Read paper.dvi text version

AIST07-J00012

http://staff.aist.go.jp/y-ichisugi/j-index.html

2008 3 31

BESOM

BESOM

1

1 1.1 1.2 1.3 1.4 1.4.1 1.4.2 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 2 2.1 2.2 2.3 2.3.1 3 3.1 BESOM BESOM

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7 7 7 8 8 9 9 9 10 10 11 11 12 12 12 13 13 16 16 16 17 18 18 18 18 19 19 19 19 19 20 20 20 20 21 21 21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Self-Organizing Map, SOM 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.1.7 3.1.8

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Bayesian network) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Independent Component Analysis, ICA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.3 3.3.1 3.3.2 3.3.3

2

3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.5 4 4.1 4.2 4.3 4.4 BESOM

(Reinforcement learning) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sarsa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 21 21 22 22 22 22 23

BESOM BESOM BESOM BESOM BESOM 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 23 24 24 24 25 25 26 26 26 26 27 28

4.5 4.6 5 5.1 5.2 5.3 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6 5.5 5.5.1 5.5.2 5.6 5.6.1 5.6.2 5.6.3 5.6.4 5.6.5 5.6.6 5.6.7 5.6.8 5.6.9 5.6.10 5.6.11

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28 28 29 29 29 30 31 31 32 32 32 32 33 33 33 33 35 35 35 35 35 35 35 36 36

5.6.12 5.6.13 5.6.14 5.6.15 6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 BESOM 6.3.1 6.3.2 6.3.3 6.4 6.4.1 6.4.2 6.4.3 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.5.5 6.5.6 6.5.7 6.6 6.6.1 6.6.2 7 7.1 7.2 7.3 7.4 7.5 7.5.1 7.5.2 7.5.3 7.5.4 7.6 7.6.1 7.6.2 7.6.3 7.6.4 7.6.5 7.6.6 t

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36 36 36 37 38 38 38 38 39 39 40 40 40 41 41 42 42 42 42 42 42 43 43 43 43 44 44 44 44 45

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

45 46 46 47 47 47 48 48 48 48 48 49 49 49 50 50

8 8.1 8.2 8.3 9 9.1 9.1.1 9.1.2 9.1.3 9.1.4 9.2 9.3 9.4 9.4.1 9.4.2 9.4.3 10

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51 51 51 51 52 52 52 52 53 53 53 53 53 53 53 53 54 54 54 54 54 54 54 56 56 56 56 56 56 56 57 57 57 57 58 58 58 58 59 60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 BESOM 10.3 BESOM 10.4 10.5 10.5.1 11 11.1 11.2 11.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.2.2 BESOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.3 11.2.4 11.3 11.4 11.5 11.6 11.7 11.7.1 11.7.2 11.7.3 11.8 12 12.1 12.1.1 12.1.2 12.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60 60 60 60

5

12.1.4 12.1.5 12.1.6 12.2 12.2.1 12.2.2 13 13.1 13.2 13.3 13.4 13.5 13.6 A A.1 A.2

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60 61 61 61 61 61 62 62 62 62 63 63 63 64

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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64 64

6

4

BESOM 2 3

1

1.1

BESOM 4

1.3

2005

1. [29] [30] [16] [17][18] 5.5 BESOM 2. [22] [21] [15] 7 3. [5] ?? 4. 4.5 7 5

1.2

BESOM

4.

1. [16][18] 5 2. [16][17][18] 3. 7 7.3 9 10.3 11.5 5 6

1.4

1.4.1

1.

2.

13 3.

