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Kernel20110619

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  • 1. M2:Monday, July 4, 2011 1
  • 2. • 3.1 • 3.2 • 3.3 FisherMonday, July 4, 2011 2
  • 3. Monday, July 4, 2011 3
  • 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. • => •( PCA ...) RKHSMonday, July 4, 2011 5
  • 6. 0Monday, July 4, 2011 6
  • 7. f<Σi ai x, y> = Σi ai <x, y>Monday, July 4, 2011 7
  • 8. Monday, July 4, 2011 8
  • 9. … http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 9
  • 10. σ → http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 10
  • 11. http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdfMonday, July 4, 2011 11
  • 12. FisherMonday, July 4, 2011 12
  • 13. Fisher • • => => 1Monday, July 4, 2011 13
  • 14. Fisher •X RKHS H Φ • => Φ(X ), ..., Φ(X ) 1 n H • H h w • =>Monday, July 4, 2011 14
  • 15. LDA • PCA ( J h ) h !Monday, July 4, 2011 15
  • 16. LDA( ) • ((3.14) ) • CCA • • LDA αMonday, July 4, 2011 16
  • 17. Monday, July 4, 2011 17
  • 18. CCA •2 X Y • X mY Y l ) (X • a b • b=1Monday, July 4, 2011 18
  • 19. a b maxMonday, July 4, 2011 19
  • 20. ( ) a b λa = λb = λMonday, July 4, 2011 20
  • 21. CCA • RKHS PCA LDA •X Y • CCA X Y m l CCA • RKHS H a b f gMonday, July 4, 2011 21
  • 22. CCAMonday, July 4, 2011 22
  • 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. 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. http://homepage.mac.com/davidrh/_papers/NC_Hardoon_2817_reg.pdfMonday, July 4, 2011 25
  • 26. 1 • CCA Xi Yi • ( ) • : WebMonday, July 4, 2011 26
  • 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