2015/09/17@_kobacky ALBERT

44.14.2

4

(4.1) (4.2) (4.3)

4.1

4.5

"##$,&,,"##$,'

)*$,&,,)*$,'

+#,-*,.$,&,,+#,-*,.$,'

()

()

1.2

3.8

()

$,/ d i($,/)

(=)

4.1

4.5

"##$,&,,"##$,6

)*$,&,, )*$,6

+#,-*,.$,&,, +#,-*,.$,6

()

()

1.2

3.8

()

$,/ d i($,/)

(=)

4.1

4

()

4.2

4.2.1 4.2.2 LDA+ 4.2.3 LDA+ 4.2.4 4.2.5 LDA+ 4.2.6 LDA+ ()

4.2.1

V 1 V = = AACAD&

/,/ = 1,2,, / ~ J/,L

J/

(4.1)

4.2.2 LDA+$,/

$,/ : $,/

PQ =1$

R$,/

'S

/D&

PQ :

word1

word2

word3

word4

1

3

1

4

$,/$,/

$,/ = 3$,/ = 0,0,1,0,0 J

PQ =14 2,0,1,1,0

J

$

K()=5

(4.2)

4.2.2 LDA+

M

K

Z$,/$,/$$

$

_$~Dir = 1,, ,Z~Dir = 1,, .

$,/~Multi $ , $,/~Multi jS,k = 1,, $

$ ~ JP$,L

(4.3)

(4.4)

(4.5)

LDA

4.2.3 LDA+

M

K

Z$,/$,/$$

$

LDA , $,, $,/

LDA

4.2.3 LDA+

M

K

Z$,/$,/$$

$

,, , , ,,, L= , ,L , (4.6)

, , , , L opq + t log , , L (4.7)

LDAt log , ,L

log , ,L = logx $ $, ,L = R log $ $,, Ly

$D&

y

$D&

4.2.3 LDA+(3.82)(3.84)(4.7)

log , , , ,L

= logzR ,, , , , , , L

= logzR , , ,, , , ,,, L

,,

zR ,, log ,, , , ,,, L

,,

= zR , , log ,

, , + log ,, L

= opq +zR log ,, L

= opq + R log , ,L

z = opq + t log , , L

(4.6)

(3.82)(3.83)

4.2.3 LDA+

$ $, ,L =12L

exp $ JP$ L

2L

$ $,, L ( $ ~ JP$,L )

t S log $ $,, L

= 12 log 2

L t S12L $

JP$ L

= 12 log 2

L 12L $

L 2$Jt jS P$ + Jt jS P$P$

J

(4.8)

(4.9)

4.2.3 LDA+$,/ = $,/,& , $,/,L ,, $,/,6 , $,/,Z = $,/ =

t S P$ =1$

R $,/ ='S

/D&

1$

R$,/

'S

/D&

t S P$P$J

= t S1$

R$,/

'S

/D&

1$

R $,/J

'S

/D&

= t S1$L RR$,/$,/

J'S

/D&

'S

/D&

=1$L R diag $,/ +R $,/

'S

//

$,/J

'S

/D&

(4.10)

(4.11)

$,/ = $,/ = 1 1,0,, 0 J +

+ $,/ = 0,, 0,1 J = $,/

(4.13)

4.2.3 LDA+

t S RR $,/$,/J

'S

/D&

'S

/D&

=R diag $,/ +R $,/$,/J

'S

//

'S

/D&

RR $,/$,/J

'S

/D&

'S

/D&

= $,&$,& J + + $,&$,/J + + $,&$,'S

J

++$,/$,& J ++ $,/$,/

J + + $,/$,'S J

++$,'S$,&

J + + $,'S$,/J + + $,'S$,'S

J

t S RR $,/$,/J

'S

/D&

'S

/D&

=

$,/ = 1 0 0 $,/ =

= diag $,/ ( = )

$,/ = 1 $,/ = 1 $,/ = 1 $,/ =

$,/ = $,/ = 1 $,/ = $,/ = = $,/$,/

J ( )

4.2.3 LDA+,L()

(4.7), Lt log , ,L

t log , ,L

= 12 log 2

L 12L

R $Ly

$D&

2J R $t jS P$

y

$D&

+ J Rt jS P$P$J

y

$D&

= Rt S log $ $, ,L

y

$D&

(4.9) (4.12)

4.2.3 LDA+

2 R$t jS P$

y

$D&

+ 2 Rt jS P$P$J

y

$D&

=

= Rt jS P$P$J

y

$D&

&

R $t jS P$

y

$D&

t log , ,L

= 0

A.9

J =

J =

J = + J

12 log 2

L 12L R $

Ly

$D&

2J R $t jS P$

y

$D&

+J R t jS P$P$J

y

$D&

(4.13)

