α 2

1.1 α α θ θ α β θ α γ 1

α 2

3

4

5

6

A 1P1 A2P1 A 3P1 7

8

9

10

Contrast L L max mn = Lmax + Lmn L L max mn β tan β = a b β = 3450 a b β = 57. 3 a b 11

12

13

14

α 15

16

17

Ω 18

2.3.2 20 20 O C O C 19

( ) k s k ( ) x k k k n ( ) ( ) ( ) x k = s k n k + N N N 1 x( k ) = x ( k ) N ( ) k x k n = 1 ( ) ( ) N 1 [ = = N =1 E x ( k )] E x ( k ) s( k ) ( ) ( ) s k x k 20

var N 1 = N 1 = [ x ( k )] E n ( k ) = var [ n ( k )] 2 1 N N 鷄 21

1 2 1 2 N N X ] = [ x1, x2, L, x n [ s, s, ] 2 S =, 1 L s n x 1 s 1 x 2 s 2 = A M M x n s n X = A S A n n S ~ X S = W X S ~ 22

s s M s 1 2 n ~ s ~ s M ~ s 1 2 n = W x x M x 1 2 n S S ~ = W X 1 W A S ~ S ~ S S X S ~ ICA ICA 23

X Correlated Z Uncorrelated ICA S ~ Independent 24

X [ ] Xˆ = X E X Xˆ [ ] [ ] 1 [ E S] A E[ X ] E X = E A S = X A A 1 E X E[ ZZ ] = I [ ] X V Z = V X Z 25

[ ] [ ] [ ] P y1 y2 = P y1 P y2 P E [( y1 µ y1)( y2 µ y2 ) ] = E[ y1 y2 ] µ y1µ y2 = 0 E[( y µ )( y µ ) ] I µ y y = E [( y1 µ y1)( y2 µ y2 ) ] = E[ y1 y2 ] µ y1µ y2 = 0 E [( y1 µ y1)( y2 µ y2 ) ] = E[ y1 y2 ] µ y1µ y2 0 Y y1 y 2 X [ ] [ ] E Z = V E X 26

ICA G( y ) J ( y ) c{ E[ G( y )] E[ G( v) ]} 2 ( y ) ( ) c v G G ( ) y G G y 1 = 1 a 1 2 ( y ) log( ( a )) G1 cosh 1 y a1 G 2 y ( ) = y exp 2 2 ( ) y 4 ( y ) y G = 3 y y = w Z J G ( w ) { E[ G( w Z )] E[ G() v ]} 2 E[ G( w Z)] E[ G( w Z)] 27

( w ) E[ Zg( w Z)] w = 0 F β = = 2 2 E[( w Z) ] w = 1 ( ) ( ) β g y = g w Z ( y ) ( a ) g1 tanh 1 y g 2 = 1 a 1 2 y ( ) = y y exp 2 2 F( w ) ( ) 3 ( y ) y g = 3 JF JF w ( w ) ( w ) = E[ ZZ g ( w Z )] βi F = w g ( y ) g1 ( y ) = tanh( a1 y ) 1 a 1 2 g 2 2 ( ) = ( ) y 1 exp y 2 g = 2 ( y ) y 3 3 y 2 Newton s method w = F JF ( w ) ( w ) 28

JF( w ) E[ ZZ g ( w Z)] E[ ZZ ] E[ g ( w Z)] = E[ g ( w Z)] I ( JF w ) { E g ( w Z)] }I [ β w w + = w + w = w E[ Zg( w E[ g ( w Z)] βw Z)] β w * = w w + + β β E[ g ( w Z)] + w = E[ Zg( w Z)] E[ g ( w Z)] w w * = w w + + w w w w w + w = 1 w 29

P wp wp 1 j= 1 ( w w ) w j P j X Xˆ wp w P E[ Zg( wp Z)] E[ g ( wp Z)] w P P w w 1 j= 1 P P ( P j ) j w w w wp wp w P w P 3.3 VEP 30

X 32 (500 100) W U U = W X 32 (500 100) 32 32 32 (500 100) 1 X 32 (500 100) = W32 32 U 32 (500 100) W 1 1 W U U r xy = S S x xy S y = N ( x x)( y y) 2 ( x x) = 1 N = 1 N = 1 ( y y) 2 1 r 1 x 1, x2, L, xn y 1, y2, L, yn x y S x S y S xy 31

