One Week Faculty Development Program on “Artificial Intelligence and Soft Computing Techniques” Under TEQIP Phase II th
nd
(28 April – 02 May 2015)
LAB MANUAL Organized by
Department of Computer Science & Engineering University Institute of Technology Rajiv Gandhi Proudyogiki Vishwavidhyalaya (State Technological University of Madhya Pradesh) Airport Road, Bhopal – 462033 Website: www.uitrgpv.ac.in
1
INDEX SNO.
LIST OF EXPERIMENTS
PAGE NO.
1.
WAP to implement Artificial Neural Network
2
2.
WAP to implement Activation Functions Functions
3
3.
WAP to implement Adaptive prediction prediction in ADALINE NN
5
4.
WAP to implement LMS and Perceptron Learning Rule
7
5.
WAP to implement ART NN
12
6.
WAP to implement BAM Network
14
7.
WAP to implement Full CPN with input pair
15
8.
WAP to implement discrete Hopfield Network
17
9.
WAP to implement Hebb Network
18
10.
WAP to implement Hetro associate neural net for mapping input vectors to output vectors
19
11.
WAP to implement Delta Learning Rule
20
12.
WAP to implement XOR function in MADALINE NN
22
13.
WAP to implement AND function in Perceptron NN
24
14.
WAP to implement Perceptron Network
26
15.
WAP to implement Feed Forward Network
32
16.
WAP to implement Instar learning Rule
38
17.
WAP to implement Weight vector Matrix
43
2
INDEX SNO.
LIST OF EXPERIMENTS
PAGE NO.
1.
WAP to implement Artificial Neural Network
2
2.
WAP to implement Activation Functions Functions
3
3.
WAP to implement Adaptive prediction prediction in ADALINE NN
5
4.
WAP to implement LMS and Perceptron Learning Rule
7
5.
WAP to implement ART NN
12
6.
WAP to implement BAM Network
14
7.
WAP to implement Full CPN with input pair
15
8.
WAP to implement discrete Hopfield Network
17
9.
WAP to implement Hebb Network
18
10.
WAP to implement Hetro associate neural net for mapping input vectors to output vectors
19
11.
WAP to implement Delta Learning Rule
20
12.
WAP to implement XOR function in MADALINE NN
22
13.
WAP to implement AND function in Perceptron NN
24
14.
WAP to implement Perceptron Network
26
15.
WAP to implement Feed Forward Network
32
16.
WAP to implement Instar learning Rule
38
17.
WAP to implement Weight vector Matrix
43
2
Experiment No. 1 AIM: WAP to implement Artificial Neural Network in MATLAB CODE: %Autoassociative net to store the vector clc; clear; x=[1 1 -1 -1]; w=zeros(4,4); w=x'*x; yin=x*w; for i=1:4 if yin(i)>0 y(i)=1; else y(i)=-1; end end disp('wieght matrix'); disp(w); if x==y disp('The vector is a known vector'); else disp('The vector is a unknown vector'); end
OUTPUT: Weight matrix 1
1
-1
-1
1
1
-1
-1
-1
-1
1
1
-1
-1
1
1
The vector is a known vector
3
Experiment No. 2 AIM: WAP to implement Activation Function in MATLAB CODE:
>> % Illustration of various activation functions used in NN's x=-10:0.1:10; tmp=exp(-x); y1=1./(1+tmp); y2=(1-tmp)./(1+tmp); y3=x; subplot(231); plot(x,y1); grid on; axis([min(x) max(x) -2 2]); title('Logistic Function'); xlabel('(a)'); axis('square') subplot(232);plot(x,y2); grid on; axis([min(x) max(x) -2 2]); title('Hyperbolic Tangent Function');qw xlabel('(b)'); axis('square'); subplot(233);plot(x,y3); grid on; axis([min(x) max(x) min(x) max(x)]); title('Identity Function'); xlabel('(c)'); axis('square');
