M2:Monday, July 4, 2011         1
• 3.1                       • 3.2                       • 3.3   FisherMonday, July 4, 2011                    2
Monday, July 4, 2011   3
•      X               X1, ..., XN                                              k                                         ...
•                     =>                           •(   PCA                                   ...)                        ...
0Monday, July 4, 2011       6
f<Σi ai x, y> = Σi ai <x, y>Monday, July 4, 2011              7
Monday, July 4, 2011   8
…                       http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011                     ...
σ    →                       http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011                ...
http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011                                             ...
FisherMonday, July 4, 2011            12
Fisher         •               •                                =>                                     =>   1Monday, July ...
Fisher               •X                                       RKHS H                                       Φ              ...
LDA                       •   PCA                           (                                 J             h             ...
LDA(        )                  •                        ((3.14)   )                  •        CCA                       • ...
Monday, July 4, 2011   17
CCA                       •2                     X   Y                           • X mY   Y   l             )             ...
a b                             maxMonday, July 4, 2011               19
(     )                               a b                       λa = λb = λMonday, July 4, 2011                 20
CCA                • RKHS          PCA           LDA                       •X   Y                •           CCA       X  ...
CCAMonday, July 4, 2011         22
• Φ(X ), Rank(K )) = N                       =>                            ..., Φ(X                                1     n...
KX                       •K   X                               Σi, jcicjkij ≧ 0                       •        Σi, jcicj <Φ...
http://homepage.mac.com/davidrh/_papers/NC_Hardoon_2817_reg.pdfMonday, July 4, 2011                                       ...
1                       • CCA    Xi   Yi                        •            (          )                        •   :    ...
2                       •                                       ?                           • :                           ...
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Kernel20110619

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Kernel20110619

  1. 1. M2:Monday, July 4, 2011 1
  2. 2. • 3.1 • 3.2 • 3.3 FisherMonday, July 4, 2011 2
  3. 3. Monday, July 4, 2011 3
  4. 4. • X X1, ..., XN k X •k RKHS Hk • (X ) Φ: X -> Hk Hk Φ(X1), ..., Φ n • => PCA PCA Hk Φ(X1), ..., Φ(Xn)Monday, July 4, 2011 4
  5. 5. • => •( PCA ...) RKHSMonday, July 4, 2011 5
  6. 6. 0Monday, July 4, 2011 6
  7. 7. f<Σi ai x, y> = Σi ai <x, y>Monday, July 4, 2011 7
  8. 8. Monday, July 4, 2011 8
  9. 9. … http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 9
  10. 10. σ → http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 10
  11. 11. http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 11
  12. 12. FisherMonday, July 4, 2011 12
  13. 13. Fisher • • => => 1Monday, July 4, 2011 13
  14. 14. Fisher •X RKHS H Φ • => Φ(X ), ..., Φ(X ) 1 n H • H h w • =>Monday, July 4, 2011 14
  15. 15. LDA • PCA ( J h ) h !Monday, July 4, 2011 15
  16. 16. LDA( ) • ((3.14) ) • CCA • • LDA αMonday, July 4, 2011 16
  17. 17. Monday, July 4, 2011 17
  18. 18. CCA •2 X Y • X mY Y l ) (X • a b • b=1Monday, July 4, 2011 18
  19. 19. a b maxMonday, July 4, 2011 19
  20. 20. ( ) a b λa = λb = λMonday, July 4, 2011 20
  21. 21. CCA • RKHS PCA LDA •X Y • CCA X Y m l CCA • RKHS H a b f gMonday, July 4, 2011 21
  22. 22. CCAMonday, July 4, 2011 22
  23. 23. • Φ(X ), Rank(K )) = N => ..., Φ(X 1 n KX X • K~ X = QNKXQN (N-1 )1N •Y (N-1 )1N • (3.10) (N-1 u v )1N u=v 1 • =>Monday, July 4, 2011 23
  24. 24. KX •K X Σi, jcicjkij ≧ 0 • Σi, jcicj <ΦX(Xi), ΦX(Xj)> ≧ 0 • <ΣiciΦX(Xi), ΣjcjΦX(Xj)> ≧ 0 • (<z, z> ) ΣiciΦX (Xi) ≠ 0 • <ΣiciΦX(Xi), ΣjcjΦX(Xj)> ≠ 0 det(KX) ≠ 0 KXMonday, July 4, 2011 24
  25. 25. http://homepage.mac.com/davidrh/_papers/NC_Hardoon_2817_reg.pdfMonday, July 4, 2011 25
  26. 26. 1 • CCA Xi Yi • ( ) • : WebMonday, July 4, 2011 26
  27. 27. 2 • ? • : • Aria Haghighi, Perry Liang, Taylor Berg- Kirkpatrick and Dan Klein. Learning Bilingual Lexicons from Monolingual Corpora. ACL-2008. • Jagadeesh Jagarlamudi, Seth Juarez, Hal Daumé III, Kernelized Sorting for Natural Language Processing, AAAI-2010.Monday, July 4, 2011 27

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