CI 4_3

ci_4_3.m

%%%
% Feed forward with back propagation algorithm
%
% @param    X ... all possible inputs
% @param    Y ... all expected outputs
% @param    T ... the network topology
% @param    l ... the iteration limit for the error min. func.
% @returns  W ... the optimal weight matrix
% @returns Ev ... the error dynamic vector
%%
function [W, Ev] = ci_4_3(X, Y, T, l)
	
	y = [0 0 0 0 0 0 0];
	W = randn(7,7);
	nn = 0.9;
 	Ev = [];
	out = [];
	
	for iterations = 1:l		
		E = 0;
		for i=1:length(Y)
			n = length(T);
			y_i = ForwardProp(W, T, X(i,:));
			out(i) = y_i(n);
			e = ErrorFunction(y_i(n), Y(i));
			E = E + e;	
			
			w = [];
			k(7) = deltaOutput(y_i(7), Y(i));
			w(:,7) = k(7)*y_i;
			for i=length(T)-size(Y, 2):-1:1
				k(i) = deltaHidden(T, W, k, y_i(i), i);
				w(:,i) = k(i)*y_i;		
			end;
			
			W = W - nn*w;
		end;
		
		Ev = [Ev, E];
		if (mod(iterations, 100) == 0)
			doPlot(Ev, Y, out, iterations);
		end;
	end;
	
	function y = ForwardProp(W, T, X)
		y = [X, zeros(1,length(T)-length(X))];
		for i=length(X)+1:length(T)
			y(i) = ActivationFunc(PropFunc(W(:,i), y, T(:,i)), 1);
		end;
	end;
	
	function p = PropFunc(w, y, t)
		p =  w' * (t'.*y)';
	end;
	
	function x = ActivationFunc(s, lambda)
		x = 1/(1+exp(-lambda*s));
	end;
	
	function e = ErrorFunction(y_i, y)
		e = (y_i - y)^2;	
	end;
	
	function f = F_(y)
		f = y*(1-y);
	end;
	
	function k = deltaOutput(y, d)
		k = 2*(y-d)*F_(y);
	end;
	
	function k = deltaHidden(T, W, k, y, n)
		sum = 0;
		for j = 1:length(T)
			if (T(n,j) == 1)
				sum = sum + W(n, j)*k(j);
			end;
		end;
		k = F_(y)*sum;
	end;
	
	function doPlot(Ev, Y, out, iterations)
		semilogy(Ev);
		drawnow();
		printf("\nIteration %d\n", iterations);
		printf("\t%d -> %f\n",  Y(1), out(1));
		printf("\t%d -> %f\n",  Y(2), out(2));
		printf("\t%d -> %f\n",  Y(3), out(3));
		printf("\t%d -> %f\n",  Y(4), out(4));
		fflush(stdout);
	end
	
end;

ci_4_3_calling.m

l = 1000; %iteration limits

%---------Solving XOR------------
X = [ 0 0 ;
      0 1 ;
      1 0 ;
      1 1];
Y = [0; 1; 1; 0];

%---------1 Hidden Layer, 4 Hidden Neurons 	

% (1)--|-----(3)----|
%      |-----(4)----|
%      |	    |---(7)
%      |-----(5)----|
% (2)--|-----(6)----|

T =[0 0 1 1 1 1 0;
    0 0 1 1 1 1 0;
    0 0 0 0 0 0 1;
    0 0 0 0 0 0 1;
    0 0 0 0 0 0 1;
    0 0 0 0 0 0 1;
    0 0 0 0 0 0 0 ];

ci_4_3(X,Y,T,l);
	
%---------1 Hidden Layer, 3 Hidden Neurons 	

% (1)--|-----(3)----|
%      |-----(4)----|---(6)
% (2)--|-----(5)----|

T =[0 0 1 1 1 0;
    0 0 1 1 1 0;
    0 0 0 0 0 1;
    0 0 0 0 0 1;
    0 0 0 0 0 1;
    0 0 0 0 0 0 ];

ci_4_3(X,Y,T,l);

%---------1 Hidden Layer, 2 Hidden Neurons 	

% (1)--|-----(3)----|
%      |            |---(5)
% (2)--|-----(4)----|

T =[0 0 1 1 0;
    0 0 1 1 0;
    0 0 0 0 1;
    0 0 0 0 1;
    0 0 0 0 0 ];

ci_4_3(X,Y,T,l);

%---------Minimal Version NN51

% (1)--|-----------|
%      |	   |
% (2)--|-----(4)---|---(5)
%      |	   |
% (3)--|-----------|

X = [ 0 0 1;
      0 1 1;
      1 0 1;
      1 1 1];
	  
T =[0 0 0 1 1;
    0 0 0 1 1;
    0 0 0 1 1;
    0 0 0 0 1;
    0 0 0 0 0 ];

ci_4_3(X,Y,T,l);

%---------Solving Classification------------

%---------2 Hidden Layer, 5 Hidden Neurons per Layer

load K40M2-NN.dat

X = K40M2_NN;
Y = [ones(1,20), zeros(1,20)];

% (1)--|----(3)----|----( 8)----|
%      |----(4)----|----( 9)----|
%      |----(5)----|----(10)----|--(13)   
%      |----(6)----|----(11)----|   
% (2)--|----(7)----|----(12)----|

T = [0 0 1 1 1 1 1 0 0 0 0 0 0; 
     0 0 1 1 1 1 1 0 0 0 0 0 0; 
     0 0 0 0 0 0 0 1 1 1 1 1 0; 
     0 0 0 0 0 0 0 1 1 1 1 1 0; 
     0 0 0 0 0 0 0 1 1 1 1 1 0; 
     0 0 0 0 0 0 0 1 1 1 1 1 0; 
     0 0 0 0 0 0 0 1 1 1 1 1 0; 
     0 0 0 0 0 0 0 0 0 0 0 0 1; 
     0 0 0 0 0 0 0 0 0 0 0 0 1; 
     0 0 0 0 0 0 0 0 0 0 0 0 1; 
     0 0 0 0 0 0 0 0 0 0 0 0 1; 
     0 0 0 0 0 0 0 0 0 0 0 0 1; 
     0 0 0 0 0 0 0 0 0 0 0 0 0];

ci_4_3(X,Y,T,l);