pk3vf5df7625v6vawp2e 153 12 California California NNP work_zpfso6pk3vf5df7625v6vawp2e 153 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 153 14 Berkeley Berkeley NNP work_zpfso6pk3vf5df7625v6vawp2e 153 15 . . . work_zpfso6pk3vf5df7625v6vawp2e 154 1 Boumal Boumal NNP work_zpfso6pk3vf5df7625v6vawp2e 154 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 3 N. N. NNP work_zpfso6pk3vf5df7625v6vawp2e 154 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 5 Mishra Mishra NNP work_zpfso6pk3vf5df7625v6vawp2e 154 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 7 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 154 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 9 Absil Absil NNP work_zpfso6pk3vf5df7625v6vawp2e 154 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 11 P.-A. P.-A. NNP work_zpfso6pk3vf5df7625v6vawp2e 154 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 13 and and CC work_zpfso6pk3vf5df7625v6vawp2e 154 14 Sepulchre Sepulchre NNP work_zpfso6pk3vf5df7625v6vawp2e 154 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 154 16 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 154 17 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 154 18 2014 2014 CD work_zpfso6pk3vf5df7625v6vawp2e 154 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 154 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 155 1 Manopt Manopt NNP work_zpfso6pk3vf5df7625v6vawp2e 155 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 155 3 a a DT work_zpfso6pk3vf5df7625v6vawp2e 155 4 mat- mat- JJ work_zpfso6pk3vf5df7625v6vawp2e 155 5 lab lab NN work_zpfso6pk3vf5df7625v6vawp2e 155 6 toolbox toolbox NN work_zpfso6pk3vf5df7625v6vawp2e 155 7 for for IN work_zpfso6pk3vf5df7625v6vawp2e 155 8 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 155 9 on on IN work_zpfso6pk3vf5df7625v6vawp2e 155 10 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 155 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 156 1 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 157 1 Machine Machine NNP work_zpfso6pk3vf5df7625v6vawp2e 157 2 Learning Learning NNP work_zpfso6pk3vf5df7625v6vawp2e 157 3 research research NN work_zpfso6pk3vf5df7625v6vawp2e 157 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 157 5 15:1455–1459 15:1455–1459 NN work_zpfso6pk3vf5df7625v6vawp2e 157 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 158 1 Xia Xia NNP work_zpfso6pk3vf5df7625v6vawp2e 158 2 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 158 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 158 4 Junbin Junbin NNP work_zpfso6pk3vf5df7625v6vawp2e 158 5 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 158 6 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 158 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 158 8 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 158 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 158 10 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 158 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 158 12 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 158 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 158 14 and and CC work_zpfso6pk3vf5df7625v6vawp2e 158 15 Harris Harris NNP work_zpfso6pk3vf5df7625v6vawp2e 158 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 158 17 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 158 18 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 159 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 159 2 2004a 2004a CD work_zpfso6pk3vf5df7625v6vawp2e 159 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 159 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 160 1 Sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 160 2 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 160 3 density density NN work_zpfso6pk3vf5df7625v6vawp2e 160 4 construction construction NN work_zpfso6pk3vf5df7625v6vawp2e 160 5 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 160 6 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 160 7 forward forward JJ work_zpfso6pk3vf5df7625v6vawp2e 160 8 regression regression NN work_zpfso6pk3vf5df7625v6vawp2e 160 9 with with IN work_zpfso6pk3vf5df7625v6vawp2e 160 10 leave leave VB work_zpfso6pk3vf5df7625v6vawp2e 160 11 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 160 12 one one CD work_zpfso6pk3vf5df7625v6vawp2e 160 13 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 160 14 out out RP work_zpfso6pk3vf5df7625v6vawp2e 160 15 test test NN work_zpfso6pk3vf5df7625v6vawp2e 160 16 score score NN work_zpfso6pk3vf5df7625v6vawp2e 160 17 and and CC work_zpfso6pk3vf5df7625v6vawp2e 160 18 local local JJ work_zpfso6pk3vf5df7625v6vawp2e 160 19 regularization regularization NN work_zpfso6pk3vf5df7625v6vawp2e 160 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 161 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 161 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 161 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 162 1 on on IN work_zpfso6pk3vf5df7625v6vawp2e 162 2 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 162 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 162 4 Man Man NNP work_zpfso6pk3vf5df7625v6vawp2e 162 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 162 6 Cybernetics Cybernetics NNP work_zpfso6pk3vf5df7625v6vawp2e 162 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 162 8 Part Part NNP work_zpfso6pk3vf5df7625v6vawp2e 162 9 B B NNP work_zpfso6pk3vf5df7625v6vawp2e 162 10 : : : work_zpfso6pk3vf5df7625v6vawp2e 162 11 Cy- Cy- NNP work_zpfso6pk3vf5df7625v6vawp2e 162 12 bernetics bernetic NNS work_zpfso6pk3vf5df7625v6vawp2e 162 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 162 14 34(4):1708–1717 34(4):1708–1717 CD work_zpfso6pk3vf5df7625v6vawp2e 162 15 . . . work_zpfso6pk3vf5df7625v6vawp2e 163 1 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 163 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 163 3 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 163 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 163 5 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 163 