Kernel20110619

M2:

Monday, July 4, 2011 1

• 3.1
• 3.2
• 3.3 Fisher


• X X1, ..., XN
k
X

•k RKHS Hk
• (X ) Φ: X -> Hk
Hk
Φ(X1), ..., Φ
n

• => PCA
PCA Hk Φ(X1), ..., Φ(Xn)


• =>
•( PCA
...)
RKHS


0


f

<Σi ai x, y> = Σi ai <x, y>


…

http://www.ism.ac.jp/~fukumizu/papers/Kernel_rois2006.pdf

σ
→


Fisher


Fisher
•
•

=>
=> 1


Fisher
•X RKHS H
Φ
• => Φ(X ), ..., Φ(X )
1 n H
• H h
w

• =>


LDA
• PCA
(
J h
)

h
!

LDA( )
• ((3.14) )
• CCA

•
• LDA

α


CCA
•2 X Y

• X mY Y l )
(X

• a b
• b=1

a b
max


( )

a b

λa = λb = λ


CCA
• RKHS PCA LDA

•X Y
• CCA X Y m l
CCA

• RKHS H a b
f g


CCA


• 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
• =>

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


http://homepage.mac.com/davidrh/_papers/NC_Hardoon_2817_reg.pdf

1

• CCA Xi Yi

• ( )
• : Web


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.


Kernel20110619

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