How to interpret an answer given by the Neural Network?

Hi.

I create a neural network with four(4) inputs and one(1) target (including 104 data for each one)with three(3) hidden layer. my script is as follows:

inputs = x; targets = y;

% Create a Fitting Network hiddenLayerSize = 3; net = fitnet(hiddenLayerSize);

% Setup Division of Data for Training, Validation, Testing net.divideParam.trainRatio = 70/100; net.divideParam.valRatio = 15/100; net.divideParam.testRatio = 15/100;

% Train the Network [net,tr] = train(net,inputs,targets);

% Test the Network outputs = net(inputs); errors = gsubtract(targets,outputs); performance = perform(net,targets,outputs)

% View the Network view(net)

In this case, I would like to extract coefficient of input data for 105th data. for example, for a equation like (X1a+X2b+X3c+X4d), I need to find X1,X2,X3,X4. How can I extract these coefficient from neural network?

Thank you very much for your answer.

Answer 1

[Greg Heath]

Please

1. Format your post so that comments and executables are on different lines

2. Use the notations

    a. Matrices: lower case; Cells: uppercase
      Inputs:   x,  X 
      Targets  t, T    
      Outputs y, Y
    b. No. of hidden nodes  h, H

3. inputs = x; targets = t; H =3

    [ I N ]= = size(x)  % [ 4 104]
    [ O N ] = size(t)   % [ 1  104 ]
    MSE00 = var(t,1) % Reference MSE

    net = fitnet(H);

% Default datadivision (0.7/0/15/0.15)

 [ net tr y e ] = train( net, x , t);
 % y = net(x); e = t-y;

 NMSE = mse(e)/MSE00    % Normalized MSE
 R2   = 1 - NMSE        % Rsquared, Coefficient of Determination
 %   https://en.wikipedia.org/wiki/R2

 % View the Network 
 view(net)

>In this case, I would like to extract coefficient of input data for 105th data. for example, for a equation like (X1a+X2b+X3c+X4d), I need to find X1,X2,X3,X4. How can I extract these coefficient from neural network?

You are confused. Let the input and target be

 x = [ x1 ; x2; x3; x4 ] ; % [ 4 104 ]
 t =  a + b*x1 +c*x2 + d*x3 + e*x4  ; % [ 1 104]

x1, x2, x3, x4 and t are known. Find a,b,c,d,e

This is a trivial linear case which can be solved by the slash solution

 N = 104, y = W*[ ones(1,N) ;x ] 

 where

 W = t / [ ones(1,N) ; x ]

It can also be solved using a neural net with 0 hidden nodes:

 net = fitnet([]);

I will let you compare the 2 solutions after plugging in the numerics.

Hope this helps.

Thank you for formally accepting my answer

Greg

[ali sahraei]

Thank you very much for your consideration.