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 163 7 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 163 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 163 9 and and CC work_zpfso6pk3vf5df7625v6vawp2e 163 10 Harris Harris NNP work_zpfso6pk3vf5df7625v6vawp2e 163 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 163 12 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 163 13 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 164 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 164 2 2008 2008 CD work_zpfso6pk3vf5df7625v6vawp2e 164 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 164 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 165 1 An an DT work_zpfso6pk3vf5df7625v6vawp2e 165 2 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 165 3 forward forward JJ work_zpfso6pk3vf5df7625v6vawp2e 165 4 regression regression NN work_zpfso6pk3vf5df7625v6vawp2e 165 5 tech- tech- NN work_zpfso6pk3vf5df7625v6vawp2e 165 6 nique nique NN work_zpfso6pk3vf5df7625v6vawp2e 165 7 for for IN work_zpfso6pk3vf5df7625v6vawp2e 165 8 sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 165 9 kernel kernel NN work_zpfso6pk3vf5df7625v6vawp2e 165 10 density density NN work_zpfso6pk3vf5df7625v6vawp2e 165 11 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 165 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 166 1 Neurocomputing neurocomputing JJ work_zpfso6pk3vf5df7625v6vawp2e 166 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 166 3 71(4 71(4 CD work_zpfso6pk3vf5df7625v6vawp2e 166 4 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 166 5 6):925 6):925 NNP work_zpfso6pk3vf5df7625v6vawp2e 166 6 – – : work_zpfso6pk3vf5df7625v6vawp2e 166 7 943 943 CD work_zpfso6pk3vf5df7625v6vawp2e 166 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 167 1 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 167 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 167 3 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 167 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 167 5 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 167 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 167 7 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 167 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 167 9 and and CC work_zpfso6pk3vf5df7625v6vawp2e 167 10 Harris Harris NNP work_zpfso6pk3vf5df7625v6vawp2e 167 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 167 12 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 167 13 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 168 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 168 2 2010 2010 CD work_zpfso6pk3vf5df7625v6vawp2e 168 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 168 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 169 1 Particle particle NN work_zpfso6pk3vf5df7625v6vawp2e 169 2 swarm swarm JJ work_zpfso6pk3vf5df7625v6vawp2e 169 3 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 169 4 aided aid VBD work_zpfso6pk3vf5df7625v6vawp2e 169 5 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 169 6 forward forward IN work_zpfso6pk3vf5df7625v6vawp2e 169 7 regression regression NN work_zpfso6pk3vf5df7625v6vawp2e 169 8 for for IN work_zpfso6pk3vf5df7625v6vawp2e 169 9 unified unified JJ work_zpfso6pk3vf5df7625v6vawp2e 169 10 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 169 11 modelling modelling NN work_zpfso6pk3vf5df7625v6vawp2e 169 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 170 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 170 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 170 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 171 1 Evo- Evo- NNP work_zpfso6pk3vf5df7625v6vawp2e 171 2 lutionary lutionary JJ work_zpfso6pk3vf5df7625v6vawp2e 171 3 Computation Computation NNP work_zpfso6pk3vf5df7625v6vawp2e 171 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 171 5 14:477–499 14:477–499 CD work_zpfso6pk3vf5df7625v6vawp2e 171 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 172 1 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 172 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 3 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 5 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 172 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 7 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 9 Harris Harris NNP work_zpfso6pk3vf5df7625v6vawp2e 172 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 11 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 12 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 14 and and CC work_zpfso6pk3vf5df7625v6vawp2e 172 15 Sharkey Sharkey NNP work_zpfso6pk3vf5df7625v6vawp2e 172 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 172 17 P. P. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 18 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 172 19 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 172 20 2004b 2004b CD work_zpfso6pk3vf5df7625v6vawp2e 172 21 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 172 22 . . . work_zpfso6pk3vf5df7625v6vawp2e 173 1 Sparse Sparse NNP work_zpfso6pk3vf5df7625v6vawp2e 173 2 modelling modelling NN work_zpfso6pk3vf5df7625v6vawp2e 173 3 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 173 4 orthogonal orthogonal JJ work_zpfso6pk3vf5df7625v6vawp2e 173 5 forward forward JJ work_zpfso6pk3vf5df7625v6vawp2e 173 6 regression regression NN work_zpfso6pk3vf5df7625v6vawp2e 173 7 with with IN work_zpfso6pk3vf5df7625v6vawp2e 173 8 PRESS PRESS NNP work_zpfso6pk3vf5df7625v6vawp2e 173 9 statistic statistic NN work_zpfso6pk3vf5df7625v6vawp2e 173 10 and and CC work_zpfso6pk3vf5df7625v6vawp2e 173 11 regulariza- regulariza- JJ work_zpfso6pk3vf5df7625v6vawp2e 173 12 tion tion NN work_zpfso6pk3vf5df7625v6vawp2e 173 13 . . . work_zpfso6pk3vf5df7625v6vawp2e 174 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 174 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 174 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 175 1 on on IN work_zpfso6pk3vf5df7625v6vawp2e 175 2 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 175 