NEURAL NETWORK MATLAB

% XOR input for x1 and x2
input = [0 0; 0 1; 1 0; 1 1];
% Desired output of XOR
output = [0;1;1;0];
% Initialize the bias
bias = [-1 -1 -1];
% Learning coefficient
coeff = 0.7;
% Number of learning iterations
iterations = 10000;
% Calculate weights randomly using seed.
rand(‘state’,sum(100*clock));
weights = -1 +2.*rand(3,3);
for i = 1:iterations
out = zeros(4,1);
numIn = length (input(:,1));
for j = 1:numIn
% Hidden layer
H1 = bias(1,1)*weights(1,1)
+ input(j,1)*weights(1,2)
+ input(j,2)*weights(1,3);

% Send data through sigmoid function 1/1+e^-x
% Note that sigma is a different m file
% that I created to run this operation
x2(1) = sigma(H1);
H2 = bias(1,2)*weights(2,1)
+ input(j,1)*weights(2,2)
+ input(j,2)*weights(2,3);
x2(2) = sigma(H2);

% Output layer
x3_1 = bias(1,3)*weights(3,1)
+ x2(1)*weights(3,2)
+ x2(2)*weights(3,3);
out(j) = sigma(x3_1);

% Adjust delta values of weights
% For output layer:
% delta(wi) = xi*delta,
% delta = (1-actual output)*(desired output – actual output)
delta3_1 = out(j)*(1-out(j))*(output(j)-out(j));

% Propagate the delta backwards into hidden layers
delta2_1 = x2(1)*(1-x2(1))*weights(3,2)*delta3_1;
delta2_2 = x2(2)*(1-x2(2))*weights(3,3)*delta3_1;

% Add weight changes to original weights
% And use the new weights to repeat process.
% delta weight = coeff*x*delta
for k = 1:3
if k == 1 % Bias cases
weights(1,k) = weights(1,k) + coeff*bias(1,1)*delta2_1;
weights(2,k) = weights(2,k) + coeff*bias(1,2)*delta2_2;
weights(3,k) = weights(3,k) + coeff*bias(1,3)*delta3_1;
else % When k=2 or 3 input cases to neurons
weights(1,k) = weights(1,k) + coeff*input(j,1)*delta2_1;
weights(2,k) = weights(2,k) + coeff*input(j,2)*delta2_2;
weights(3,k) = weights(3,k) + coeff*x2(k-1)*delta3_1;
end
end
end

%Matlab code for Radial Basis Functions
clc;x=-1:0.05:1;
%generating training data with Random Noise
fori=1:length(x)
y(i)=1.2*sin(pi*x(i))-cos(2.4*pi*x(i))+0.3*randn;
end
% Framing the interpolation matrix for training data
t=length(x);
fori=1:1:t
forj=1:1:t
h=x(i)-x(j); k=h^2/.02;
train(i,j)=exp(-k);
end
end
W=inv(train)*y’;
% Testing the trained RBF
xtest=-1:0.01:1;
%ytest is the desired output
ytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);
% Framing the interpolation matrix for test data
t=length(x);
fori=1:1:t
forj=1:1:t
h=x(i)-x(j); k=h^2/.02;
train(i,j)=exp(-k);
end
end
W=inv(train)*y’;
% Testing the trained RBF
xtest=-1:0.01:1;
%ytest is the desired output
ytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);
% Framing the interpolation matrix for test data
t1=length(xtest);
t=length(x);
fori=1:1:t1
forj=1:1:t
h=xtest(i)-x(j);
k=h^2/.02;
test(i,j)=exp(-k);
end
end
actual_test=test*W;
% Plotting the Performance of the network
figure;
plot(xtest,ytest,’b-‘,xtest,actual_test,’r+’);
xlabel(‘Xtest value’);
ylabel(‘Ytest value’);
h = legend(‘Desired output’,’Approximated curve’,2);
set(h);

Classes are transformed to vectors it can be treated as target
t = ind2vec(c);
LVQ network represents clusters of vectors with hidden neurons, and groups the clusters with output neurons to form the desired classes
colormap(hsv);
plotvec(x,c)
title(‘Input Vectors’);
xlabel(‘x(1)’);
ylabel(‘x(2)’);

network is then configured for inputs X and targets T
net = lvqnet(4,0.1);
net = configure(net,x,t);

Train the network:
net.trainParam.epochs=150;
net=train(net,x,t);

cla;
plotvec(x,c);
hold on;
plotvec(net.IW{1}’,vec2ind(net.LW{2}),’o’);