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3.1 Perception 3.2 3.3 BP3.4 (BP)3.5 (GA)3.6

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3.7 3.8 3.9

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3.1 Perception 3.1.1 3.1.2 3.1.3 3.1.4

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3.1.1 X=X1,X2,,XmY=(Y1,Y2,,Yn) XRn, WRnY{1,-1} X= (X,-1),W= (W,)

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w21wmjw22wmnw12w11xmx1x2w1nw2mwmjwijw2jw1jyjxix1x2xm 3.1 3.2 wm1

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Wn+1=, Xn+1=-1, Wi(0)Wi(t)ti1in,Wn+1(t)t X=(X1,X2,,Xn,T),T XAT=1XBT=-1

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Wi(t+1)= Wi(t)+(T-Y(t))Xi i=(1,2,,n,n+1) 0

Y=W1X1+W2X2- 3.1

000011101110

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W1+W2-

3.1.2 XYWf fRn {1,-1}, XRn, f X1W1+X2W2+X3W3= X1W1+X2W2+(X1X2)W3=

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3.2

0000010110011110

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3.4

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3.1 f (1)Xk=1() (2)Yk0(f)

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kW*kW*Xk> >0 t=1W(t)0 k{1,N}X(t)=Xk W(t)X(t)0 W(t+1)=W(t)+X(t),t=t+1,

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C(t)W(t)W*

W*W(t+1)=W*[W(t)+X(t)]=W*W(t)+W*X(t)W*W(t)+ W*W(t)tW(t+1)2=W(t)2+2W(t)X(t)+X(t)2

3.1.3 nn1n2 (j=1,2,,n1) (k=1,2,,n2)

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(A) 3.5

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3.2 3.5(B)

nn1nnn=2n1=3j (j=1,2,3)

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(B) 3.5

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Wijj3.6(A)AB 3.6(B)

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Y2={(X1,X2)[(W11X1+W21 X2 -1)>0(W12 X1+ W22 X2- 2)>0(W13 X1+W23 X2-3)>0]} Y3={(X1,X2)[Y12Y22]} 3 6 ={(X1,X2)[((W1jX1+W2j X2 -j )>0)((W1j X1 j=1 j=4 +W2j X2- j )>0)]}

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(A) (B) 3.6

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Y11=1X1+1 X2-1 Y21=(-1) X1+(-1) X2-(-1.5) Y2=1 Y11+1 Y21-2

3.7

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3.8

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3.1.4 3.9

3.9

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u = W1X1+W2X2

(0.5, 0.05)(0.05, 0.5) A (0.95,0.5)(0.5,0.95) B

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W1(t+1)=W1(t)+(T-Y)X1 W2(t+1)=W2(t)+(T-Y)X2 (t+1)=(t)+(T-Y)

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3.3 (a) 3.3 (b)

X1X2YW0.200.500.050.990.100.050.500.99u00.200.950.500.010.400.50 0.95 0.010.300.01 200

140

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3.2 3.2.1 3.2.2 3.2.3

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3.2.1 XK TKK{1,2,,N}NXKRnTKRm

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3.12

140

140

(0

Sigmoid(-1,1)

( -1 < f(x)

3.4

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3.2.2 E (W) =g ( f ( W, XK, TK ) ),K=1,2,,NEYKTKNm

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(XK , TK) , (K=1,2,,N)W{XkRn}{YkRm} f XkRn YkRm

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mn2XK,TKW(W1,W2,.,W mn2)E(W)(mn2+1)mn2+1E (W) WE(W)E(W)E(W)

140

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3.2.3 E(W)W

N(XK, TK), K=(1,2,,N), XKYKiYiKijWijj

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140

1j

2j

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3.3 BP 3.3.1 BP3.3.2 BP

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3.3.1 BP Sigmoid

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Yi1i Yj2j Yk3k Tkk Wijij Wjkjk j j k k 3.14

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t=0Wij(t)[-1,1]Wjk(t)[-1,1],j(t)[-1,1], k(t)[-1,1] () XK,TK,K{1,2,,N}NXKRnTKRm

j{1,2,,n1}

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k{1,2,,m}

() k{1,2,,m}

kWjkkkjWjkk

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jWijjjiWijj EEEt = t+1

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WEYNNYYN3.15 BP

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3.153.16

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Memond(t-1)W(t-1)tW(t)MemondmMemond W (t+1) = W(t)+mW(t-1) tW(t)MemondW(t-1)W(t)Memond W (t+1) = W(t)+m(t)W(t-1) m(t) = m + m(t-1)

140

140

u0Memond m=0.9 memondm=0.6 m=0.02 0.55531 0.6 4743 0.7 63 61

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3.3.2 BP 3.4 (X)KRnf(X)=f(X1,X2,,Xn)K>0NCii(i=1,2,,N)Wij(i=1,2,,N;j=1,2,,n)

(3.3.16) >0(X)fRnRm

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BP 1 2 3

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4 5

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3.4 (BP) 3.4.1 BP 3.4.2 BP 3.4.3 BI(Back Impedance)

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3.4.1 BP 1

0.9 (t+1)(t)

- / (1- )

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2 =1.5 / =0.9 3 (0)(0)/(t+1) (t) = (0)/(t+1)

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4

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()

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3.4.2 BP 1 ij(0) ij(t)= ij(t-1) u

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u1/d1.11.30.7-0.9 2DeltaBarDelta DeltaBarDelta ij(0)

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(t)

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u(5.00.0950.0850.035)d (0.90.850.666)0.7u

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3.4.3 BI(Back Impedance) 1BI

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Wij(t+1)= Wij(t) + aj Yi + b(Wij(t) - Wij(t-1))+ c(Wij(t-1) - Wij(t-2)) abc abc a= 1 / (1+J+M+D) b= (2J+M) / (J+M+D) c= J / (J+M+D)