8

1.1: [22]

1.4.2

1.5

1.5.1

1990

fMRI

1.1 [22]

9

1.5.3

1990

1.5.2

3

1

1

1988 [4] 1998 [10] 2001 [6]

10

1.6

BESOM

12

1.5.4

13

11

2

BESOM

x1 x2 w2 . . . xn w1

wn

y = ( wi xi )

i

BESOM 2.1:

2.1

BESOM

20 -y

y = (

i

wi xi )

(2.1)

xi wi 2.1 (w1 , w2 , · · · wn )T (x1 , x2 , · · · xn )T (2.1)

2.2

wi wi + (xi y - wi ) xi wi y wi (2.2)

12

wi = 0

12.1.4

3

2.3.1

(2.2) wi , xi , y

2.3

4

2.2 2.3

2.3

1

V1

1mm2 "Cells that fire together, wire together."

2

2.4 1mm2 1mm

1 2

6.6.2

3

4

13

2.3:

[5] (V1 )

(RGC) (HC)

(LGN)

14

I II III IV V VI

2.5:

6.2.1

2.2:

Commons

Wikimedia Gray726-Brodman.png 1mm (180 )

Gray727-Brodman.png

2mm 2.5

I II III IV V VI

5.5

2.4:

15

3

BESOM

BESOM

BESOM

3.1 Organizing Map, SOM

3.1.1

[2]

Self-

3.2 x1, x2

w4

3.3 3.1

3.4

3.5

[2]

3.4

3.5

3.1:

16

x2

w1

w2

w3

w4

w5

3.4:

x1

[2]

(1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0)T

3.2:

3.1.2

1

3.4

x2

w3 w2

w4

w5

w1

x1

3.3:

1

17

3.1.4

3.5 3.5

3.5:

3.4 [2]

3.1.5 3.1.3

x f (x) f (x)

f (x) f (x) x

x2 = f (x1 ) 3.3

3.1.6

[2]

18

3.1.7

n O(2n )

6

3.1.8

3.2.2

[4]

3.2 network)

3.2.1

(Bayesian

3.6

1/2

P( X Y P(X= )=P(X= )=1/2 X P( | |

)

P(

) P( )

)

P (Y = P (Y = P (Y = P (Y =

|X = |X = |X = |X =

) = 1/5 ) = 4/5 ) = 3/5 ) = 2/5 P (X = |Y = )

s m Ui P (X|U1 , · · · , Um ) X sm

19

5

5.6.5

3.6: BEL(x) = (x)(x) (x) =

u1 ,···,um

3.2.5

P (x|u1 , · · · , um )

k

X (uk )

(x) =

l

Yl (x) Yj (x)

j=l

Yl (x) = (x) X (uk ) = (x)

x

3.3

P (x|u1 , · · · , um ) X (ui )

i=k

Independent Component Analysis, ICA

[7]

u1 ,···,um /uk

3.7:

[4] n A n yi xi

3.7 y = Ax (3.1)

3.2.3

A

y y x

[31][40]

3.2.4

3.8 m 5 O(2m )

6

20

y2

0

y1

3.8:

3.3.1

6.2.1 [34][36][37] 3.8 (NMF)[9] NMF [9]

3.4.2

sarsa

sarsa

3.3.2

Q(s,a) s 6 a

2

Q(s, a) Q(s, a) + [r + Q(s , a ) - Q(s, a)](3.2) r s', a' Q(s,a) s a Q(s,a) s s

3.3.3

3.4 learning)

3.4.1

[11]

(Reinforcement

2

21

3.4.3

[12] [13]

3.5

BESOM

BESOM

3.4.4

s n a O(2 )

n

BESOM Backpropagation,

7

BESOM 10

AI

prolog

9

(Hopfield net) (Boltzmann machine) BESOM BESOM

7.4

11.6

9

3.4.5

sarsa

22

4

BESOM

...

...

...

2

3 BESOM BESOM

... ...