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 175 4 Man Man NNP work_zpfso6pk3vf5df7625v6vawp2e 175 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 175 6 Cybernetics Cybernetics NNP work_zpfso6pk3vf5df7625v6vawp2e 175 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 175 8 Part Part NNP work_zpfso6pk3vf5df7625v6vawp2e 175 9 B B NNP work_zpfso6pk3vf5df7625v6vawp2e 175 10 : : : work_zpfso6pk3vf5df7625v6vawp2e 175 11 Cybernetics Cybernetics NNP work_zpfso6pk3vf5df7625v6vawp2e 175 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 175 13 34(2):898–911 34(2):898–911 CD work_zpfso6pk3vf5df7625v6vawp2e 175 14 . . . work_zpfso6pk3vf5df7625v6vawp2e 176 1 Choudhury choudhury NN work_zpfso6pk3vf5df7625v6vawp2e 176 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 176 3 A. a. NN work_zpfso6pk3vf5df7625v6vawp2e 177 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 177 2 2002 2002 CD work_zpfso6pk3vf5df7625v6vawp2e 177 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 177 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 178 1 Fast fast JJ work_zpfso6pk3vf5df7625v6vawp2e 178 2 Machine machine NN work_zpfso6pk3vf5df7625v6vawp2e 178 3 Learning Learning NNP work_zpfso6pk3vf5df7625v6vawp2e 178 4 Algorithms Algorithms NNP work_zpfso6pk3vf5df7625v6vawp2e 178 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 178 6 Large Large NNP work_zpfso6pk3vf5df7625v6vawp2e 178 7 Data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 178 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 179 1 PhD phd NN work_zpfso6pk3vf5df7625v6vawp2e 179 2 thesis thesis NN work_zpfso6pk3vf5df7625v6vawp2e 179 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 179 4 School School NNP work_zpfso6pk3vf5df7625v6vawp2e 179 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 179 6 Engineering Engineering NNP work_zpfso6pk3vf5df7625v6vawp2e 179 7 Sciences Sciences NNPS work_zpfso6pk3vf5df7625v6vawp2e 179 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 179 9 University University NNP work_zpfso6pk3vf5df7625v6vawp2e 179 10 of of IN work_zpfso6pk3vf5df7625v6vawp2e 179 11 Southampton Southampton NNP work_zpfso6pk3vf5df7625v6vawp2e 179 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 180 1 Dempster dempster NN work_zpfso6pk3vf5df7625v6vawp2e 180 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 180 3 A. a. NN work_zpfso6pk3vf5df7625v6vawp2e 180 4 P. P. NNP work_zpfso6pk3vf5df7625v6vawp2e 180 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 180 6 Laird Laird NNP work_zpfso6pk3vf5df7625v6vawp2e 180 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 180 8 N. N. NNP work_zpfso6pk3vf5df7625v6vawp2e 180 9 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 180 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 180 11 and and CC work_zpfso6pk3vf5df7625v6vawp2e 180 12 Rubin Rubin NNP work_zpfso6pk3vf5df7625v6vawp2e 180 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 180 14 D. D. NNP work_zpfso6pk3vf5df7625v6vawp2e 180 15 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 181 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 181 2 1977 1977 CD work_zpfso6pk3vf5df7625v6vawp2e 181 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 181 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 182 1 Maximum maximum JJ work_zpfso6pk3vf5df7625v6vawp2e 182 2 likelihood likelihood NN work_zpfso6pk3vf5df7625v6vawp2e 182 3 from from IN work_zpfso6pk3vf5df7625v6vawp2e 182 4 incomplete incomplete JJ work_zpfso6pk3vf5df7625v6vawp2e 182 5 data datum NNS work_zpfso6pk3vf5df7625v6vawp2e 182 6 via via IN work_zpfso6pk3vf5df7625v6vawp2e 182 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 182 8 EM EM NNP work_zpfso6pk3vf5df7625v6vawp2e 182 9 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 182 10 . . . work_zpfso6pk3vf5df7625v6vawp2e 183 1 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 183 2 Royal Royal NNP work_zpfso6pk3vf5df7625v6vawp2e 183 3 Statistical Statistical NNP work_zpfso6pk3vf5df7625v6vawp2e 183 4 Society Society NNP work_zpfso6pk3vf5df7625v6vawp2e 183 5 B B NNP work_zpfso6pk3vf5df7625v6vawp2e 183 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 183 7 39:1–38 39:1–38 CD work_zpfso6pk3vf5df7625v6vawp2e 183 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 184 1 Duda Duda NNP work_zpfso6pk3vf5df7625v6vawp2e 184 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 184 3 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 184 4 O. O. NNP work_zpfso6pk3vf5df7625v6vawp2e 184 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 184 6 Hart Hart NNP work_zpfso6pk3vf5df7625v6vawp2e 184 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 184 8 P. P. NNP work_zpfso6pk3vf5df7625v6vawp2e 184 9 E. E. NNP work_zpfso6pk3vf5df7625v6vawp2e 184 10 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 184 11 1973 1973 CD work_zpfso6pk3vf5df7625v6vawp2e 184 12 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 184 13 . . . work_zpfso6pk3vf5df7625v6vawp2e 185 1 Pattern Pattern NNP work_zpfso6pk3vf5df7625v6vawp2e 185 2 Classification Classification NNP work_zpfso6pk3vf5df7625v6vawp2e 185 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 185 4 Scene Scene NNP work_zpfso6pk3vf5df7625v6vawp2e 185 5 Analysis Analysis NNP work_zpfso6pk3vf5df7625v6vawp2e 185 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 186 1 Wiley Wiley NNP work_zpfso6pk3vf5df7625v6vawp2e 186 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 186 3 New New NNP work_zpfso6pk3vf5df7625v6vawp2e 186 4 York York NNP work_zpfso6pk3vf5df7625v6vawp2e 186 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 186 6 1973 1973 CD work_zpfso6pk3vf5df7625v6vawp2e 186 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 187 1 Girolami Girolami NNP work_zpfso6pk3vf5df7625v6vawp2e 187 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 187 3 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 187 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 187 5 He He NNP work_zpfso6pk3vf5df7625v6vawp2e 187 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 187 7 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 187 8 