20 15 10 IV VI Oz Ampltude(uV) 5 0-5 V V II -10 III -15-20 0 50 100 150 200 250 300 350 400 450 500 Latency(m sec) 32

33

34

III-IV-V 35

III-IV-V III-IV-V III-IV-V ( ) ( ) 36

37

38

39

4-14 40

4-15 4-16 41

4-17 - - 5% + + 19% - - 9% + + 23% - + 33% - + 41% + - 43% + - 27% 42

( ) ( ) 4 5 9 6 7 9 1 2 43

44 ( ) ( )

4-21 45

4-22 4-23 Subject2004_0221 Average 18.11 18.52 18.87 17.4 14.79 14.7 SD 7.9 6.05 10.88 9.46 10.71 6.88 46

4-24 4-25 47

4-2 Subject2003_0212 Average 8.31 7.5 8.79 8.15 10.9 10.79 SD 4.98 3.91 4.78 4.17 7.43 6.26 4.98 3.91 4.78 4.17 7.43 6.26 48

4-27 4-28 4-4 4-27 4-28 Oz 139 Sorted rals 80 60 40 20-27.2-200 -100 0 100 200 300 400 me (ms) µv 27.2 70 0-70 -139 49

Oz 77.8 Sorted rals -34.7 µv 34.7 80 60 40 20-200 -100 0 100 200 300 400 me (ms) 38.9 0-38 -77 4-28 Subject2004_0302 (uv) 0.423 139-139 0.452 77.8-77.8 4- Subject2004_0302 0.423 0.452 139uV-139uV 77.8uV -77.8uV 4-29 4-30 4-5 4-29 4-30 50

Oz 62.3 Sorted rals µv 13-13 80 60 40 20-200 -100 0 100 200 300 400 me (ms) 31.2 0-31 -62 Sorted rals µv 16-16 80 60 40 20 Oz -200-100 0 100 200 300 400 me (ms) 20.6 10.3 0-10 -20 4-30 Subject2004_0413 (uv) 0.255 62.3-62.3 0.309 20.6-20.6 4-5 0.255 51

0.309 62.3uV-62.3uV 20.6uV-20.6uV 4-31 4-32 4-6 4-31 4-32 Oz 25.4 Sorted rals 80 60 40 20-17.8-200 -100 0 100 200 300 400 me (ms) µv 17.8 12.7 0-12 -25 Oz 25.8 Sorted rals 80 60 40 20-20.4-200 -100 0 100 200 300 400 me (ms) µv 20.4 12.9 0-12 -25 4-32 52

Subject2004_0419 (uv) 0.413 25.4-25.4 0.482 25.8-25.8 4-6 25.4uV -25.4uV 25.8uV-25.8uV 0.413 0.482 53

10 8 P2 subject20030212 1 Raw Average Data Average Com ponent 6 P3 Ampltude(uV) 4 2 P1 0-2 N3 N4 N2-4 0 50 100 150 200 250 300 350 400 450 500 Latency(msec) 54

55

56

57

58

59

60

α α α 61

62

歩 63

64

65

( 66

67

A 1. 2. 4. 5. 6. 7. 5K Ω b. 10. 11. 12. 68

B n [ ] C = E XX = EDE = d e e X = 1 d1 0 L 0 0 d 2 O 0 D = M O O M 0 0 L d n E E[ XX ] D E[ XX ] V 1/ 2 V = ED E 1/ D 2 d1 0 = M 0 1/ 2 d 0 1/ 2 2 O 0 L O O L 0 0 M 1/ 2 d n V E Z Z E E E = EE = I 2 1/ 2 E[ ZZ ] = VE[ XX ] V = ED 1/ E EDE ED E = I A A ~ ~ Z = V X = V ( AS) = A S A Y = W Z = W ~ ( A S ) = ( W V ) A S S 1 1 A = V W 69

C x 0 2 ( x) 0 = f ( x ) + f ( x )( x x ) O( h ) f = + 0 0 2 h = x x 0 ( O h ) f ( x ) f ( x )( x x ) 0 n 1 + n 1 n 1 = 0 2 ( O h ) x1 x0 x, f ( ) x g n ( ) ( )( ) ( ) ( ( )) n x n g x = f x x x + f x n n n n ( x) 0 g n 1 = xn x n = x n 1 f f ( xn 1 ) ( x ) n 1 x x n x n 1 ε ε ε 70