(4.14)

2

4.2.3 LDA+ L

t log , ,L

L = 0

L =1

R$Ly

$D&

2J R $ P$

y

$D&

+ J R P$P$Jy

$D&

12 log 2

L 12L R $

Ly

$D&

2J R $t jS P$

y

$D&

+J R t jS P$P$J

y

$D&

=1

R$Ly

$D&

J R $ P$

y

$D&

(4.14)

(4.15)

(4.16)

4.2.3 LDA+ $,/ =

J P$ =1$

RJ$,/

'S

/D&

=1$

RRZ $,/ = 6

ZD&

'S

/D&

J P$ $,/ =

=1$

Z

J P$P$J =1$LR Jdiag $,/ +RJ$,/$,/

J 'S

//

'S

/D&

J P$P$J

$,/ = =

1$L ZL + 2Z R $,/

J 'S

//

=1$L R RZL $,/ =

6

ZD&

+R Z $,/ = 6

ZD&

R $,/J

'S

//

'S

/D&

(4.10)

(4.11)

(4.17)

(4.18)

(4.19)

(4.20)

$,/ 2

4.2.3 LDA+ $,/ =

$,/ =

R RZ $,/ = 6

ZD&

R $,/J

'S

//

'S

/D&

= 2ZR $,/J

'S

//

& $,& = 1 +L $,& = 2 $,L J &L

+ $, J &L

& $,L = 1 +L $,L = 2 $,& J &L

+ $, J &L

& $, = 1 +L $, = 2 $,& J &L

+ $,L J &L

& $,L J &L

+ $, J &L

+ 0

0+ & $,L = 1 +L $,L = 2 &

0 + & $, = 1 +L $, = 2 &

+

+

+

+

$,& = 1

$ = 3, = 2 $,& = 1

& R $,/J

/&

4.2.3 LDA+ $,/ = $,/

$,/ $,/ =

= 0

$,/ = exp z Z logZ,S,k Z exp z $ log$,Z $

exp$ZL$

1

2L$L ZL + 2Z R $,/

J 'S

//

= R $,/ = 6

ZD&

z Z $ log $,/ Z $,/ = $ Z$

R $,/ = log $,/ = 6

ZD&

+12L 2$

J P$ J P$P$J

LDA(3.97)(4.9) $,/

(4.21)

(4.22)

(4.18) (4.20)

(3.99)

4.2.4

, , = , expJ J

> 0 1

, J

,, L =12L

exp J L

2L

=12L

exp L

2L expJ JJ/2

L

= L , = &L

exp

L J = JJ/2

(4.23)

(4.24)

4.2.4

, = , exp

, L =12L

exp L

2L =12L

exp L

2L exp L/2

L

L ,

= J(4.23)

= J

, = J

(4.25)

(4.26)

4.2.4

=1!

exp =1! exp log

= log = exp

=1! exp exp

, , =

1! exp

J exp J

= J

= 1 , = &

! J = exp J

(4.27)

(4.28)

4.2.5 LDA+

$ $, , = $, exp$JP$ JP$

, , , , opq + t log ,,

t log $ $, ,

LDA P$

= log $, +$Jt P$ t

JP$

LDA+

(4.29)

(4.30)

(4.31)

4.2.6 LDA+

, ,

= , ,

= 0

$ $, =1! exp $

JP$ exp JP$

t S exp JP$

(4.32)

= 1

4.2.6 LDA+ t exp

JP$ = t exp1$

RJ$,/

'S

/D&

= t xexp1$

J$,/

'S

/D&

= xt , exp1$

J$,/

'S

/D&

= xR $,/ = exp1$

Z

6

ZD&

'S

/D&

$,/ = J$,/=Z

t / exp JP$ =xR $,/ = exp

1$

Z

6

ZD&

'S

//

Z

t exp JP$ =R

$,/ = $

'S

/D&

expZ$

t / exp JP$

(4.33)

(4.34)

(4.35)

(4.33)$$

= $$ + $

$ + $

$

4.2.6 LDA+

log , , =

1R $

y

$D&

P$ t exp

JP$

(4.35)

(4.31)

log , , / = 0()

(A.4)

4.2.6 LDA+ $,/ =

t exp JP$

$,/ = = exp

Z$

t / exp JP$

log , $,/ =

= Z$

$,/ = t exp

JP$

$,/ = exp z Z logZ,S,k Z exp z $ log$,Z $

exp

$,/ = log ,

(4.37)

(4.38)

(4.39)

(4.32)

(4.33)