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 187 9 2003 2003 CD work_zpfso6pk3vf5df7625v6vawp2e 187 10 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 187 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 188 1 Probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 188 2 density density NN work_zpfso6pk3vf5df7625v6vawp2e 188 3 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 188 4 from from IN work_zpfso6pk3vf5df7625v6vawp2e 188 5 optimally optimally RB work_zpfso6pk3vf5df7625v6vawp2e 188 6 condensed condense VBN work_zpfso6pk3vf5df7625v6vawp2e 188 7 data data NN work_zpfso6pk3vf5df7625v6vawp2e 188 8 samples sample NNS work_zpfso6pk3vf5df7625v6vawp2e 188 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 189 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 189 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 189 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 190 1 on on IN work_zpfso6pk3vf5df7625v6vawp2e 190 2 Pattern Pattern NNP work_zpfso6pk3vf5df7625v6vawp2e 190 3 Analysis Analysis NNP work_zpfso6pk3vf5df7625v6vawp2e 190 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 190 5 Machine Machine NNP work_zpfso6pk3vf5df7625v6vawp2e 190 6 In- In- NNP work_zpfso6pk3vf5df7625v6vawp2e 190 7 telligence telligence NN work_zpfso6pk3vf5df7625v6vawp2e 190 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 190 9 25(10):1253–1264 25(10):1253–1264 CD work_zpfso6pk3vf5df7625v6vawp2e 190 10 . . . work_zpfso6pk3vf5df7625v6vawp2e 191 1 Hager Hager NNP work_zpfso6pk3vf5df7625v6vawp2e 191 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 191 3 W. W. NNP work_zpfso6pk3vf5df7625v6vawp2e 191 4 W. W. NNP work_zpfso6pk3vf5df7625v6vawp2e 191 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 191 6 Zhang Zhang NNP work_zpfso6pk3vf5df7625v6vawp2e 191 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 191 8 H. H. NNP work_zpfso6pk3vf5df7625v6vawp2e 191 9 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 191 10 2006 2006 CD work_zpfso6pk3vf5df7625v6vawp2e 191 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 191 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 192 1 A a DT work_zpfso6pk3vf5df7625v6vawp2e 192 2 survey survey NN work_zpfso6pk3vf5df7625v6vawp2e 192 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 192 4 nonlinear nonlinear JJ work_zpfso6pk3vf5df7625v6vawp2e 192 5 conjugate conjugate NN work_zpfso6pk3vf5df7625v6vawp2e 192 6 gradient gradient NN work_zpfso6pk3vf5df7625v6vawp2e 192 7 methods method NNS work_zpfso6pk3vf5df7625v6vawp2e 192 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 193 1 Pacific Pacific NNP work_zpfso6pk3vf5df7625v6vawp2e 193 2 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 193 3 Optimization Optimization NNP work_zpfso6pk3vf5df7625v6vawp2e 193 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 193 5 2:35–58 2:35–58 CD work_zpfso6pk3vf5df7625v6vawp2e 193 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 194 1 Harandi Harandi NNP work_zpfso6pk3vf5df7625v6vawp2e 194 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 3 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 5 aqnd aqnd NN work_zpfso6pk3vf5df7625v6vawp2e 194 6 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 7 Shen Shen NNP work_zpfso6pk3vf5df7625v6vawp2e 194 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 9 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 10 H. H. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 12 Lovell Lovell NNP work_zpfso6pk3vf5df7625v6vawp2e 194 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 14 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 16 and and CC work_zpfso6pk3vf5df7625v6vawp2e 194 17 Sanderson Sanderson NNP work_zpfso6pk3vf5df7625v6vawp2e 194 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 194 19 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 194 20 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 194 21 2014 2014 CD work_zpfso6pk3vf5df7625v6vawp2e 194 22 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 194 23 . . . work_zpfso6pk3vf5df7625v6vawp2e 195 1 Extrin- Extrin- NNP work_zpfso6pk3vf5df7625v6vawp2e 195 2 sic sic NN work_zpfso6pk3vf5df7625v6vawp2e 195 3 methods method NNS work_zpfso6pk3vf5df7625v6vawp2e 195 4 for for IN work_zpfso6pk3vf5df7625v6vawp2e 195 5 coding code VBG work_zpfso6pk3vf5df7625v6vawp2e 195 6 and and CC work_zpfso6pk3vf5df7625v6vawp2e 195 7 dictionary dictionary JJ work_zpfso6pk3vf5df7625v6vawp2e 195 8 learning learning NN work_zpfso6pk3vf5df7625v6vawp2e 195 9 on on IN work_zpfso6pk3vf5df7625v6vawp2e 195 10 Grassmann Grassmann NNP work_zpfso6pk3vf5df7625v6vawp2e 195 11 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 195 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 196 1 arXiv:1401.8126 arXiv:1401.8126 NNP work_zpfso6pk3vf5df7625v6vawp2e 196 2 . . . work_zpfso6pk3vf5df7625v6vawp2e 197 1 Haykin Haykin NNP work_zpfso6pk3vf5df7625v6vawp2e 197 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 197 3 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 197 4 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 197 5 2009 2009 CD work_zpfso6pk3vf5df7625v6vawp2e 197 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 197 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 198 1 Neural Neural NNP work_zpfso6pk3vf5df7625v6vawp2e 198 2 Networks Networks NNPS work_zpfso6pk3vf5df7625v6vawp2e 198 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 198 4 Learning Learning NNP work_zpfso6pk3vf5df7625v6vawp2e 198 5 Machines Machines NNPS work_zpfso6pk3vf5df7625v6vawp2e 198 6 . . . work_zpfso6pk3vf5df7625v6vawp2e 199 1 Pearson Pearson NNP work_zpfso6pk3vf5df7625v6vawp2e 199 2 Education Education NNP work_zpfso6pk3vf5df7625v6vawp2e 199 3 Inc. Inc. NNP work_zpfso6pk3vf5df7625v6vawp2e 199 4 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 199 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 6 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 199 7 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 8 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 199 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 10 