2. • 3.1
• 3.2
• 3.3 Fisher
Monday, July 4, 2011 2
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
...)
RKHS
Monday, July 4, 2011 5
7. f
<Σi ai x, y> = Σi ai <x, y>
Monday, July 4, 2011 7
9. …
http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdf
Monday, July 4, 2011 9
10. σ
→
http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdf
Monday, July 4, 2011 10
13. Fisher
•
•
=>
=> 1
Monday, July 4, 2011 13
14. Fisher
•X RKHS H
Φ
• => Φ(X ), ..., Φ(X )
1 n H
• H h
w
• =>
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15. LDA
• PCA
(
J h
)
h
!
Monday, July 4, 2011 15
16. LDA( )
• ((3.14) )
• CCA
•
• LDA
α
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18. CCA
•2 X Y
• X mY Y l )
(X
• a b
• b=1
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19. a b
max
Monday, July 4, 2011 19
20. ( )
a b
λa = λb = λ
Monday, July 4, 2011 20
21. CCA
• RKHS PCA LDA
•X Y
• CCA X Y m l
CCA
• RKHS H a b
f g
Monday, July 4, 2011 21
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 KX
Monday, July 4, 2011 24
26. 1
• CCA Xi Yi
• ( )
• : Web
Monday, 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