4
OUTPUT:
Logistic Function
Hyperbolic Tangent Function 2 10
2 1
1
5
0
0
0
-1
-1
-5
-2 -10
0 (a)
10
-2 -10
0 (b)
10
-10 -10
Identity Function
0 (c)
10
5
Experiment No. 3 AIM: WAP to implement Adaptive Prediction in ADALINE Network CODE:
% Adaptive Prediction with Adaline clear; clc; %Input signal x(t) f1=2; %kHz ts=1/(40*f1); % 12.5 usec -- sampling time N=100; t1=(0:N)*4*ts; t2=(0:2*N)*ts+4*(N+1)*ts; t=[t1 t2]; %0 to 7.5 sec N=size(t,2); % N = 302 xt=[sin(2*pi*f1*t1) sin(2*pi*2*f1*t2)]; plot(t, xt), grid, title('Signal to be predicted') p=4; % Number of synapses % formation of the input matrix X of size p by N %use the convolution matrix. Try convmtx(1:8, 5) X = convmtx(xt, p) ; X=X(:,1:N); d=xt; % The target signal is equal to the input signal y=zeros(size(d)); % memory allocation for y eps=zeros(size(d)); % memory allocation for eps eta=0.4 ; %learning rate/gain w=rand(1, p) ; % Initialisation of weight vector for n=1:N % learning loop y(n)=w*X(:,n); %predicted output signal eps(n)=d(n)-y(n); %error signal w=w+eta*eps(n)*X(:,n)'; end figure(1) plot(t, d, 'b',t,y, '-r'), grid, ... title('target and predicted signals'), xlabel('time[sec]') figure(2) plot(t, eps), grid, title('prediction error'), xlabel('time[sec]')
6
OUTPUT: target and predicted signals 2
1.5
1
0.5
0
-0.5
-1
-1.5
0
1
2
3
4 time[sec]
5
6
7
8
5
6
7
8
prediction error 0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4 time[sec]
7
Experiment No. 4 AIM: WAP to implement LMS and Perceptron Learning rule CODE:
%For the following 2-class problem determine the decision boundaries %obtained by LMS and perceptron learning laws. % Class C1 : [-2 2]', [-2 3]', [-1 1]', [-1 4]', [0 0]', [0 1]', [0 2]', % [0 3]' and [1 1]' % Class C2 : [ 1 0]', [2 1]', [3 -1]', [3 1]', [3 2]', [4 -2]', [4 1]', % [5 -1]' and [5 0]' clear; inp=[-2 -2 -1 -1 0 0 0 0 1 1 2 3 3 3 4 4 5 5;2 3 1 4 0 1 2 3 1 0 1 -1 1 2 -2 1 -1 0]; out=[1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0]; choice=input('1: Perceptron Learning Law\n2: LMS Learning Law\n Enter your choice :'); switch choice case 1 network=newp([-2 5;-2 4],1); network=init(network); y=sim(network,inp); figure,plot(inp,out,inp,y,'o'),title('Before Training'); axis([-10 20 -2.0 2.0]); network.trainParam.epochs = 20; network=train(network,inp,out); y=sim(network,inp); figure,plot(inp,out,inp,y,'o'),title('After Training'); axis([-10 20 -2.0 2.0]); display('Final weight vector and bias values : \n'); Weights=network.iw{1}; Bias=network.b{1}; Weights Bias Actual_Desired=[y' out']; Actual_Desired case 2 network=newlin([-2 5;-2 4],1); network=init(network); y=sim(network,inp); network=adapt(network,inp,out); y=sim(network,inp); display('Final weight vector and bias values : \n'); Weights=network.iw{1}; Bias=network.b{1}; 8
Weights Bias Actual_Desired=[y' out']; Actual_Desired otherwise error('Wrong Choice'); end OUTPUT: 1: Perceptron Learning Law 2: LMS Learning Law Enter your choice :1
Final weight vector and bias values : \n
Weights =
-1
1
Bias =
0
Actual_Desired =
1
1 9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
Before Training 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -10
-5
0
5
10
15
20
10
15
20