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 199 11 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 12 Qatawneh Qatawneh NNP work_zpfso6pk3vf5df7625v6vawp2e 199 13 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 14 A. a. NN work_zpfso6pk3vf5df7625v6vawp2e 199 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 16 Daqrouq Daqrouq NNP work_zpfso6pk3vf5df7625v6vawp2e 199 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 18 K. K. NNP work_zpfso6pk3vf5df7625v6vawp2e 199 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 20 Sheikh Sheikh NNP work_zpfso6pk3vf5df7625v6vawp2e 199 21 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 22 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 199 23 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 24 and and CC work_zpfso6pk3vf5df7625v6vawp2e 199 25 Morfeq Morfeq NNP work_zpfso6pk3vf5df7625v6vawp2e 199 26 , , , work_zpfso6pk3vf5df7625v6vawp2e 199 27 A. a. NN work_zpfso6pk3vf5df7625v6vawp2e 200 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 200 2 2013 2013 CD work_zpfso6pk3vf5df7625v6vawp2e 200 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 200 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 201 1 Sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 201 2 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 201 3 density density NN work_zpfso6pk3vf5df7625v6vawp2e 201 4 function function NN work_zpfso6pk3vf5df7625v6vawp2e 201 5 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 201 6 using use VBG work_zpfso6pk3vf5df7625v6vawp2e 201 7 the the DT work_zpfso6pk3vf5df7625v6vawp2e 201 8 minimum minimum JJ work_zpfso6pk3vf5df7625v6vawp2e 201 9 integrated integrate VBN work_zpfso6pk3vf5df7625v6vawp2e 201 10 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 201 11 error error NN work_zpfso6pk3vf5df7625v6vawp2e 201 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 202 1 Neurocomputing neurocomputing JJ work_zpfso6pk3vf5df7625v6vawp2e 202 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 202 3 115:122–129 115:122–129 CD work_zpfso6pk3vf5df7625v6vawp2e 202 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 203 1 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 203 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 3 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 203 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 5 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 203 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 7 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 203 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 9 Chen Chen NNP work_zpfso6pk3vf5df7625v6vawp2e 203 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 11 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 203 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 13 and and CC work_zpfso6pk3vf5df7625v6vawp2e 203 14 Zia Zia NNP work_zpfso6pk3vf5df7625v6vawp2e 203 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 203 16 T. T. NNP work_zpfso6pk3vf5df7625v6vawp2e 203 17 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 203 18 2015 2015 CD work_zpfso6pk3vf5df7625v6vawp2e 203 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 203 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 204 1 Sparse sparse JJ work_zpfso6pk3vf5df7625v6vawp2e 204 2 density density NN work_zpfso6pk3vf5df7625v6vawp2e 204 3 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 204 4 on on IN work_zpfso6pk3vf5df7625v6vawp2e 204 5 the the DT work_zpfso6pk3vf5df7625v6vawp2e 204 6 multinomial multinomial JJ work_zpfso6pk3vf5df7625v6vawp2e 204 7 manifold manifold NN work_zpfso6pk3vf5df7625v6vawp2e 204 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 205 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 205 2 Transactions transaction NNS work_zpfso6pk3vf5df7625v6vawp2e 205 3 on on IN work_zpfso6pk3vf5df7625v6vawp2e 205 4 Neural Neural NNP work_zpfso6pk3vf5df7625v6vawp2e 205 5 Networks Networks NNPS work_zpfso6pk3vf5df7625v6vawp2e 205 6 and and CC work_zpfso6pk3vf5df7625v6vawp2e 205 7 Learning Learning NNP work_zpfso6pk3vf5df7625v6vawp2e 205 8 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 205 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 205 10 26(11):2972–2977 26(11):2972–2977 CD work_zpfso6pk3vf5df7625v6vawp2e 205 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 206 1 Hong Hong NNP work_zpfso6pk3vf5df7625v6vawp2e 206 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 206 3 X. X. NNP work_zpfso6pk3vf5df7625v6vawp2e 206 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 206 5 Gao Gao NNP work_zpfso6pk3vf5df7625v6vawp2e 206 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 206 7 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 207 1 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 208 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 208 2 2016 2016 CD work_zpfso6pk3vf5df7625v6vawp2e 208 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 208 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 209 1 A a DT work_zpfso6pk3vf5df7625v6vawp2e 209 2 fast fast JJ work_zpfso6pk3vf5df7625v6vawp2e 209 3 algorithm algorithm NN work_zpfso6pk3vf5df7625v6vawp2e 209 4 to to TO work_zpfso6pk3vf5df7625v6vawp2e 209 5 estimate estimate VB work_zpfso6pk3vf5df7625v6vawp2e 209 6 the the DT work_zpfso6pk3vf5df7625v6vawp2e 209 7 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 209 8 root root NN work_zpfso6pk3vf5df7625v6vawp2e 209 9 of of IN work_zpfso6pk3vf5df7625v6vawp2e 209 10 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 209 11 density density NN work_zpfso6pk3vf5df7625v6vawp2e 209 12 function function NN work_zpfso6pk3vf5df7625v6vawp2e 209 13 . . . work_zpfso6pk3vf5df7625v6vawp2e 210 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 210 2 Proceeding Proceeding NNP work_zpfso6pk3vf5df7625v6vawp2e 210 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 210 4 AI-2016 ai-2016 JJ work_zpfso6pk3vf5df7625v6vawp2e 210 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 210 6 Thirty thirty CD work_zpfso6pk3vf5df7625v6vawp2e 210 7 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 