% Sigmoid Function Definition
function [result] = sigmoid(x)
result = 1.0 ./ (1.0 + exp(-x));
end
% Inputs
input = [1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0;
0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1;
0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0;
0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1];
% Desired outputs
output = [1;1;1;1];
% Initializing the bias (Bias or threshold are the same thing, essential for learning, to translate the curve)
% Also, the first column of the weight matrix is the weight of the bias values
bias = [-1 -1 -1 -1];
% Learning coefficient
coeff = 1.0;
% Number of learning iterations
iterations = 100;
disp('No. Of Learning Iterations = ');
disp(iterations);
% Initial weights
weights = ones(36,36);
% Main Algorithm Begins
for i = 1:iterations
out = zeros(4,1);
numIn = length (input(:,1));
for j = 1:numIn
% 1st neuron in the hidden layer
H1 = bias(1,1)*weights(1,1) + input(j,1)*weights(1,2) + input(j,2)*weights(1,3) + input(j,3)*weights(1,4)+ input(j,4)*weights(1,5) + input(j,5)*weights(1,6) + input(j,6)*weights(1,7)
+ input(j,7)*weights(1,8) + input(j,8)*weights(1,9) + input(j,9)*weights(1,10)+ input(j,10)*weights(1,11) + input(j,11)*weights(1,12) + input(j,12)*weights(1,13)
+ input(j,13)*weights(1,14) + input(j,14)*weights(1,15) + input(j,15)*weights(1,16)+ input(j,16)*weights(1,17) + input(j,17)*weights(1,18) + input(j,18)*weights(1,19)
+ input(j,19)*weights(1,20) + input(j,20)*weights(1,21) + input(j,21)*weights(1,22)+ input(j,22)*weights(1,23) + input(j,23)*weights(1,24) + input(j,24)*weights(1,25)
+ input(j,25)*weights(1,26) + input(j,26)*weights(1,27) + input(j,27)*weights(1,28)+ input(j,28)*weights(1,29) + input(j,29)*weights(1,30) + input(j,30)*weights(1,31)
+ input(j,31)*weights(1,32) + input(j,32)*weights(1,33) + input(j,33)*weights(1,34)+ input(j,34)*weights(1,35) + input(j,35)*weights(1,36)
x2(1) = sigmoid(H1);
% 2nd neuron in the hidden layer
H2 = bias(1,2)*weights(2,1) + input(j,1)*weights(2,2) + input(j,2)*weights(2,3) + input(j,3)*weights(2,4)+ input(j,4)*weights(2,5) + input(j,5)*weights(2,6) + input(j,6)*weights(2,7)
+ input(j,7)*weights(2,8) + input(j,8)*weights(2,9) + input(j,9)*weights(2,10)+ input(j,10)*weights(2,11) + input(j,11)*weights(2,12) + input(j,12)*weights(2,13)
+ input(j,13)*weights(2,14) + input(j,14)*weights(2,15) + input(j,15)*weights(2,16)+ input(j,16)*weights(2,17) + input(j,17)*weights(2,18) + input(j,18)*weights(2,19)
+ input(j,19)*weights(2,20) + input(j,20)*weights(2,21) + input(j,21)*weights(2,22)+ input(j,22)*weights(2,23) + input(j,23)*weights(2,24) + input(j,24)*weights(2,25)
+ input(j,25)*weights(2,26) + input(j,26)*weights(2,27) + input(j,27)*weights(2,28)+ input(j,28)*weights(2,29) + input(j,29)*weights(2,30) + input(j,30)*weights(2,31)
+ input(j,31)*weights(2,32) + input(j,32)*weights(2,33) + input(j,33)*weights(2,34)+ input(j,34)*weights(2,35) + input(j,35)*weights(2,36)
x2(2) = sigmoid(H2);
% 3rd neuron in the hidden layer
H3 = bias(1,3)*weights(3,1) + input(j,1)*weights(3,2) + input(j,2)*weights(3,3) + input(j,3)*weights(3,4)+ input(j,4)*weights(3,5) + input(j,5)*weights(3,6) + input(j,6)*weights(3,7)
+ input(j,7)*weights(3,8) + input(j,8)*weights(3,9) + input(j,9)*weights(3,10)+ input(j,10)*weights(3,11) + input(j,11)*weights(3,12) + input(j,12)*weights(3,13)
+ input(j,13)*weights(3,14) + input(j,14)*weights(3,15) + input(j,15)*weights(3,16)+ input(j,16)*weights(3,17) + input(j,17)*weights(3,18) + input(j,18)*weights(3,19)
+ input(j,19)*weights(3,20) + input(j,20)*weights(3,21) + input(j,21)*weights(3,22)+ input(j,22)*weights(3,23) + input(j,23)*weights(3,24) + input(j,24)*weights(3,25)
+ input(j,25)*weights(3,26) + input(j,26)*weights(3,27) + input(j,27)*weights(3,28)+ input(j,28)*weights(3,29) + input(j,29)*weights(3,30) + input(j,30)*weights(3,31)
+ input(j,31)*weights(3,32) + input(j,32)*weights(3,33) + input(j,33)*weights(3,34)+ input(j,34)*weights(3,35) + input(j,35)*weights(3,36)
x2(3) = sigmoid(H3);
% Output layer
x3_1 = bias(1,4)*weights(4,1) + x2(1)*weights(4,2) + x2(2)*weights(4,3) + x2(3)*weights(4,4);
out(j) = sigmoid(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;
delta2_3 = x2(3)*(1-x2(3))*weights(3,4)*delta3_1;
% Add weight changes to original weights and then use the new weights.
% delta weight = coeff*x*delta
for k = 1:4
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)*delta2_3;
weights(4,k) = weights(4,k) + coeff*bias(1,4)*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*input(j,3)*delta2_3;
weights(4,k) = weights(4,k) + coeff*x2(k-1)*delta3_1;
end
end
end
end
disp('For the Input');
disp(input);
disp('Output Is');
disp(out);
disp('Test Case: For the Input');
input = [1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0];