Slide 11
Slide 11 text
Canonical correlation analysis (CCA)
ਖ਼४૬ؔੳͱ͍͏໊લͰֶ෦ͷ࣌ͱ͔ʹशͬͨΑ͏ͳؾ͕͢Δ. ࣜҎԼ
(Bach and Jordan, (2005)).
p(zi
) = N(zs
i
|0, ILs
)N(zx
i
|0, ILx
)N(zy
i
|0, ILy
p(yi
|zi
) = N(yi
|By
zy
i
+ Wy
zs
i
+ µy
, σ2IDy
)
p(xi
|zi
) = N(xi
|Bx
zx
i
+ Wx
zs
i
+ µx
, σ2IDx
)
PLS Λ synmetric ʹͨ͠ͷ. ͭ·Γ, zi
Λڞ௨ͷ zs
i
ͱ zx
i
ͱ zy
i
ʹղ͢Δ
͜ͱ.
vi
ͷ͖݅:
p(vi
|θ) = N(vi
|W zi + µ, σI)N(zi
|0, I)dzi = N(vi
|µ, W W T + σID)
where W =
Wx
Bx
0
Wy 0 By
and
W W T =
Wx
W T
x
+ Bx
BT
x
Wx
W T
y
Wy
W T
y
Wy
W T
y
+ By
BT
y
MLE Λ EM Ͱղ͘ classic ͳ non-probabilistic ͳ݁ՌͱҰக͢Δ (Bach and
Jordan, (2005))
Daisuke Yoneoka Supervised PCA ͱͦͷपล February 22, 2015 11 / 11