4.1: BESOM

BESOM

4.1

BESOM

5.4.3

BESOM

BESOM BESOM 2.3.1 BESOM 5 6 BESOM BESOM 5 ICA 7 4.1 6.5.1

5.3 4.1 6.3 BESOM 4.1

4.2

BESOM

BESOM

BESOM 5 4.2

4.2

R

23

BESOM 200,000mm 40,000mm 1mm 4.1: BESOM 6.5.7 BESOM 1013

2 2 2

1 10 50

BESOM

0.01mm2

RA R R A B A B BR

BESOM

4.2: BESOM

1

5 5 A, B 4.2 R B R A B B A

6

4.4

BESOM

BESOM

4.3

BESOM

4.4.1

4.3

1

BESOM

BESOM

24

A

B

C

D

... Recognized

R

pattern

...

...

Hyper column in V1

...

Input

4.4: BESOM

4.3:

PATON [14] BESOM PATON BESOM is-a BESOM 10 11.3 BESOM

4.4.3

[19] 4.5

4.4.2

4.4

[21] 4.5 7

25

(s,a)

s

a

4.4.6

4.5:

BESOM

[20]

Xt

Yt

BESOM 6.5.2

Xt-1

Yt-1

At

Bt

Ct

At-1

Bt-1

Ct-1

4.6:

BESOM

4.4.4

4.6 BESOM [20]

8

4.4.5

s s' (s,s'a) BESOM 9 a

4.5

BESOM

26

11.7

BESOM

11.6

4.6

BESOM

27

5

SOM Selective Attention Model (SAM)[19] SAM

SAM

BESOM SAM [32][27][31]

5.1

SOM (BidirEctional SOM) SOM SOM BESOM SAM BESOM

(self-organizing map, SOM)[2] SOM SOM

5.2

SOM [4] [31][40]

BESOM

BESOM

5.1 5.4

6 28

BESOM

SOM SOM

Node

Unit

U1

...

Uk

X

... U m

Node

X

SOM

Y1

...

Yl

... Yn

Node

Yl

5.1: BESOM

X xi 5.4

l l l l wij wij + i (vj - wij )

Yl

l yj

l wij

(5.1)

ai 1/n BESOM BESOM 1 xi

xi

n ai

i i /(1 + i ) SOM 5.1

l wij

(5.2)

l P (Yl = yj |X = xi )

A.1

5.3

SOM X Yl (l = 1, · · · , n) SOM

l yi

5.4

Yl l BEL(yi ) vl

l l 1 (if BEL(yj ) = maxi BEL(yi )) 0 (otherwise)

Yl

l vj =

5.4.1

5.2 X P (X|U1 , ..., Um ) m

29

BESOM

SOM

5.1: BESOM SOM

U1

...

xi

Uk

...

Um

X

Y1

...

Yl

...

Yn

Y1

Y2

Y3

5.3:

v3 = (0, 0, 0, 0, 1)T

v1 = (0, 0, 1, 0, 0)T v2=(0, 1, 0, 0, 0)T

X

Yl Yl

Yl (x) Yl (x)

5.2: 5.3 [31] BESOM OR model [4] noisy-

X SOM P (X|U1 , · · · , Um )

i

P (X|Ui )

(5.3)

(5.3)

5.4.2

3.7 Yl (x) X (uk )

30

t t+1 (x) = ZYl + Yl yl n

t (yl )P (yl |x)

lt+1 = z t + W XY ot Y Y XY

t+1

(x) =

l=1

t+1 (x) Yl P (x|uk )BEL (uk )

t uk m

ot+1 = X

Y children(X)

lt+1 XY

t+1 (x) Uk

=

kt+1 = W T bt UX U UX pt+1 = X

Uparents(X)

kt+1 UX

t+1 (x) =

k=1

t+1 (x) Uk

rt+1 = ot+1 pt+1 X X X

t+1 ZX = i t+1 (rX )i (= rt+1 X 1

t+1 (x) = t+1 (x) t+1 (x)

t+1 ZX = x t+1 BELt+1 (x) = t+1 (x)/ZX

= ot+1 · pt+1 ) X X

t+1 (x)

t+1 t+1 t+1 z t+1 = (ZX , ZX , · · · , ZX )T X t+1 bt+1 = (1/ZX )r t+1 X X

5.4: x y = (x1 y1 , x2 y2 , · · · , xn yn )T 5.6:

U1

...

xi

Uk

...