After Training 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -10
-5
0
5
11
Best Training Performance is 0.5 at epoch 0 0
Train Best
10
) -0.1 e 10 a m ( r -0.2 o r r 10 E e t u -0.3 l o 10 s b A n -0.4 a 10 e M -0.5
10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2 Epochs
12
Experiment No. 5 AIM: WAP to implement ART Neural Network CODE:
%ART Neural Net clc; clear; b=[0.57 0.0 0.3;0.0 0.0 0.3;0.0 0.57 0.3;0.0 0.47 0.3]; t=[1 1 0 0;1 0 0 1;1 1 1 1]; vp=0.4; L=2; x=[1 0 1 1]; s=x; ns=sum(s); y=x*b; con=1; while con for i=1:3 if y(i)==max(y) J=i; end end x=s.*t(J,:); nx=sum(x); if nx/ns >= vp b(:,J)=L*x(:)/(L-1+nx); t(J,:)=x(1,:); con=0; else y(J)=-1; con=1; end if y+1==0 con=0; end end disp('Top Down Weights'); disp(t); disp('Bottom up Weights'); disp(b);
13
OUTPUT: Top Down Weights 1 1 0 0 1 0 0 1 1 1 1 1 Bottom up Weights 0.5700 0.6667 0.3000 0 0 0.3000 0 0 0.3000 0 0.6667 0.3000
14
Experiment No. 6 AIM: WAP to implement BAM Network CODE:
%Bidirectional Associative Memory neural net clc; clear; s=[1 1 0;1 0 1]; t=[1 0;0 1]; x=2*s-1 y=2*t-1 w=zeros(3,2); for i=1:2 w=w+x(i,:)'*y(i,:); end disp('the calculated weight matrix'); disp(w); OUTPUT: x= 1 1
1 -1
-1 1
y= 1 -1
-1 1
the calculated weight matrix 0 0 2 -2 -2 2
15
Experiment No. 7 AIM: WAP to implement Full Counter Propagation Network with input pair CODE:
%Full Counter Propagation Network for given input pair clc; clear; %set initial weights v=[0.6 0.2;0.6 0.2;0.2 0.6;0.2 0.6]; w=[0.4 0.3;0.4 0.3;]; x=[0 1 1 0]; y=[1 0]; alpha=0.3; for j=1:2 D(j)=0; for i=1:4 D(j)=D(j)+(x(i)-v(i,j))^2; end for k=1:2 D(j)=D(j)+(y(k)-w(k,j))^2; end end for j=1:2 if D(j)==min(D) J=j; end end disp('After one step the weight matrix are'); v(:,J)=v(:,J)+alpha*(x'-v(:,J)) w(:,J)=w(:,J)+alpha*(y'-w(:,J))
16
OUTPUT: After one step the weight matrix are v= 0.4200
0.2000
0.7200
0.2000
0.4400
0.6000
0.1400
0.6000
w= 0.5800
0.3000
0.2800
0.3000
17
Experiment No. 8 AIM: WAP to implement Discrete Hopfield Network CODE:
% discrete hopfield net clc; clear; x=[1 1 1 0]; tx=[0 0 1 0]; w=(2*x'-1)*(2*x-1); for i=1:4 w(i,i)=0; end con=1; y=[0 0 1 0] while con up=[4 2 1 3]; for i= 1:4 yin(up(i))=tx(up(i))+y*w(1:4,up(i)); if yin(up(i))>0 y(up(i))=1; end end if y==x disp('convergence has been obtained'); disp('the convergence output'); disp(y); con=0; end end
OUTPUT: y= 0
0
1
0
convergence has been obtained the convergence output 1
1
1
0
18
Experiment No. 9 AIM: WAP to implement Hebb Network CODE:
%Hebb Net to classify two dimensional inputs patterns clear; clc; %Input Patterns E=[1 1 1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 1]; F=[1 1 1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1]; x(1,1:20)=E; x(2,1:20)=F; w(1:20)=0; t=[1 -1]; b=0; for i=1:2 w=w+x(i,1:20)*t(i); b=b+t(i); end disp('Weight matrix'); disp(w); disp('Bias'); disp(b); OUTPUT: Weight matrix Columns 1 through 12 0
0
0
0
0
0
0
0
2
2
0
0
0
0
Columns 13 through 20 0
0
0
0
0
2
Bias 0
19
Experiment No.10 AIM: WAP to implement Hetro associate neural net for mapping input vectors to output vectors CODE:
%Hetro associate neural net for mapping input vectors to output vectors clc; clear; x=[1 1 0 0;1 0 1 0;1 1 1 0;0 1 1 0]; t=[1 0;1 0;0 1;0 1]; w=zeros(4,2); for i=1:4 w=w+x(i,1:4)'*t(i,1:2); end disp('weight matrix'); disp(w);
