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

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jalpa shah 2016-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/303019-how-to-get-the-transfer-function-equation-for-the-implemented-neural-network

回答： Greg Heath 2016-11-9

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

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Answer 1

Greg Heath 2016-11-9

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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

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Answer 2

Greg Heath 2016-9-14

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编辑：Greg Heath 2016-9-14

在 MATLAB Online 中打开

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

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jalpa shah 2016-10-24

编辑：Walter Roberson 2016-10-27

在 MATLAB Online 中打开

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 2016-11-2

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 2016-11-5

在 MATLAB Online 中打开

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