Um

BELt(uk) t(yl), ZYlt

Yl

ZX X

BEL(x) Yl (x) ZX

Y1

...

...

Yn

5.5: (5.3)

5.4.3

Yl (x) X (uk ) = 1

uk

Uk (x)

(5.4) 5.4 A.2 (yl )

5.4.4

ZYl 5.5 (yl ) Uk (x) BEL(x)

BEL(uk ) (x), BEL(x), ZX loopy

5.4 5.6

T t, t + 1 t

31

t+1 bX XY lXY WXY

X UX BESOM s WXY X s×s lXY , oX , s s× n

Y ZX kUX , pX , rX , z X , bX 5.9 pX , rX , bX xi wij WXY i lXY Y yj X j kXY P (Y = yj |X = xi )

i

lXY , oX , kUX , X WXY WXY xi BESOM

5.4.6

BESOM

WXY oX (observation ) rX bX (belief ) ) pX (prediction

5.5

5.5.1

5.4.5

BESOM s m, n s m, n [30]

[29]

1

6

1

32

I II III IV V VI Higher areas Lower areas

U (x)

k

X ( yl ) Y (x) BEL(x)

l

X (uk )

BEL(u k )

(x)

( yl )

Z Yl

ZX

I II III IV V VI

Higher areas

Lower areas

5.7:

5.8:

5.7

5.6

5.6.1 5.5.2

noisy-OR model

5.8 Uk (x) ZX BEL(x)

5.6.2

5.3 SOM

SOM 2.5 5.9 Yl (x) (x) (x) BEL(X) 8 5.9 (1) (2) (3) 2.5 SOM 6.6.2 6 SOM Selective Attention Model (SAM)[19] SOM

33

1 BEL(U 1 = u1 )

BEL(U 1 = u1 ) 2

1 BEL(U 1 = u3 )

I

+

U ( X = x1 )

1

BEL(U 2 = u )

2 1 2 BEL(U 2 = u2 ) 2 BEL(U 2 = u3 )

+ + +

U ( X = x2 )

1

U ( X = x1 )

2

+ +

U ( X = x2 )

2

II

U1

U2

( X = x1 )

( X = x1 )

( X = x2 ) ( X = x1 )

1

( X = x2 ) Y ( X = x2 )

( X = x2 )

Z Y1

1 (Y1 = y1 )

III

(Y1 = y1 ) 2

Y ( X = x1 )

1

X

Y1 Y2

+

Y ( X = x1 )

2

+

Y ( X = x2 )

2

1 (Y1 = y3 )

+

+

Z Y2

(Y2 = y )

2 1 2 (Y2 = y2 )

IV V VI

/

ZX

BEL( X = x1 )

/

BEL( X = x2 )

2 (Y2 = y3 )

+

( X = x1 ) ( X = x2 )

ZX BEL( X = x1 ) BEL( X = x2 )

The left circuit calculates values of two units, x1 and x2, in node X in the above network.

5.9: BESOM

34

5.6.6

[2]

5.6.7 5.6.3

MOSAIC [41] (NMF)[9] BESOM MOSAIC NMF

5.6.8

BESOM

5.6.4

[42] p. 471

5.6.9

11.1

5.6.5

BESOM loopy

35

5.6.10

1.

5.9 2.

X-cell, Y-cell 4c, 4ab X-cell, Y-cell 3.

5.6.11

5.6.14

5.6.12

(5.1)

5.6.13

BESOM

36

5.6.15

BESOM

37

5

6

1.

2.

(ICA)

BESOM (ICA) ICA

6.2

ICA

6.2.1

ICA[7]

6.1

ICA

[8] ICA [7] 21

ICA TE [3] 1mm 5

[33]

38

ICA

6.2.2

...