OUTPUT: weight matrix 2
1
1
2
1
2
0
0
20
Experiment No. 11 AIM: WAP to implement Delta Learning Rule CODE:
% Determine the weights of a network with 4 input and 2 output units using % Delta Learning Law with f(x)=1/(1+exp(-x)) for the following input-output % pairs: % % Input: [1100]' [1001]' [0011]' [0110]' % output: [11]' [10]' [01]' [00]' % Discuss your results for different choices of the learning rate parameters. % Use suitable values for the initial weights. in=[1 1 0 0 -1;1 0 0 1 -1; 0 0 1 1 -1; 0 1 1 0 -1]; out=[1 1; 1 0; 0 1; 0 0]; eta=input('Enter the learning rate value = '); it=input('Enter the number of iterations required = '); wgt=input('Enter the weights,2 by 5 matrix(including weight for bias):\n'); for x=1:it for i=1:4 s1=0; s2=0; for j=1:5 s1=s1+in(i,j)*wgt(1,j); s2=s2+in(i,j)*wgt(2,j); end wi=eta*(out(i,1)-logsig(s1))*dlogsig(s1,logsig(s1))*in(i,:); wgt(1,:)=wgt(1,:)+wi; wi=eta*(out(i,2)-logsig(s2))*dlogsig(s2,logsig(s2))*in(i,:); wgt(2,:)=wgt(2,:)+wi; end end wgt
21
OUTPUT: Enter the learning rate value = 0.6 Enter the number of iterations required = 1 Enter the weights,2 by 5 matrix(including weight for bias): [1 2 1 3 1;1 0 1 0 2]
wgt =
1.0088
1.9508
0.9177
2.9757
1.0736
1.0476
0.0418
1.0420
0.0478
1.9104
22
Experiment No. 12 AIM: WAP to implement XOR function for MADALINE NN CODE:
%Madaline for XOR function clc; clear; %Input and Target x=[1 1 -1 -1;1 -1 1 -1]; t=[-1 1 1 -1]; %Assume initial weight matrix and bias w=[0.05 0.1;0.2 0.2]; b1=[0.3 0.15]; v=[0.5 0.5]; b2=0.5; con=1; alpha=0.5; epoch=0; while con con=0; for i=1:4 for j=1:2 zin(j)=b1(j)+x(1,i)+x(1,i)*w(1,j)+x(2,i)*w(2,j); if zin(j)>=0 z(j)=1; else z(j)=-1; end end yin=b2+z(1)*v(1)+z(2)*v(2); if yin>=0 y=1; else y=-1; end if y~=t(i) con=1; if t(i)==1 if abs(zin(1))>abs(zin(2)) k=2; else k=1; end b1(k)=b1(k)+alpha*(1-zin(k)); w(1:2,k)=w(1:2,k)+alpha*(1-zin(k))*x(1:2,i);else 23
for k=1:2 if zin(k)>0; b1(k)=b1(k)+alpha*(-1-zin(k)); w(1:2,k)=w(1:2,k)+alpha*(-1-zin(k))*x(1:2,i); end end end end end epoch=epoch+1; end disp('weight matrix of hidden layer'); disp(w); disp('Bias of hidden layer'); disp(b1); disp('Total Epoch'); disp(epoch);
OUTPUT: weight matrix of hidden layer 0.2812 -2.1031 -0.6937
0.9719
Bias of hidden layer -1.3562 -1.6406
Total Epoch 3
24
Experiment No. 13 AIM: WAP to implement AND function in Perceptron NN CODE:
%Perceptron for AND function clear; clc; x=[1 1 -1 -1;1 -1 1 -1]; t=[1 -1 -1 -1]; w=[0 0]; b=0; alpha=input('Enter Learning rate='); theta=input('Enter Threshold value'); con=1; epoch=0; while con con=0; for i=1:4 yin=b+x(1,i)*w(1)+x(2,i)*w(2); if yin>theta; y=1; end if yin<=theta & yin>=-theta y=0; end if yin<-theta y=-1; end if y-t(i) con=1; for j=1:2 w(j)=w(j)+alpha*t(i)*x(j,i); end b=b+alpha*t(i); end end epoch=epoch+1; end disp('Perceptron for AND function'); disp('Final weight matrix'); disp(w); disp('Final Bias'); disp(b);
25
OUTPUT: Enter Learning rate=0.6 Enter Threshold value0.8 Perceptron for AND function Final weight matrix 1.2000
1.2000
Final Bias -1.2000
26
Experiment No. 14 AIM: WAP to implement Perceptron Network CODE:
