Error Backpropagation - