Equation that compute a Neural Network in Matlab

I created a neural network matlab. This is the script:

      load dati.mat;
      inputs=dati(:,1:8)';
      targets=dati(:,9)';
      hiddenLayerSize = 10;
      net = patternnet(hiddenLayerSize);
      net.inputs{1}.processFcns = {'removeconstantrows','mapminmax', 'mapstd','processpca'};
      net.outputs{2}.processFcns = {'removeconstantrows','mapminmax', 'mapstd','processpca'};

      net = struct(net);
      net.inputs{1}.processParams{2}.ymin = 0;
      net.inputs{1}.processParams{4}.maxfrac = 0.02;
      net.outputs{2}.processParams{4}.maxfrac = 0.02;
      net.outputs{2}.processParams{2}.ymin = 0;
      net = network(net);

      net.divideFcn = 'divideind';  
      net.divideMode = 'sample';  % Divide up every sample
      net.divideParam.trainInd = 1:428;
      net.divideParam.valInd = 429:520;
      net.divideParam.testInd = 521:612;
      net.trainFcn = 'trainscg';  % Scaled conjugate gradient backpropagation
      net.performFcn = 'mse';  % Mean squared error
      net.plotFcns = {'plotperform','plottrainstate','ploterrhist', 'plotregression', 'plotconfusion', 'plotroc'};
      net=init(net);
      net.trainParam.max_fail=20;

      [net,tr] = train(net,inputs,targets);

      outputs = net(inputs);
      errors = gsubtract(targets,outputs);
      performance = perform(net,targets,outputs)

Now I want to save the weights and biases of the network and write the equation. I had saved the weights and biases:

      W1=net.IW{1,1};
      W2=net.LW{2,1};
      b1=net.b{1,1};
      b2=net.b{2,1};

So, I've done the data preprocessing and I wrote the following equation

      max_range=0;
      [y,ps]=removeconstantrows(input, max_range);

      ymin=0;
      ymax=1;
      [y,ps2]=mapminmax(y,ymin,ymax);

      ymean=0;
      ystd=1;
      y=mapstd(x,ymean,ystd);

      maxfrac=0.02;
      y=processpca(y,maxfrac);

      in=y';

      uscita=tansig(W2*(tansig(W1*in+b1))+b2);

But with the same input input=[1:8] I get different results. why? What's wrong? Help me please! It's important!

I use Matlab R2010B

Answer 1

[Greg Heath]

% VERY SORRY FOR THE ROTTEN FORMATING. THIS EDITOR SUCKS.

Equation that compute a Neural Network in Matlab

Gianvito asked about 23 hours ago

I created a neural network matlab. This is the script:

      load dati.mat;
      inputs=dati(:,1:8)';
      targets=dati(:,9)';

% SEE DOCUMENTATION (DOC) FOR DEFAULTS OF PATTERNNET

%

% SINCE THIS IS PATTERN RECOGNITION WITH ONE OUTPUT,

% TARGETS SHOULD BE UNIPOLAR BINARY {0,1}, WITH NO NEED

% FOR TRANSFORMATIONS. THE MOST APPROPRIATE OUTPUT

% ACTIVATION IS LOGSIG. HOWEVER, PURELIN CAN BE USED

% EVEN THOUGH OUTPUTS ARE NOT RESTRICTED TO (0,1).

% TO SEE THE SIZE AND SCALE OF THE DATA

==> [ I N ] = size(inputs) % [ 8 612 ]

==> [ O N ] = size(targets) % [ 1 612 ]

==> minmaxin = minmax(inputs)

==> minmaxtarg = minmax(targets)

% TO ESTIMATE A REASONABLE VALUE FOR H

==> Ntrn = round(0.7*N) % 428

==> Neq = Ntrn*O % 428 No. of training equations

% Nw = O+(I+O+1)*H = 101 No. of unknown weights % For good weight estimates when training to convergence % require Neq >= Nw but desire Neq >> Nw % % Hub = floor((Neq-O)/(I+O+1)) % 42 Upper bound for H

      hiddenLayerSize = 10; % H

% H =10 ==> Neq/Nw = 428/101 is only a factor of 4. However, % not worried because using Early Stopping (aka Stopped Training) % with a validation set.