clear; clc; p1=[1 1]';p2=[1 2]'; p3=[-2 -1]';p4=[2 -2]'; p5=[-1 2]';p6=[-2 -1]'; p7=[-1 -1]';p8=[-2 -2]'; % define the input matrix , which is also a target matrix for auto % association P=[p1 p2 p3 p4 p5 p6 p7 p8]; %we will initialize the network to zero initial weights net= newlin([min(min(P)) max(max(P)); min(min(P)) max(max(P))],2); weights = net.iw{1,1} %set training goal (zero error) net.trainParam.goal=0.0; %number of epochs net.trainParam.epochs=400; [net, tr]= train(net,P,P); %target matrix T=P %default training function is Widrow-Hoff Learning for newlin defined %weights and bias after the training W=net.iw{1,1} B=net.b{1} Y=sim(net,P); %Haming like distance criterion criterion=sum(sum(abs(P-Y)')') %calculate and plot the errors rs=Y-P; legend(['criterion=' num2str(criterion)]) figure plot(rs(1,:),rs(2,:),'k*') test=P+rand(size(P))/10; %let's add some noise in the input and test the networkagain Ytest=sim(net,test); criteriontest=sum(sum(abs(P-Ytest)')') figure output=Ytest-P %plot errors in the output plot(output(1,:),output(2,:),'k*')
27
OUTPUT: weights =
0
0
0
0
W= 1.0000 -0.0000 -0.0000
1.0000
B= 1.0e-12 * -0.1682 -0.0100 criterion = 1.2085e-12 Warning: Plot empty. > In legend at 287 criteriontest = 0.9751 output = Columns 1 through 7 0.0815
0.0127
0.0632
0.0278
0.0958
0.0158
0.0957
0.0906
0.0913
0.0098
0.0547
0.0965
0.0971
0.0485
Column 8 0.0800 0.0142 28
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-15
-2
x 10
-4
-6
-8
-10
-12
-14
-16 -3
-2.5
-2
-1.5
-1
-0.5 -13
x 10
29
0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Best Training Performance is 1.3086e-26 at epoch 400 0
10
Train Best
) 10-5 e s m (
r -10 o 10 r r E d e r a -15 u 10 q S n a e -20 M10
-25
10
0
50
100
150
200
250
300
350
400
400 Epochs 30
Validation Checks = 0, at epoch 400 1 0.8 0.6 0.4 0.2 l i a f l a v
0 -0.2 -0.4 -0.6 -0.8 -1
0
50
100
150
200 250 400 Epochs
300
350
400
31
Training: R=0.97897 50
Validation: R=0.92226 50
Data
1 . 1
Fit
+ t40 e g r a T *30 5 9 .
Data
4 . 1
Fit
+ t40 e g r a T *30 1 9 .
Y=T
0
Y=T
0
= 20 ~ t u p t u 10 O
= 20 ~ t u p t u 10 O
10
50
20
30
40
50
30
40
Test: R=0.90828
All: R=0.96404 50
Fit
+ t40 e g r a T *30 4 9 .
Y=T
0
50
Data
1 . 1
Fit
+ t40 e g r a T *30 1 9 .
20
Target
Data
5 . 1
10
Target
Y=T
0
= 20 ~ t u p t u 10 O
= 20 ~ t u p t u 10 O
10
20
30
Target
40
50
10
20
30
40
50
Target
32
Experiment No.15 AIM: WAP to implement feed forward network CODE:
% a)Design and Train a feedforward network for the following problem: % Parity: Consider a 4-input and 1-output problem, where the output should be % 'one' if there are odd number of 1s in the input pattern and 'zero' % other-wise. clear inp=[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1;0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1;... 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1;0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1]; out=[0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0]; network=newff([0 1;0 1; 0 1; 0 1],[6 1],{'logsig','logsig'}); network=init(network); y=sim(network,inp); figure,plot(inp,out,inp,y,'o'),title('Before Training'); axis([-5 5 -2.0 2.0]); network.trainParam.epochs = 500; network=train(network,inp,out); y=sim(network,inp); figure,plot(inp,out,inp,y,'o'),title('After Training'); axis([-5 5 -2.0 2.0]); Layer1_Weights=network.iw{1}; Layer1_Bias=network.b{1}; Layer2_Weights=network.lw{2}; Layer2_Bias=network.b{2}; Layer1_Weights Layer1_Bias Layer2_Weights Layer2_Bias Actual_Desired=[y' out']; Actual_Desired OUTPUT: Layer1_Weights =