210 8 sixth sixth JJ work_zpfso6pk3vf5df7625v6vawp2e 210 9 SGAI SGAI NNP work_zpfso6pk3vf5df7625v6vawp2e 210 10 International International NNP work_zpfso6pk3vf5df7625v6vawp2e 210 11 Conference Conference NNP work_zpfso6pk3vf5df7625v6vawp2e 210 12 on on IN work_zpfso6pk3vf5df7625v6vawp2e 210 13 Artificial Artificial NNP work_zpfso6pk3vf5df7625v6vawp2e 210 14 Intelligence Intelligence NNP work_zpfso6pk3vf5df7625v6vawp2e 210 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 210 16 Cambridge Cambridge NNP work_zpfso6pk3vf5df7625v6vawp2e 210 17 , , , work_zpfso6pk3vf5df7625v6vawp2e 210 18 UK UK NNP work_zpfso6pk3vf5df7625v6vawp2e 210 19 . . . work_zpfso6pk3vf5df7625v6vawp2e 211 1 Lui Lui NNP work_zpfso6pk3vf5df7625v6vawp2e 211 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 211 3 Y. Y. NNP work_zpfso6pk3vf5df7625v6vawp2e 211 4 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 211 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 211 6 2012 2012 CD work_zpfso6pk3vf5df7625v6vawp2e 211 7 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 211 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 212 1 Advances advance NNS work_zpfso6pk3vf5df7625v6vawp2e 212 2 in in IN work_zpfso6pk3vf5df7625v6vawp2e 212 3 matrix matrix NN work_zpfso6pk3vf5df7625v6vawp2e 212 4 manifolds manifold NNS work_zpfso6pk3vf5df7625v6vawp2e 212 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 212 6 computer computer NN work_zpfso6pk3vf5df7625v6vawp2e 212 7 vision vision NN work_zpfso6pk3vf5df7625v6vawp2e 212 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 213 1 Image image NN work_zpfso6pk3vf5df7625v6vawp2e 213 2 and and CC work_zpfso6pk3vf5df7625v6vawp2e 213 3 Vision Vision NNP work_zpfso6pk3vf5df7625v6vawp2e 213 4 Computing Computing NNP work_zpfso6pk3vf5df7625v6vawp2e 213 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 213 6 30:380–388 30:380–388 CD work_zpfso6pk3vf5df7625v6vawp2e 213 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 214 1 McLachlan McLachlan NNP work_zpfso6pk3vf5df7625v6vawp2e 214 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 214 3 G. G. NNP work_zpfso6pk3vf5df7625v6vawp2e 214 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 214 5 Peel Peel NNP work_zpfso6pk3vf5df7625v6vawp2e 214 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 214 7 D. D. NNP work_zpfso6pk3vf5df7625v6vawp2e 214 8 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 214 9 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 214 10 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 214 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 215 1 Finite Finite NNP work_zpfso6pk3vf5df7625v6vawp2e 215 2 Mixture Mixture NNP work_zpfso6pk3vf5df7625v6vawp2e 215 3 Models Models NNPS work_zpfso6pk3vf5df7625v6vawp2e 215 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 216 1 Wiley Wiley NNP work_zpfso6pk3vf5df7625v6vawp2e 216 2 : : : work_zpfso6pk3vf5df7625v6vawp2e 216 3 New New NNP work_zpfso6pk3vf5df7625v6vawp2e 216 4 York York NNP work_zpfso6pk3vf5df7625v6vawp2e 216 5 . . . work_zpfso6pk3vf5df7625v6vawp2e 217 1 Mishra Mishra NNP work_zpfso6pk3vf5df7625v6vawp2e 217 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 3 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 217 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 5 Meyer Meyer NNP work_zpfso6pk3vf5df7625v6vawp2e 217 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 7 G. G. NNP work_zpfso6pk3vf5df7625v6vawp2e 217 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 9 Bach Bach NNP work_zpfso6pk3vf5df7625v6vawp2e 217 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 11 F. F. NNP work_zpfso6pk3vf5df7625v6vawp2e 217 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 13 and and CC work_zpfso6pk3vf5df7625v6vawp2e 217 14 Sepulchre Sepulchre NNP work_zpfso6pk3vf5df7625v6vawp2e 217 15 , , , work_zpfso6pk3vf5df7625v6vawp2e 217 16 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 217 17 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 217 18 2013 2013 CD work_zpfso6pk3vf5df7625v6vawp2e 217 19 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 217 20 . . . work_zpfso6pk3vf5df7625v6vawp2e 218 1 Low low JJ work_zpfso6pk3vf5df7625v6vawp2e 218 2 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 218 3 rank rank NN work_zpfso6pk3vf5df7625v6vawp2e 218 4 optimization optimization NN work_zpfso6pk3vf5df7625v6vawp2e 218 5 with with IN work_zpfso6pk3vf5df7625v6vawp2e 218 6 trace trace NN work_zpfso6pk3vf5df7625v6vawp2e 218 7 norm norm NN work_zpfso6pk3vf5df7625v6vawp2e 218 8 penalty penalty NN work_zpfso6pk3vf5df7625v6vawp2e 218 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 219 1 SIAM SIAM NNP work_zpfso6pk3vf5df7625v6vawp2e 219 2 Journal Journal NNP work_zpfso6pk3vf5df7625v6vawp2e 219 3 on on IN work_zpfso6pk3vf5df7625v6vawp2e 219 4 Optimization Optimization NNP work_zpfso6pk3vf5df7625v6vawp2e 219 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 219 6 23:2124–2149 23:2124–2149 CD work_zpfso6pk3vf5df7625v6vawp2e 219 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 220 1 References References NNPS work_zpfso6pk3vf5df7625v6vawp2e 220 2 Parzen Parzen NNP work_zpfso6pk3vf5df7625v6vawp2e 220 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 220 4 E. E. NNP work_zpfso6pk3vf5df7625v6vawp2e 220 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 220 6 1962 1962 CD work_zpfso6pk3vf5df7625v6vawp2e 220 7 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 220 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 221 1 On on IN work_zpfso6pk3vf5df7625v6vawp2e 221 2 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 221 3 of of IN work_zpfso6pk3vf5df7625v6vawp2e 221 4 a a DT work_zpfso6pk3vf5df7625v6vawp2e 221 5 probability probability NN work_zpfso6pk3vf5df7625v6vawp2e 221 6 density density NN work_zpfso6pk3vf5df7625v6vawp2e 221 7 function function NN work_zpfso6pk3vf5df7625v6vawp2e 221 8 and and CC work_zpfso6pk3vf5df7625v6vawp2e 221 9 mode mode NN work_zpfso6pk3vf5df7625v6vawp2e 221 10 . . . work_zpfso6pk3vf5df7625v6vawp2e 222 1 Annals Annals NNP work_zpfso6pk3vf5df7625v6vawp2e 222 2 of of IN