How to get the transfer function equation for the implemented neural network

I have implemented neural network of two layers and hidden layer size is 3. for both layers activation function is purelin. When I calculate theoretically output of neural network it is not matching with output provided by neural network of matalab. Plz let me know where i am doing wrong. Thanks

Answer 1

[Greg Heath]

You have to obtain xsettings and tsettings from x and t.

Then apply them to x2 and t2.

Hope this helps.

Thank you for formally accepting my answer

Greg

Answer 2

[Greg Heath]

I misplaced my turban and crystal ball. Therefore I cannot tell you where you have gone wrong.

OH! It just occurred to me!

 1. Why don't you post your code?
 2. Include any comments and error messages that result when you try
    to run your code.
3. Include the results of running your code on data in the help 
   and doc documentation. e.g.,

 help fitnet
 doc fitnet

Thank you for formally accepting my answer

Greg

PS. Have you included

 a. the normalization of input and target
 b. The denormalization of the output

Hope this helps.

Greg

[Greg Heath]

MEA CULPA!

I tried to move your latest comment from the ANSWER box to a COMMENT BOX .. and I accidently erased it.

Please repost in a COMMENT BOX.

VERY SORRY!

Greg

[jalpa shah]

I have pasted code below for your reference. I have not done any normalization and denormalization because as per the link ( http://in.mathworks.com/help/nnet/ug/choose-neural-network-input-output-processing-functions.html) preprocessing and post processing is already there in neural network.

when I try to find the output using equation O=purelin(W2*logsig(W1i*Xi+B1)+B2), I am not getting same answer as produced by neural network when i test it after training.

what i do is i train the network and then i test it and after that i compare the result of network during testing with equation. But both are not matching.

plz let me know how remove default normalization and denormalization and where i am doing wrong when i am comparing results. thanks

-------code------------

clc
clear
close all
diary on

load training_testing_data.mat

trainFcn = 'trainlm';  % Levenberg-Marquardt backpropagation.

hiddenLayerSize=3;  % no of neurons in hidden layer

net = feedforwardnet(hiddenLayerSize,trainFcn);
net.layers{1}.transferFcn = 'logsig';

numNN =10 ;     % to train the network ten times

NN = cell(1,numNN);
perfs = zeros(1,numNN);
for i=1:numNN
  disp(['Training ' num2str(i) '/' num2str(numNN)])
  [NN{i},tr] = train(net,x1,t1);

    y1= NN{i}(x1);
    y2 = NN{i}(x2);           %to test network

    MSE_Training(i) = mse(NN{i},t1,y1)

    R2_Training(i)= regression(t1,y1)

MSE_Testing(i) = mse(NN{i},t2,y2)

    R2_Testing(i)= regression(t2,y2)

fprintf('Network Configuration\n');
fprintf('Internal weights for each layer\n\n');

fprintf(':::: Input Layer/Hidden1 ::::\n');
for R=1:NN{i}.inputs{1}.size
fprintf('X%d\n',R)              %weight of input 1 to all neurons, xi= i input to all neurons
for S=1:hiddenLayerSize(1)
fprintf('W(%d,%d)=%f\n',R,S,NN{i}.IW{1}(S,R));
end
fprintf('-------\n');
end
fprintf('Node Bias\n');
for R=1:NN{i}.layers{1}.dimensions
fprintf('b(%d)=%f\n',R,NN{i}.b{1}(R));
end
fprintf('-------\n');
fprintf('Activation function: %s\n',net.layers{1}.transferFcn);
fprintf('*********************************\n');

b2=NN{i}.b{2}

LW2= NN{i}.LW{2,1}  % or net.LW{2}

end

save ('nn_all_out.mat')
diary off

[jalpa shah]

Hi, if anyone is has worked on neural network implementation then plz reply.

[Greg Heath]

Whenever you have a code problem, please test it on a MATLAB example dataset see

 help nndatasets

and

 doc nndatasets

This is so that others can reproduce your problem.

http://www.mathworks.com/matlabcentral/newsreader/view_thread/341631#936181

Hope this helps.

 *Thank you for formally accepting my answer*

[jalpa shah]

Hi, thanks for replying. Can u plz tell me how to deactivate the normalization step which is by default as per the link ( http://in.mathworks.com/help/nnet/ug/choose-neural-network-input-output-processing-functions.html). Thanks

[jalpa shah]

Dear Greg, I have tried your tutorial code and pasted the code which i have tried. In code for lines (1), (2) and (3), when I put X and t instead of x2 and t2 then ya from equation and y are matching. But when I put x2 and t2 then yn and ya both are coming as 0.678 from equations and y2 from simulation of net coming as 4.3997. Means y2 output from simulation does not match with ya calculated from equation.

can you please tell me why its happening like this? your help will be appreciated. thanks

 x= [9.71771231870987,9.83342660442415,9.97628374728129]

 t= [4.39863796358009,4.69563206044186,4.91324004903954]

 x2= [9.62398374728130]
 t2= [4.09380849773465]

 net = fitnet; 

 rng( 4151941 )

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

 y2=sim(net,x2);

 % THE ANALYTIC I/O RELATIONSHIP

   xn = mapminmax(x2);   %.....(1)

 [ tn, tsettings ] = mapminmax(t2); %....(2)

 [p,N]= size(x2);  %......(3)

b1 = net.b{1} ; % [ H 1 ]

IW = net.IW{ 1 ,1 }; % [ H I ]

b2 = net.b{2} ; % [ O 1 ]

LW = net.LW{ 2, 1 }; % [ O H ]

whos b1 IW b2 LW

B1 = repmat( b1 , 1, N ) ;

B2 = repmat( b2 , 1, N ) ; % For O > 1

yn = B2 + LW * tanh( B1 + IW * xn );

ya = mapminmax.reverse(yn,tsettings);

end