How can I check the neural network is correct?

I have some data (p is the input and t the output). The net works well but I want to ckeck it manually. When I compute it, it doesn't work. I explain it better in the code:

p=[4.21470484282808,4.61178342351945,4.92103025244236,5.16780470857077,5.36888616086475,5.53567693961333,5.67614306410908,5.79599161759301,5.89941107438887,5.98953800357575
 0.0841938476119945,0.0688748497618962,0.0506266219880575,0.0313984679864031,0.0122666193874076,-0.00620394471778739,-0.0237367071204724,-0.0402208466896825,-0.0556358572482061,-0.0700100771974078
 0.624790077024891,0.933828019025972,1.24834383939203,1.55431911928733,1.84468199477835,2.11642821064707,2.3688169191345,2.60230677876707,2.81795118085545,3.01705857857006
 0.00257893224675201,0.00368824779406364,0.00453083959629498,0.00489009192682788,0.0046033702524108,0.00357272498883625,0.00175843692227414,-0.000832738095460411,-0.00416162543741231,-0.00816576040624318
 ];

 t=[2.83606065756777,3.31180314379271,3.70377438426516,4.02978774606033,4.30397305613069,4.53713048911324,4.7374656190205,4.91123610026158,5.06326477923633,5.19730529195449
 0.0485161358312315,0.0461344489481127,0.0391584214613128,0.0290027475982773,0.016808673107218,0.00342380868886163,-0.0105496421711672,-0.0246959627873845,-0.0387354315195166,-0.0524841437666582
 0.930574382489153,1.30350896221403,1.66272401320841,1.99818564751866,2.30664368564685,2.58817825301552,2.84437665551212,3.07741070830855,3.28958545610536,3.48311553793172
 0.00580490407681004,0.00759806971982089,0.00862898201442169,0.00863448538934149,0.0074887953804546,0.00517928895558281,0.00176746424529477,-0.00263950757984306,-0.00791199822691147,-0.0139137399633852
 ];

n=5;
logsig=@(x) 1./(1+exp(-x));
net = fitnet(n,'trainlm');
net.layers{1}.transferFcn='logsig'

[net,tr]=train(net,p,t);
nntraintool

Y_pred=net(p)
error=abs(t-Y_pred)
plotregression(t,Y_pred)

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

a1=logsig(W1*p+b1)
a2=W2*a1+b2

% my doubt is: why a2 is not the same that Y_pred? What am I doind bad?

Answer 1

[Lokesh]

Hi Bernardino,

I understand that you want to compute the output of a neural network manually.

In your code, there seems to be a mismatch between the variable "a2" and "Y_pred" due to missing normalization parameters.

To compute the output of neural network manually, we should first determine whether the input data needs to be normalized using “mapminmax”. If normalization is required, we can proceed with the normalization process. Similarly, we should also check if the output needs to be reverse normalized using "mapminmax” and perform the reverse normalization if necessary.

Please refer to the following code for manually computing the output of a neural network:

%% Set “p” and “t” to input and output respectively 
p=[]; t=[];  
n=5; 
logsig=@(x) 1./(1+exp(-x)); 
net = fitnet(n,'trainlm'); 
net.layers{1}.transferFcn='logsig' 
[net,tr]=train(net,p,t); 
Y_pred=net(p); 
error=abs(t-Y_pred); 
plotregression(t,Y_pred); 

%% Code to compute output manually 
w = cellfun(@transpose,[net.IW{1},net.LW(2:size(net.LW,1)+1:end)],'UniformOutput',false); %% Extract Weights 
b = cellfun(@transpose,net.b','UniformOutput',false); %% Extract Biases 
tf = cellfun(@(x)x.transferFcn,net.layers','UniformOutput',false); 

%% mapminmax on inputs 
if strcmp(net.Inputs{1}.processFcns{:},'mapminmax') 
    xoffset = net.Inputs{1}.processSettings{1}.xoffset; 
    gain = net.Inputs{1}.processSettings{1}.gain; 
    ymin = net.Inputs{1}.processSettings{1}.ymin; 
    In0 = bsxfun(@plus,bsxfun(@times,bsxfun(@minus,p,xoffset),gain),ymin); %% Normalize Inputs 
else 
    In0 = inputs; 
end 

In = cell(1,length(w)); 
Out = In; 
In{1} = In0'*w{1}+b{1}; 
Out{1} = eval([tf{1},'(In{1})']); 
for i=2:length(w) 
    In{i} = Out{i-1}*w{i}+b{i}; 
    Out{i} = eval([tf{i},'(In{',num2str(i),'})']); %% Calculate Output of each layer 
end 

%% reverse mapminmax on outputs 
if strcmp(net.Outputs{end}.processFcns{:},'mapminmax') 
    gain = net.outputs{end}.processSettings{:}.gain; 
    ymin = net.outputs{end}.processSettings{:}.ymin; 
    xoffset = net.outputs{end}.processSettings{:}.xoffset; 
    output = bsxfun(@plus,bsxfun(@rdivide,bsxfun(@minus,Out{end}',ymin),gain),xoffset) %% Reverse Normalization 
else 
    output = Out{end} 
end 
%% output matches Y_pred 

Please refer to the following MATLAB documentation links to know more about the concepts and functions used in the code:

• Neural Network Subobject Properties: https://www.mathworks.com/help/deeplearning/ug/neural-network-subobject-properties.html
• “cellfun”: https://www.mathworks.com/help/matlab/ref/cellfun.html
• “bsxfun”: https://www.mathworks.com/help/matlab/ref/bsxfun.html
• “eval”: https://www.mathworks.com/help/matlab/ref/eval.html

I hope you find this helpful.

Best Regards,

Lokesh