work_zpfso6pk3vf5df7625v6vawp2e 222 3 Mathematical Mathematical NNP work_zpfso6pk3vf5df7625v6vawp2e 222 4 Statistics Statistics NNPS work_zpfso6pk3vf5df7625v6vawp2e 222 5 , , , work_zpfso6pk3vf5df7625v6vawp2e 222 6 33:1066–1076 33:1066–1076 CD work_zpfso6pk3vf5df7625v6vawp2e 222 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 223 1 Pinheiro Pinheiro NNP work_zpfso6pk3vf5df7625v6vawp2e 223 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 223 3 A. A. NNP work_zpfso6pk3vf5df7625v6vawp2e 223 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 223 5 Vidakovic Vidakovic NNP work_zpfso6pk3vf5df7625v6vawp2e 223 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 223 7 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 224 1 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 224 2 1998 1998 CD work_zpfso6pk3vf5df7625v6vawp2e 224 3 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 224 4 . . . work_zpfso6pk3vf5df7625v6vawp2e 225 1 Estimating estimate VBG work_zpfso6pk3vf5df7625v6vawp2e 225 2 the the DT work_zpfso6pk3vf5df7625v6vawp2e 225 3 square square JJ work_zpfso6pk3vf5df7625v6vawp2e 225 4 root root NN work_zpfso6pk3vf5df7625v6vawp2e 225 5 of of IN work_zpfso6pk3vf5df7625v6vawp2e 225 6 density density NN work_zpfso6pk3vf5df7625v6vawp2e 225 7 via via IN work_zpfso6pk3vf5df7625v6vawp2e 225 8 compactly compactly RB work_zpfso6pk3vf5df7625v6vawp2e 225 9 supported support VBN work_zpfso6pk3vf5df7625v6vawp2e 225 10 wavelets wavelet NNS work_zpfso6pk3vf5df7625v6vawp2e 225 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 226 1 Computational Computational NNP work_zpfso6pk3vf5df7625v6vawp2e 226 2 Statistics Statistics NNPS work_zpfso6pk3vf5df7625v6vawp2e 226 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 226 4 Data Data NNPS work_zpfso6pk3vf5df7625v6vawp2e 226 5 Analysis Analysis NNP work_zpfso6pk3vf5df7625v6vawp2e 226 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 226 7 25:399–415 25:399–415 CD work_zpfso6pk3vf5df7625v6vawp2e 226 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 227 1 Rutkowski Rutkowski NNP work_zpfso6pk3vf5df7625v6vawp2e 227 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 227 3 L. L. NNP work_zpfso6pk3vf5df7625v6vawp2e 227 4 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 227 5 2004 2004 CD work_zpfso6pk3vf5df7625v6vawp2e 227 6 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 227 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 228 1 Adaptive adaptive JJ work_zpfso6pk3vf5df7625v6vawp2e 228 2 probabilistic probabilistic JJ work_zpfso6pk3vf5df7625v6vawp2e 228 3 neural neural JJ work_zpfso6pk3vf5df7625v6vawp2e 228 4 networks network NNS work_zpfso6pk3vf5df7625v6vawp2e 228 5 for for IN work_zpfso6pk3vf5df7625v6vawp2e 228 6 pattern pattern NN work_zpfso6pk3vf5df7625v6vawp2e 228 7 classifi- classifi- NNP work_zpfso6pk3vf5df7625v6vawp2e 228 8 cation cation NN work_zpfso6pk3vf5df7625v6vawp2e 228 9 in in IN work_zpfso6pk3vf5df7625v6vawp2e 228 10 time time NN work_zpfso6pk3vf5df7625v6vawp2e 228 11 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 228 12 varying vary VBG work_zpfso6pk3vf5df7625v6vawp2e 228 13 environment environment NN work_zpfso6pk3vf5df7625v6vawp2e 228 14 . . . work_zpfso6pk3vf5df7625v6vawp2e 229 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 229 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 229 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 230 1 Neural Neural NNP work_zpfso6pk3vf5df7625v6vawp2e 230 2 Networks Networks NNP work_zpfso6pk3vf5df7625v6vawp2e 230 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 230 4 15:811 15:811 CD work_zpfso6pk3vf5df7625v6vawp2e 230 5 – – : work_zpfso6pk3vf5df7625v6vawp2e 230 6 827 827 CD work_zpfso6pk3vf5df7625v6vawp2e 230 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 231 1 Silverman Silverman NNP work_zpfso6pk3vf5df7625v6vawp2e 231 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 231 3 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 231 4 W. W. NNP work_zpfso6pk3vf5df7625v6vawp2e 231 5 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 231 6 1986 1986 CD work_zpfso6pk3vf5df7625v6vawp2e 231 7 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 231 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 232 1 Density Density NNP work_zpfso6pk3vf5df7625v6vawp2e 232 2 Estimation Estimation NNP work_zpfso6pk3vf5df7625v6vawp2e 232 3 for for IN work_zpfso6pk3vf5df7625v6vawp2e 232 4 Statistics Statistics NNPS work_zpfso6pk3vf5df7625v6vawp2e 232 5 and and CC work_zpfso6pk3vf5df7625v6vawp2e 232 6 Data Data NNPS work_zpfso6pk3vf5df7625v6vawp2e 232 7 Analysis Analysis NNP work_zpfso6pk3vf5df7625v6vawp2e 232 8 . . . work_zpfso6pk3vf5df7625v6vawp2e 233 1 Chap- Chap- NNP work_zpfso6pk3vf5df7625v6vawp2e 233 2 man man NN work_zpfso6pk3vf5df7625v6vawp2e 233 3 and and CC work_zpfso6pk3vf5df7625v6vawp2e 233 4 Hall Hall NNP work_zpfso6pk3vf5df7625v6vawp2e 233 5 : : : work_zpfso6pk3vf5df7625v6vawp2e 233 6 London London NNP work_zpfso6pk3vf5df7625v6vawp2e 233 7 . . . work_zpfso6pk3vf5df7625v6vawp2e 234 1 Vapnik Vapnik NNP work_zpfso6pk3vf5df7625v6vawp2e 234 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 234 3 V. V. NNP work_zpfso6pk3vf5df7625v6vawp2e 234 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 234 5 Mukherjee Mukherjee NNP work_zpfso6pk3vf5df7625v6vawp2e 234 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 234 7 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 234 8 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 234 9 2000 2000 CD work_zpfso6pk3vf5df7625v6vawp2e 234 10 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 234 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 235 1 Support support NN work_zpfso6pk3vf5df7625v6vawp2e 235 2 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 235 3 machine machine NN work_zpfso6pk3vf5df7625v6vawp2e 235 4 for for IN work_zpfso6pk3vf5df7625v6vawp2e 235 5 multivariate multivariate JJ work_zpfso6pk3vf5df7625v6vawp2e 235 6 den- den- NN work_zpfso6pk3vf5df7625v6vawp2e 235 7 sity sity NN work_zpfso6pk3vf5df7625v6vawp2e 235 8 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 235 