Neural networks

 Program 1:

%Write a program to generate a few activation function that are being used in neural networks.

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 function');

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');

output:

Program 2:

%Generate ANDNOT function using Mcculloch-pits neural net by a %MATLAB program getting weights & threashold values

disp('Enter weight:');

w1=input('weight w1');

w2=input('weight w2');

disp('Enter your threashold value:');

theta=input('theta');

y=[0 0 0 0];

x1=[0 0 1 1];

x2=[0 1 0 1];

z=[0 0 1 0];

con=1;

while con

    zin=x1*w1+x2*w2;

    for i=1:4

        if zin(i)>=theta

            y(i)=1;

        else 

            y(i)=0;

        end

    end

    disp('Output of net');

    disp(y);

    if y==z

        con=0;

    else

            disp('Net is not learning. Enter another set of weights and threshold value');

            w1=input('weight w1=');

            w2=input('weight w2=');

            theta=input('theta=');

    end

            disp('mcculloch-pits net for ANDNOT function');

    end

Output:

Enter weight:

weight w1 1

weight w2 1

Enter your threashold value:

theta 0.1

Output of net

     0 1 1 1

Net is not learning. Enter another set of weights and threshold value

weight w1=1

weight w2=-1

theta=1

mcculoch-pits net for ANDNOT function

Output of net

     0 0 1 0

mcculoch-pits net for ANDNOT function

Program 3:

%Generate XOR function using Mcculloch-pits neuron by writing %an m-file.

clear;

clc;

disp('Enter weight:');

w11=input('weight w11');

w12=input('weight w12');

w21=input('weight w21');

w22=input('weight w22');

v1=input('weight v1');

v2=input('weight v2');

disp('Enter your threashold value:');

theta=input('theta'); 

x1=[0 0 1 1];

x2=[0 1 0 1];

z=[0 1 1 0];

con=1;

while con

    zin1=x1*w11+x2*w21;

    zin2=x1*w21+x2*w22;

    for i=1:4

        if zin1(i)>=theta

            y1(i)=1;

        else 

            y1(i)=0;

        end

        if zin2(i)>=theta

            y2(i)=1;

        else 

            y2(i)=0;

        end

    end

    yin=y1*v1+y2*v2;

    for i=1:4

        if yin(i)>=theta

            y(i)=1;

        else

            y(i)=0;

        end

    end

    disp('Output of net');

    disp(y);

    if y==z

        con=0;

    else

            disp('Net is not learning. Enter another set of weights and threshold value');

disp('Enter weight:');

w11=input('weight w11');

w12=input('weight w12');

w21=input('weight w21');

w22=input('weight w22');

v1=input('weight v1');

v2=input('weight v2');

disp('Enter your threashold value:');

theta=input('theta');

    end

end

            disp('mcculoch-pits net for XOR function');   

Output:

Enter weight:

weight w11 1

weight w12 -1

weight w21 -1

weight w22 1

weight v1 1

weight v2 1

Enter your threashold value:

theta 1

Output of net

     0 1 1 0

Program 4:

% Write a MATLAB program for perceptron net for an AND %function with bipolar inputs and targets.

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 threshoald 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);

Output:

enter learning rate 1

enter threshoald value0.5

perceptron for AND function

final weight matrix

     1 1

final bias

    -1 

Program 5: With a suitable example demonstrate the perceptron learning with its decision region using MATLAB. Give the output in graphical form.

clear

p=5;

N=50;

X=2*rand(p-1,2*N)-1;

nn=round((2*N-1)*rand(N,1))+1;

X(:,nn)=sin(X(:,nn));

X=[X;ones(1,2*N)];

wht=3*rand(1,p)-1; wht=wht/norm(wht);

wht;

D=(wht*X>=0);

Xv=X(:, N+1:2*N);

Dv=D(:,N+1:2*N);

X=X(:,1:N);

D=D(:,1:N);

%[X;D]

pr=[1,3];

