_NEURAL NETWORKS AND CHARACTER RECOGNITION_
by Ken Karnofsky

[LISTING ONE]
  
R = 35;             % number of inputs
S1 = 10;            % number of neurons in layer 1
S2 = 26;            % number of neurons in layer 2
[W1,B1] = nwlog(S1,R);  % initial conditions for layer 1
W2 = rands(S2,S1)*0.01; % initial conditions  


[LISTING TWO]
  
P = alphabet;                 % input matrix - 26x35
T = targets;                  % target matrix - 26x26
disp_freq = 20;               % define training parameters
max_epoch = 5000;         %         "
err_goal = 0.1;               %         "
lr = 0.01;                %         "
lr_inc = 1.05;                %         " 
lr_dec = 0.7;                 %         "
momentum = 0.95;              %         "
err_ratio = 1.04;             %         " 

% All training parameters are packed into the vector TP
TP = [disp_freq, max_epoch, err_goal, lr, lr_inc, lr_dec, momentum, err_ratio];

% The function trainbpx trains the network using the specified initial 
%   conditions and transfer functions. It returns the trained network 
%   weights and biases, the number of epochs (iterations) required, and a 
%   record of errors and learning rate at each epoch.
[W1,B1,W2,B2,epochs,TR] =  trainbpx(W1,B1,UlogsigU,W2,B2,UlogsigU,P,T,TP);



[LISTING THREE]


max_epoch = 300;                       % define training parameters
err_goal = 0.6;                            %         "
TP = [disp_freq ... AS ABOVE ... err_ratio];    
for pass = 1:10,
 P = [alphabet, alphabet, ...              % clean training vectors
      (alphabet + rand(R,Q)*0.1), ...      % and with varying
      (alphabet + rand(R,Q)*0.2)];         % amounts of noise
 T = [targets, targets, targets, targets]; % 4 target vectors batched together
 [W1,B1,W2,B2,TE,TR] = ...                 % training procedure
     trainbpx(W1,B1,UlogsigU,W2,B2,UlogsigU,P,T,TP);
end





[LISTING FOUR]
 
% Define an input example with random noise added.  
noisyM = alphabet(:,13) + randn(35,1)*0.2;  
        
% Output A2 is a function of the input vector, the transfer function for each 
%  layer, and the trained weights and biases.
A2 = logsig(W2*logsig(W1*noisyM,B1),B2);

% Because A2 may be noisy (not exactly 1 or 0); the competitive function
%   picks the element closest to one.  The FIND function returns its index.
answer = find(compet(A2) == 1);