9 . . . work_zpfso6pk3vf5df7625v6vawp2e 236 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 236 2 S. S. NNP work_zpfso6pk3vf5df7625v6vawp2e 236 3 Solla Solla NNP work_zpfso6pk3vf5df7625v6vawp2e 236 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 236 5 T. T. NNP work_zpfso6pk3vf5df7625v6vawp2e 236 6 L. L. NNP work_zpfso6pk3vf5df7625v6vawp2e 236 7 and and CC work_zpfso6pk3vf5df7625v6vawp2e 236 8 Müller Müller NNP work_zpfso6pk3vf5df7625v6vawp2e 236 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 236 10 K. K. NNP work_zpfso6pk3vf5df7625v6vawp2e 236 11 R. R. NNP work_zpfso6pk3vf5df7625v6vawp2e 236 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 236 13 editors editor NNS work_zpfso6pk3vf5df7625v6vawp2e 236 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 236 15 Advances advance NNS work_zpfso6pk3vf5df7625v6vawp2e 236 16 in in IN work_zpfso6pk3vf5df7625v6vawp2e 236 17 Neural Neural NNP work_zpfso6pk3vf5df7625v6vawp2e 236 18 Infromation Infromation NNP work_zpfso6pk3vf5df7625v6vawp2e 236 19 Processing Processing NNP work_zpfso6pk3vf5df7625v6vawp2e 236 20 Systems Systems NNPS work_zpfso6pk3vf5df7625v6vawp2e 236 21 , , , work_zpfso6pk3vf5df7625v6vawp2e 236 22 pages page VBZ work_zpfso6pk3vf5df7625v6vawp2e 236 23 659–665 659–665 CD work_zpfso6pk3vf5df7625v6vawp2e 236 24 . . . work_zpfso6pk3vf5df7625v6vawp2e 237 1 MIT MIT NNP work_zpfso6pk3vf5df7625v6vawp2e 237 2 Press Press NNP work_zpfso6pk3vf5df7625v6vawp2e 237 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 238 1 Weston Weston NNP work_zpfso6pk3vf5df7625v6vawp2e 238 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 3 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 5 Gammerman Gammerman NNP work_zpfso6pk3vf5df7625v6vawp2e 238 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 7 A. A. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 8 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 9 Stitson Stitson NNP work_zpfso6pk3vf5df7625v6vawp2e 238 10 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 11 M. M. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 13 Vapnik Vapnik NNP work_zpfso6pk3vf5df7625v6vawp2e 238 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 15 V. V. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 16 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 17 Vovk Vovk NNP work_zpfso6pk3vf5df7625v6vawp2e 238 18 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 19 V. V. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 20 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 21 and and CC work_zpfso6pk3vf5df7625v6vawp2e 238 22 Watkins Watkins NNP work_zpfso6pk3vf5df7625v6vawp2e 238 23 , , , work_zpfso6pk3vf5df7625v6vawp2e 238 24 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 238 25 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 238 26 1999 1999 CD work_zpfso6pk3vf5df7625v6vawp2e 238 27 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 238 28 . . . work_zpfso6pk3vf5df7625v6vawp2e 239 1 Suppot Suppot NNP work_zpfso6pk3vf5df7625v6vawp2e 239 2 vector vector NN work_zpfso6pk3vf5df7625v6vawp2e 239 3 density density NN work_zpfso6pk3vf5df7625v6vawp2e 239 4 estimation estimation NN work_zpfso6pk3vf5df7625v6vawp2e 239 5 . . . work_zpfso6pk3vf5df7625v6vawp2e 240 1 In in IN work_zpfso6pk3vf5df7625v6vawp2e 240 2 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 240 3 Schölkopf Schölkopf NNP work_zpfso6pk3vf5df7625v6vawp2e 240 4 , , , work_zpfso6pk3vf5df7625v6vawp2e 240 5 C. C. NNP work_zpfso6pk3vf5df7625v6vawp2e 240 6 B. B. NNP work_zpfso6pk3vf5df7625v6vawp2e 240 7 and and CC work_zpfso6pk3vf5df7625v6vawp2e 240 8 Smola Smola NNP work_zpfso6pk3vf5df7625v6vawp2e 240 9 , , , work_zpfso6pk3vf5df7625v6vawp2e 240 10 A. A. NNP work_zpfso6pk3vf5df7625v6vawp2e 240 11 J. J. NNP work_zpfso6pk3vf5df7625v6vawp2e 240 12 , , , work_zpfso6pk3vf5df7625v6vawp2e 240 13 editors editor NNS work_zpfso6pk3vf5df7625v6vawp2e 240 14 , , , work_zpfso6pk3vf5df7625v6vawp2e 240 15 Advances advance NNS work_zpfso6pk3vf5df7625v6vawp2e 240 16 in in IN work_zpfso6pk3vf5df7625v6vawp2e 240 17 Kernel Kernel NNP work_zpfso6pk3vf5df7625v6vawp2e 240 18 Methods Methods NNPS work_zpfso6pk3vf5df7625v6vawp2e 240 19 , , , work_zpfso6pk3vf5df7625v6vawp2e 240 20 pages page VBZ work_zpfso6pk3vf5df7625v6vawp2e 240 21 293–306 293–306 CD work_zpfso6pk3vf5df7625v6vawp2e 240 22 . . . work_zpfso6pk3vf5df7625v6vawp2e 241 1 MIT MIT NNP work_zpfso6pk3vf5df7625v6vawp2e 241 2 Press Press NNP work_zpfso6pk3vf5df7625v6vawp2e 241 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 242 1 Yin Yin NNP work_zpfso6pk3vf5df7625v6vawp2e 242 2 , , , work_zpfso6pk3vf5df7625v6vawp2e 242 3 H. H. NNP work_zpfso6pk3vf5df7625v6vawp2e 242 4 and and CC work_zpfso6pk3vf5df7625v6vawp2e 242 5 Allinson Allinson NNP work_zpfso6pk3vf5df7625v6vawp2e 242 6 , , , work_zpfso6pk3vf5df7625v6vawp2e 242 7 N. N. NNP work_zpfso6pk3vf5df7625v6vawp2e 242 8 W. W. NNP work_zpfso6pk3vf5df7625v6vawp2e 242 9 ( ( -LRB- work_zpfso6pk3vf5df7625v6vawp2e 242 10 2001 2001 CD work_zpfso6pk3vf5df7625v6vawp2e 242 11 ) ) -RRB- work_zpfso6pk3vf5df7625v6vawp2e 242 12 . . . work_zpfso6pk3vf5df7625v6vawp2e 243 1 Self self NN work_zpfso6pk3vf5df7625v6vawp2e 243 2 - - HYPH work_zpfso6pk3vf5df7625v6vawp2e 243 3 organizing organize VBG work_zpfso6pk3vf5df7625v6vawp2e 243 4 mixture mixture NN work_zpfso6pk3vf5df7625v6vawp2e 243 5 networks network NNS work_zpfso6pk3vf5df7625v6vawp2e 243 6 for for IN work_zpfso6pk3vf5df7625v6vawp2e 243 7 probabil- probabil- NNP work_zpfso6pk3vf5df7625v6vawp2e 243 8 ity ity NNP work_zpfso6pk3vf5df7625v6vawp2e 243 9 density density NN work_zpfso6pk3vf5df7625v6vawp2e 243 10 estimation estimation NNP work_zpfso6pk3vf5df7625v6vawp2e 243 11 . . . work_zpfso6pk3vf5df7625v6vawp2e 244 1 IEEE IEEE NNP work_zpfso6pk3vf5df7625v6vawp2e 244 2 Trans Trans NNPS work_zpfso6pk3vf5df7625v6vawp2e 244 3 . . . work_zpfso6pk3vf5df7625v6vawp2e 245 1 Neural Neural NNP work_zpfso6pk3vf5df7625v6vawp2e 245 2 Networks Networks NNP work_zpfso6pk3vf5df7625v6vawp2e 245 3 , , , work_zpfso6pk3vf5df7625v6vawp2e 245 4 12:405–411 12:405–411 CD work_zpfso6pk3vf5df7625v6vawp2e 245 5 . . .