6.1

6.1:

y1

y2

y3

x1

x2

x3

6.2:

6.2.1 ICA

6.2.3

ICA

6.3 ICA

BESOM [8][36][37] ICA

39

Source signal

xi = f i ( y1 , y2 , y3 )

Input signal

ICA

6.2

ICA BESOM

y1

y2

y3

x1

x2

x3 Other retinal areas or modalities.

6.5:

6.3

6.3:

BESOM

BESOM

6.3.1

SOM [34] ICA

6.5

SOM

n n SOM

O(2n )

6.4:

6.3.2

[36] ICA SOM 6.4 SOM

40

6.4

Basis Node

B3-1

...

B2-1 B2-2

...

...

B1-2 B1-3

SOM O(ns) O(n2 s2 )

n

s

B1-1

...

...

6.6:

6.3.3

ICA SOM ICA

SOM 6.7: ICA

[17]

...

6.4

6.2.1 6.8:

41

6.4.3 6.4.1

2.3 [39] 2.3

6.5

6.5.1

2.3

6.6 (basis)

B2-1

B1-1

6.4.2

fixation neuron passive visual neuron

1

B1-1

B1-2

6.5.2

1

[38]

p.124

42

6.7

6.8

1.

2.

6.5.3

ICA

SOM

6.5.4

n n

6.5.5

6.5.6

43

n

6.6.2

[6] 1. n

2. 6.3 [36]

3

3. n

2n

2n n s

n

s

6.5.7

[15]

6.6

6.6.1

2

2

[7] p.342

3

[28]

p.542

44

7

BESOM

9

7.1

[21] SOM (s,a) a s

7.1: [5]

Q

Q

BESOM [21] [22]

s

Q

Q

Q

Q

a

s

Q

a

[22]

Q

Q

(s,a)

7.2

BESOM 7.2:

45

7.2

7.3:

(M1)

[45] 1.

7.3 2.

3. M1 M1

Q-KOHONEN

[44] M1

7.2

7.3

( (M1) (PM) ) (M1) (9/46 )

46

a 7.2

7.2

s

M1

47?

s

a

9/46

PM/SMA

a s

PM/SMA PM/SMA

PM

SMA

a

M1 M1 M1 M1 M1 M1

s

s

as

a

MI

7.4:

7.5: (M1)

(PM)

(SMA)

SMA [23] SOM 7.4 M1 PM M1 PM

PM 7.1

[24]

7.5

7.5.1

7.4

(SMA) 7.5 47 PM

sarsa

1.

1

2.

3.

7.5.2

1. 2.

3.

7.5.3

[13]

BESOM (s, a)

sarsa[11]

Q(s, a) Q(s, a) + (s, a)[r + Q(s , a ) - Q(s, a)](7.1) (7.2) (s, a) s s a a Q(s, a)

7.5.4

(s, a) (s, a)/(1 + (s, a)) sarsa

12.2.1

7.6

1

7.6.1

[11] (p.166)

7.2

48

[11]

7.6.2

[11]

2

O(n)

O(1)

7.6.3 7.6.4

BESOM Q(s1,a1), Q(s2,a2), BESOM Q(s2,a3) 3:2:2 a1 s2 a2 a3

2

Q-KOHONEN

[44]

49

7.6.5

[43]

7.6.6

t

t

t BESOM 5.6.7 200msec t 5Hz

50

8

BESOM [46][47] BESOM

8.1

BESOM

1. 2. 3.

BESOM

8.2

5.5.2 [29]

5

4.6

8.3

51

9

9.1

9.1.1

· · · · ·

(s, a) (s, p, a) p (s,p,a) t-1 s a (s,p,a) (s,a)

s p a

s

a

s' 9.1:

[5]

(s,p,a)

(s,a)

(s,p,a)

(s,a)

9.1.2

s p a s p a

9.1 9.2

1.

2.

(s,p,a) (s,a)

(s,p,a)

(s,a)

s

p

a

s

p

a

BESOM

3.

