Kernel20110619
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Kernel20110619

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Kernel20110619 Kernel20110619 Presentation Transcript

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