1.0765
2.1119
2.6920
2.3388
-10.4592 -10.9392 10.0824 10.9071 6.0739
9.4600 -5.3666 -5.9492 33
-6.0494 -18.5892 -5.9393
5.6923
-2.5863 -1.7445 -11.6903
3.7168
10.7251 -10.5659
9.8250 -10.4745
Layer1_Bias =
-16.0634 5.4848 9.5144 9.6231 7.4340 5.7091
Layer2_Weights =
-2.5967 -23.3294 15.7618 23.4261 -22.5208 -23.3569
Layer2_Bias =
18.4268
34
Actual_Desired =
0.0000
0
1.0000
1.0000
0.9999
1.0000
0.0000
0
1.0000
1.0000
0.0000
0
0.0000
0
0.9998
1.0000
1.0000
1.0000
0.0000
0
0.0000
0
0.9999
1.0000
0.0000
0
1.0000
1.0000
1.0000
1.0000
0.0000
0
35
Before Training 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -5
-4
-3
-2
-1
0
1
2
3
4
5
1
2
3
4
5
After Training 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -5
-4
-3
-2
-1
0
36
Best Training Performance is 3.3016e-09 at epoch 26
0
10
Train Best ) 10-2 e s m ( r o r r -4 E 10 d e r a u q -6 S 10 n a e M -8
10
0
5
10
15
20
25
26 Epochs
37
10 t n e i d a r g
10 10
10
Gradient = 1.9837e-08, at epoch 26
0
-5
-10
Mu = 1e-13, at epoch 26
0
u 10-10 m
10
-20
Validation Checks = 0, at epoch 26 1 l i a f l a v
0 -1
0
5
10
15 26 Epochs
20
25
Training: R=1 1 Data 0.9
Fit Y = T
0.8
5 0 e 0.7 6 . 1 + 0.6 t e g r a 0.5 T * 1 = 0.4 ~ t u p 0.3 t u O 0.2
0.1
0 0
0.2
0.4
0.6
0.8
1
Target 38
Experiment No. 16 AIM: WAP to implement Instar learning Rule CODE:
% Using the Instar learning law, group all the sixteen possible binary % vectors of length 4 into four different groups. Use suitable values for % the initial weights and for the learning rate parameter. Use a 4-unit % input and 4-unit output network. Select random initial weights in the % range [0,1] in=[0 0 0 0;0 0 0 1;0 0 1 0;0 0 1 1;0 1 0 0;0 1 0 1;0 1 1 0;0 1 1 1;1 0 0 0;1 0 0 1;1 0 1 0;1 0 1 1;1 1 0 0;1 1 0 1;1 1 1 0;1 1 1 1]; wgt=[0.4 0.1 0.2 0.7; 0.9 0.7 0.4 0.7; 0.1 0.2 0.9 0.8 ; 0.5 0.6 0.7 0.6]; eta=0.5; it=3000; for t=1:it for i=1:16 for j=1:4 w(j)=in(i,:)*wgt(j,:)'; end [v c]=max(w); wgt(c,:)=wgt(c,:)+eta*(in(i,:)-wgt(c,:)); k=power(wgt(c,:),2); f=sqrt(sum(k)); wgt(c,:)=wgt(c,:)/f; end end for i=1:16 for j=1:4 w(j)=in(i,:)*wgt(j,:)'; end [v c]=max(w); if(v==0) c=4; end s=['Input= ' int2str(in(i,:)) ' Group= ' int2str(c)]; display(s); end wgt
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OUTPUT: s=
Input= 0 0 0 0 Group= 4
s=
Input= 0 0 0 1 Group= 1
s=
Input= 0 0 1 0 Group= 3
s=
Input= 0 0 1 1 Group= 3
s=
Input= 0 1 0 0 Group= 2
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s=
Input= 0 1 0 1 Group= 4
s=
Input= 0 1 1 0 Group= 2
s=
Input= 0 1 1 1 Group= 4
s=
Input= 1 0 0 0 Group= 1
s=
Input= 1 0 0 1 Group= 1
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s=
Input= 1 0 1 0 Group= 3
s=
Input= 1 0 1 1 Group= 3
s=
Input= 1 1 0 0 Group= 2
s=
Input= 1 1 0 1 Group= 1
s=
Input= 1 1 1 0 Group= 2
42
s=
Input= 1 1 1 1 Group= 4
wgt =
0.6548
0.4318
0.0000
0.6203
0.5646
0.6819
0.4651
0.0000
0.5646
0.0000
0.6819
0.4651
0.3877
0.5322
0.5322
0.5322
43