Xp=X(pr,:);

wp=wht([pr p]);

c0=find(D==0); c1=find(D==1);

figure(1),clf reset

plot(Xp(1,c0),Xp(2,c0),'o',Xp(1,c1),Xp(2,c1),'X')

axis(axis),hold on

L=[-1 1];

S=-diag([1 1]./wp(1:2.))*(wp([2,1])'*L+wp(3));

plot([S(1,:) L],[L S(2,:)]), grid, drawnow

%PART 2:Learning

eta=0.5;%The training gain

wh=2*rand(1,p)-1;

wp=wh([pr p]);

S=-diag([1 1]./wp(1:2))*(wp([2,1])'*L +wp(3));

plot([S(1,:) L],[L S(2,:)]),grid on, drawnow

C=50;

E=[C+1,zeros(1,C)];

WW=zeros(C*N,p);

c=1;

cw=0;

while(E(c)>1)||(c==1)

    c=c+1;

    plot([S(1,:) L],[L S(2,:)],'w'),drawnow;

for n=1:N

        eps=D(n)-((wh*X(:,n))>=0);%eps(n)=d(n)-y(n)

        wh=wh+eta*eps*X(:,n)';

        cw=cw+1;

        WW(cw,:)=wh/norm(wh);

        E(c)=E(c)+abs(eps);

end;

    wp=wh([pr p]);

    S=-diag([1 1]./wp(1:2))*(wp([2 1])'*L+wp(3));

    plot([S(1,:) L],[L S(2,:)],'g'),drawnow

end;

WW=WW(1:cw,pr);

E=E(2:c+1);

Output: 

Program 6:

Develop a MATLAB program to perform adaptive %prediction with Adaline.

clear;

clc;

f1=2';

ts=1/(40*f1);

N=100;

t1=(0:N)*4*ts;

t2=(0:2*N)*ts+4*(N+1)*ts;

t=[t1 t2];

N=size(t,2);

xt=[sin(2*pi*f1*t1) sin(2*pi*f1*t2)];

plot(t,xt),grid

title('signal to be detected ')

p=4;

X=convmtx(xt,p);

X=X(:,1:N);

d=xt;

y=zeros(size(d));

eps=zeros(size(d));

eta=0.4;

w=rand(1,p);

for n=1:N

    y(n)=w*X(:,n);

    eps(n)=d(n)-y(n);

    w=w+eta*eps(n)*X(:,n)';

end

figure(1);

plot(t,d,'b',t,y,'-r'),grid 

title('target and prediction signal'),xlabel('time[sec]')

figure(2);

plot(t,eps),grid 

title('prediction error'),xlabel('time[sec]')

Output:

Program 7:

.Write a M-file for adaptive system identification using Adaline network.

clc;

f=0.8;

ts=0.005;

N1=800;

N2=400;N=N1+N2;

t1=(0:N1-1)*ts;

t2=(N1:N-1)*ts;

t=[t1 t2];

xt=sin(3*t.*sin(2*pi*f*t));

p=3;

b1=[1 -0.6 0.4];

b2=[0.9 -0.5 0.7];

[d1,stt]=filter(b1,1,xt(1:N1));

d2=filter(b2,1,xt(N1+1:N),stt);

dd=[d1 d2];

X=convmtx(xt,p);

X=X(:,1:N);

d=[b1*X(:,1:N1) b2*X(:,N1+1:N)];

y=zeros(size(d));

eps=zeros(size(d));

eta=0.2;

w=2*(rand(1,p)-0.5);

for n=1:N

    y(n)=w*X(:,n);

    eps(n)=d(n)-y(n);

    w=w+eta*eps(n)*X(:,n)';

   if n==N1-1,w1=w;

   end

end

figure(1);

subplot(2,1,1)

plot(t,xt),grid 

title('Input singnal ,x(t)'),xlabel('time[sec]')

subplot(2,1,2)

plot(t,d,'b',t,y,'-r'),grid 

title('target and prediction signal'),xlabel('time[sec]')

figure(2);

plot(t,eps),grid 

title(['prediction error for eta=',num2str(eta)]),xlabel('time[sec]')