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JMD

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3.18

140

2

X=[0,1]ABCD=KX+PA=0.5, B=0.75, C=3, K=-5, P=12BI3.6 99.206%

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3.6

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3.5 (GA) GA(chromosome)(gene) (Population)(N)GA GA(fitness function)

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(Coding) (Selection) (Crossover)

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(Mutation) (1)NS (2)S

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(3)K(1

GA

3.20

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35164j (3.5.1) k (3.5.2) Sigmoid (3.5.3)

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GA 1. 35*16+16*4+16+4-1.0+1.0 2.

i=1,2,,Np=1,,4K=1,2,3,4Tk

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3. N=10K1 4. (1)10-1.0+1.0 (2)E(i)f (i)

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(3)PselC1C2 (4)PcrossC1C2C1' C2' (5)C1' C2'PmutC1'' C2'' (6)C1''C2''Ef (7)N+2K2K (8)E

3.22

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3.23

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3.24

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3.6 3.6.1 3.6.2

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3.6.1 mmxxjj

j10mlog2 m

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3.6.2 3.4 SI/O

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l1987HechtNielsenANN2N+1N

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21987RPLinnmannM2M H=log2T HT 31988Kuarycki31

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BP208Linnmann M2=82=16Kuarycki3M2=48 4ANN 1990NelsonIllingworth4NANN0.02N444=16646420

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5 LippmannM1(N+1) KuaryckiM13 A .J.Maren(M1N)1/2M1

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6 n K< C in1Kn1n i=1 i >n1 Cin1=0 mn110 n1=log2n n

140

BP

140

140

3.8

xk,wkRn,k k=w0k , x0=1

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3.44 Adaline

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1 XkRn XkRn+llXkxik i=1,2,,nn=2F1F2 F3 3.45(a) F1=x1k2 F2=x1kx2k F3=x2k2 yk Yk= wik xik+w11 F1+w12 F2+w22 F3 i=0 =w0k+x1kw1k+x2kw2k+w11x21k+w22x22k+ w12x1kx2k yk=0

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3.45aAdaline(b)XOR(c) AAND

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n 2n+C2n=2n+n(n-1) / 12 = (n2+3n) /2 2Madaline Adaline

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3.46 (a)Madaline (b)Madaline

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Adaline 1Adaline 2XkTk(3.8.1)Tk 30 4

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50 6 7 8MRIIAdalineLMS

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w(t0+1) w(t0)Xk(t0)(t0)t0 Xk(t0) +1-1X(t0)2 X(t0 )2=x12(t0 )+ x22(t0 )++ xn+12(t0 )=n+1 3.8.5(t0) (t0)=Tk(t0)-XT(t0)W(t0)

140

(t0)= [T(t0 )-XT(t0 )W(t0 )]=-XT(t0 )W(t0 ) W(t0 )=W(t0+1)-W(t0 )=( / Xk(t0 )2 )(t0 )X(t0 ) (t0)=- XTk(t0 ) [ / Xk(t0 )2] (t0) Xk(t0 )=- (t0) 1.0>>0.1

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3.9 3.9.1 3.9.2

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3.9.1 3.49

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3.9.2 b CK=| CK1 ,CK2 ,, CKn | K=1,2,N X

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Gauss f (x)=exp(-x2 / b)=exp(- 2K / b) Gaussb yK=f (K) j

Wj =[w1j ,w2j ,, wNj ] , Z=[z1 , z2 ,, zN ]

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3.50 Gauss

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RBFRBFbb RBF bwBP

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3.7 3.7.1

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3.7.1 2004l

140

3.26

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1 3.27(a)abcd (3.7.1)

l010

140

3.27 jl5

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2 ni5nij (j=1,,5)TiTin1Ti (1)niVij(j=1,,5)

j=15 (3.7.2) Ti kp,kp=1,,5(3.7.3)

140

(2) n1Vij'0.2Vij0.2Ti (3.7.4) Ti 3

140

3.28 2.29 (a)

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3.30

140

3.31

140

AC-l+lA'=A+0.5CAA'10003.32

140

3.32

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1

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3.13

00.196909O.2558330.257407O.1447570.18260810.2006180.2525650.2558010.1512540.18555720.4887890.3021450.6858840.7380451.01677230.2309640.2930880.2814020.1736100.204479220.2220850.2688120.2636200.1648590.186757230.3012080.3679700.3492080.2431080.271468240.6160160.6106360.3677400.5664090.321578

140

3.14

1000001000001000001000001

140

3.33

140

2 f(x)=1/(1+exp(-x/U0)) (3.7.5) (1)WjiVkjjk (2)1 (3) Uj= Wji Ii+ j (3.7.6) Hi=f(Uj) (3.7.7)

140

3.34

140

(4) Sk= Vkj Hj + k , Ok=f(Sk) (3.7.8) (5)TkOkkVkjk k : k=(Ok Tk) Ok (1Ok) (6)kVkjHjjWjij j : j=k Vk Hj (1- Hj) (3.7.9)

140

(7)kVkjjHjVkjkj Vkj= Wji + k Hi , k = k + k (3.7.10) (8)jWjijIiWjijj Wji= Wji+j Ii , j = j + j (3.7.11)

140

(9)E E= Ok - Tk (3.7.12) E(2)(3)

140

3.35

140

3

3.36

140

3.21

0.9520790.0221980.0213390.0204230.0l0000 0.0283280.9816660.0100000.0100000.0100000.0106780.0100000.9900000.0100000.0100000.0100000.0100000.0100000.9874710.0387660.0100000.0100000.0147230.0100000.990000

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1.(10000000) 2.(01000000) 3.(0099800) 4.(0009980) 5.(00001000)

140

3.37

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