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## how to adjust derivatives of backpropagation according to custom error function

Asked by Sergey Ohanyan

### Sergey Ohanyan (view profile)

on 14 Jan 2019
Latest activity Edited by Sergey Ohanyan

### Sergey Ohanyan (view profile)

on 14 Feb 2019
Accepted Answer by Greg Heath

### Greg Heath (view profile)

I want to implement custom error function to backpropagation algorithm, and enforce to update weights with taking into account output layer outputs.
Network consists of one hidden layer. The inputs are (n,1) vector, outputs have the same dimensions.
Lets say we have given input and target, I want to calculate error function as
E = ((input*output-target)^2)/2
so at each iteration target updates to reach initial target.
updatedTarget = input*output
According to this, derivatives are modified to
dE_dOutput(j) = sum(input .* netOutputLayerOutputs - initialTarget(j)) * input(j);
the code part of backpropagation algorithm is provided below
for i = 1:100
for j = 1 : length(input)
% forward propagation
netHiddenLayerValues(j) = sum(netHiddenLayerWeights(:,j) .* input(j)) + netBiasValue1 * 1;
netHiddenLayerOutputs(j) = 1/(1 + exp(-netHiddenLayerValues(j)));
netOutputLayerValues(j) = sum(netOutputLayerWeights(:,j) * netHiddenLayerOutputs(j)) + netBiasValue2 * 1;
netOutputLayerOutputs(j) = 1/(1 + exp(-netOutputLayerValues(j)));
% Custom target function
target(j) = input(j) * netOutputLayerOutputs(j);
% back propagation for output layer
% customized error derivative with respect to output layer outputs
dE_dOutput(j) = sum(input .* netOutputLayerOutputs - initialTarget(j)) * input(j);
%dE_dOutput(j) = -(target(j) - netOutputLayerOutputs(j)); % this is for standart mse
% partial derivative of logistic function with respect to network output value
dOutput_dNetout(j) = netOutputLayerOutputs(j) * (1 - netOutputLayerOutputs(j));
% partial derivative of network output with respect to weight
dNetout_dw(j) = netHiddenLayerOutputs(j);
% calculate total error for output layer
d_EtotalOut(j) = dE_dOutput(j) * dOutput_dNetout(j) * netHiddenLayerOutputs(j);
% calculate back propagation error for hidden layer
d_EtotalHidden_dOut(j) = dE_dOutput(j) * dOutput_dNetout(j) * netOutputLayerWeights(j);
dOut_dNetHidden(j) = netHiddenLayerOutputs(j) * (1 - netHiddenLayerOutputs(j));
dNetHidden_dw(j) = input(j);
d_EtotalHiddenOut(j) = d_EtotalHidden_dOut(j) * dOut_dNetHidden(j) * dNetHidden_dw(j);
% update weights for hidden layer
netHiddenLayerWeights(:,j) = netHiddenLayerWeights(:,j) - eta * d_EtotalHiddenOut(j);
% update weights for output layer
netOutputLayerWeights(:,j) = netOutputLayerWeights(:,j) - eta * d_EtotalOut(j);
end
end     The figures above shows how are changes during iterations (5,10,20,50,100 iterations respectively), outputs of net(orange) and updated target (blue). The static curves are inputs (yellow) and initial or real target (magenta).
The issue is that updated at each iteration target doesnot reach real initial target.
Please write if you notice error in algorithm implementation or logic.
The backpropagation algorithm with mse error is described here step-by-step-backpropagation-example.
Thanks.

Greg Heath

### Greg Heath (view profile)

on 16 Jan 2019
Why in the world do you think this is better than the current performance measures?
Greg

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## 2 Answers

Answer by Greg Heath

### Greg Heath (view profile)

on 4 Feb 2019
Accepted Answer

Your error function is not at a minimum when output = target
Why did you not use the standard
E = (output - target)^2
Thank you for formally accepting my correct answer
Greg

Sergey Ohanyan

### Sergey Ohanyan (view profile)

on 14 Feb 2019
Thank you for answer, currently I'm trying another approach. I will write about results after completion.
Thanks.

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Answer by BERGHOUT Tarek

### BERGHOUT Tarek (view profile)

on 3 Feb 2019

try this code : https://www.mathworks.com/matlabcentral/fileexchange/69947-back-propagation-algorithm-for-training-an-mlp?s_tid=prof_contriblnk

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