[b1;w1]

[b2;w]

Output:

Program 8:

Develop a MATLAB program for adaptive noise cancellation using Adaline network.

clear;

clc;

f=4e3;

fm=300;

fa=200;

ts=2e-5;

N=400;

t=(0:N-1)*ts;

ut=(1+0.2*sin(2*pi*fa*t)).*sin(2*pi*f*(1+0.2*cos(2*pi*fm*t)).*t);

xt=sawtooth(2*pi*1e3*t,0.7);

b=[1 -0.6 0.3];

vt=filter(b,1,xt);

dt=ut+vt;

figure(1);

subplot(2,1,1);

plot(1e3*t,ut,1e3*t,dt),grid 

title('Input singnal ,u(t)and noisy input signal d(t)'),xlabel('time[sec]')

subplot(2,1,2)

plot(1e3*t,xt,1e3*t,vt),grid 

title('noise x(t)and coloured noise u(t)'),xlabel('time[sec]')

p=4;

X=convmtx(xt,p);

X=X(:,1:N);

y=zeros(1,N);

eps=zeros(1,N);

eta=0.05;

w=2*(rand(1,p)-0.5);

for c=1:4

for n=1:N

    y(n)=w*X(:,n);

    eps(n)=dt(n)-y(n);

    w=w+eta*eps(n)*X(:,n)';

   end

   eta=0.8*eta;

end

figure(2);

subplot(2,1,1)

plot(1e3*t,ut,1e3*t,eps),grid 

title('Input singnal ,u(t) and estimated signal uh(t)'),xlabel('time[sec]')

subplot(2,1,2)

plot(1e3*t(p:N),ut(p:N)-eps(p:N)),grid 

title('estimation error'),xlabel('time[sec]')

Output:

\

Program 9: Develop a MATLAB program for adaptive noise cancellation using adalinenetwork.

clear;

clc;

f=4e3;

fm=300;

fa=200;

ts=2e-5;

N=400;

t=(0:N-1)*ts;

ut=(1+0.2*sin(2*pi*fa*t)).*sin(2*pi*f*(1+0.2*cos(2*pi*fm*t)).*t);

xt=sawtooth(2*pi*1e3*t,0.7);

b=[1 -0.6 -0.3];

vt=filter(b,1,xt);

dt=ut+vt;

figure(1)

subplot(2,1,1)

plot(1e3*t, ut, 1e3*t, dt),grid,title('Input u(t) and noisy input signal d(t)'),xlabel('time -- msec')

subplot(2,1,2)

plot(1e3*t, xt, 1e3*t, vt),grid,title('Noise x(t) and coloured noise v(t)'),xlabel('time --- msec')

p=4;

X=convmtx(xt,p); X=X(:,1:N);

y=zeros(1,N);

eps=zeros(1,N);

eta=0.05;

w=2*(rand(1,p)-0.5);

for c=1:4

for n=1:N

        y(n)=w*X(:,n);

        eps(n)=dt(n)-y(n);

        w=w+eta*eps(n)*X(:,n)';

end

    eta=0.8*eta;

end

    figure(2)

    subplot(2,1,1)

    plot(1e3*t,ut,1e3*t,eps),grid,...

        title('Input signal u(t) and estimated signal uh(t)'),...

        xlabel('time--msec')

    subplot(2,1,2)

    plot(1e3*t(p:N),ut(p:N)-eps(p:N)),grid,...

        title('estimation error'),xlabel('time --[msec]')

Output:

Program 10: Write a MATLAB program for calculating the weights for the following pattern using hetro associative neural net for mapping four input vectors to two output vectors

S1

S2

S3

S4

T1

T2

1

1

0

0

1

0

1

0

1

0

1

0

1

1

1

0

0

1

0

1

1

0

0

1

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