4.

9.2: s a

52

9.1.3

9.4

9.4.1

9.1.4

9.4.2

[5]

6.5.2

9.2

(s,p,a), (s,a),s,a 10 [25] 9/46

9.4.3

9.2

9.3

9.2 11.2.3

53

PATON [14]

10

10.1

BESOM 11.3

PATON

10.3

BESOM

is-a

is-a

BESOM

BESOM

is-a

10.4

is-a is-a BESOM

10.2

BESOM

BESOM

is-a

is-a

is-a

10.5

10.5.1

10.1:

54

55

11

1/2 X=Y=1 X=Y=0

11.2.2

BESOM

BESOM

11.1

BESOM loopy

BESOM

11.2.3

BESOM

11.2

11.2.1 11.2.4

X Z 0 X xor Y X=Y=0 Y Z= X=Y=1

Z=0 P(X=0)=P(X=1)=P(Y=0)=P(Y=1)=1/2

56

11.3

· BESOM

· BESOM BESOM

11.4

·

·

5W1H

what, who how

where when

why

where when

11.5

5W1H

11.6

1. 2. BESOM

·

57

12.2.1

11.7

1

11.7.1

BESOM

11.7.2

[45](p.100)

2

11.7.3

1 2

BESOM

·

58

11.8

11/12

[26]

s v

a (s,a,v)

59

12.1.3

12

n BESOM

O(n)

O(log n)

12.1.4

12.1

12.1.1

1.5.3

BESOM

12.1.2

60

12.1.5

12.1.6

7.5

12.2

12.2.2

5.4

12.2.1

6

61

13

13.2

100TFLOPS

13.1

BESOM

10 100TFLOPS 1byte 100TFLOPS 2007 10Tbytes 10Tbytes

13.3

13.1

62

·

13.1:

13.4

13.5

13.6

1. · · · · · 2. · ·

63

=

k uk

P (x|uk )X (uk )

u1 ,···,um /uk i=k

X (ui )

A

=

k uk

P (x|uk )X (uk )

Yl (x) Yl (x) = (x)

j=l

Yj (x)

(x)

Yj (x)

j

A.1

X n wij (n) yj ai = 1/n n>1 wij (n) wij (n) = wij (n - 1) + i (vj (n) - wij (n - 1)) = (1 - i )wij (n - 1) + i vj (n) = ((n - 1)wij (n - 1) + vj (n))/n = ((n - 1)(m(n - 1)/(n - 1)) + vj (n))/n = (m(n - 1) + vj (n))/n = m(n)/n xi yj P (Y = yj |X = xi ) (A.1) = = X Y vj (n) {0, 1} n Y m(n) = i=1 vj (i) wij (1) = vj (1) = m(1)

n

xi n

= (x)(x)

u1 ,···,um /uk

P (x|u1 , · · · , um )

i=k

X (ui )

P (x|u1 , · · · , um )

u1 ,···,um /uk i=k

X (ui ) X (ui )

i=k

wij (n - 1) = m(n - 1)/(n - 1)

(

u1 ,···,um /uk j=k

P (x|uj ) + P (x|uk ))

P (x|uj )

u1 ,···,um /uk j=k i=k

X (ui ) X (ui )

+P (x|uk )

u1 ,···,um /uk i=k

P (x|uj )

u1 ,···,um j i

X (ui ) + P (x|uk )

A.2

= (x) + P (x|uk ) X (uk )

(x) (x) =

u1 ,···,um

X (uk ) =

x

(x)

u1 ,···,um /uk

P (x|u1 , · · · , um )

i=k

X (ui )

P (x|u1 , · · · , um )

i

X (ui )

x

(x)((x) + P (x|uk ))

u1 ,···,um

(

k

P (x|uk ))

i

X (ui ) =

x

(x)(x) +

x

(x)P (x|uk ) 5.4

=

u1 ,···,um k

P (x|uk )

i

X (ui )

64

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