      net = patternnet(hiddenLayerSize);

%WHY ASSUME THE DEFAULT OF TRAINLM THEN CHANGE LATER? %DON'T KNOW FINAL I AND O YET BECAUSE OF CONSTANT %ROWS AND PCA DIMENSIONALITY REDUCTION

       net.inputs{1}.processFcns = {'removeconstantrows','mapminmax', 'mapstd','processpca'};
%XX: USE MAPSTD, BUT NOT MAPMINMAX WITH PROCESSPCA
% WARNING: PCA MAY NOT BE USEFUL FOR SOME PATTERN 
% RECOGNITION PROBLEMS

      net.outputs{2}.processFcns = {'removeconstantrows','mapminmax','mapstd','processpca'}; 
%XX: WHY USE PCA FOR 'ANY' OUTPUT??
%XX: WHY TRANSFORM 'THIS' OUTPUT? ISN'T IT UNIPOLAR BINARY?

     net = struct(net);
%XX: WHY IS THIS NECESSARY?... DELETE?

      net.inputs{1}.processParams{2}.ymin = 0;
%XX: DELETE, USE MAPSTD FOR INPUT

      net.outputs{2}.processParams{2}.ymin = 0;

      net.inputs{1}.processParams{4}.maxfrac = 0.02;
      net.outputs{2}.processParams{4}.maxfrac = 0.02;
%XX: DON'T USE PCA FOR OUTPUTS

      net = network(net); 
%XX INVALID (SEE DOC). SHOULD DEFINE NET TOPOLOGY.

      net.divideFcn = 'divideind';  
      net.divideMode = 'sample';  % Divide up every sample
      net.divideParam.trainInd = 1:428;
      net.divideParam.valInd = 429:520;
      net.divideParam.testInd = 521:612;

      net.trainFcn = 'trainscg';  % Scaled conjugate gradient backpropagation
% DEFINE IN CALL OF PATTERNET

      net.performFcn = 'mse';  % Mean squared error
% UNNECESSARY. DEFAULT

      net.plotFcns = {'plotperform','plottrainstate','ploterrhist', 'plotregression', 
'plotconfusion', 'plotroc'};

      net=init(net);
% AREN'T WEIGHTS ALREADY INITIALIZED?

      net.trainParam.max_fail=20;
% PROBABLY TOO HIGH

     [net,tr] = train(net,inputs,targets);      
      outputs = net(inputs);
      errors = gsubtract(targets,outputs);
      performance = perform(net,targets,outputs)
% WHAT VALUES DO YOU GET?

Now I want to save the weights and biases of the network and write the equation. I had saved the weights and biases:

      W1=net.IW{1,1};
      W2=net.LW{2,1};
      b1=net.b{1,1};
      b2=net.b{2,1};

So, I've done the data preprocessing and I wrote the following equation

      max_range=0;
%  WHY BOTHER SPECIFYING DEFAULTS?
      [y,ps]=removeconstantrows(input, max_range); 

     ymin=0;
      ymax=1;
      [y,ps2]=mapminmax(y,ymin,ymax); 
%  DO NOT USE y ON BOTH SIDES OF AN EQUATION
%XX  DELETE MINMAX TRANSFORMATION

      ymean=0;
      ystd=1;
% WHY BOTHER SPECIFYING DEFAULTS?
      y=mapstd(x,ymean,ystd);
%XX    x IS NOT DEFINED

      maxfrac=0.02;
      y=processpca(y,maxfrac);      
      in=y';      
     uscita = tansig(W2*(tansig(W1*in+b1))+b2);

% WHY NOT LOGSIG FOR OUTPUT LAYER??

But with the same input input=[1:8] I get different results.

why? What's wrong? Help me please! It's important!

I use Matlab R2010B

% HARD TO TELL. THIS CODE CANNOT RUN WITHOUT DEFINING x.

% WHAT ABOUT THE OUTPUT NORMALIZATION AND & TRANSFORMATION ?

Hope this helps.

Greg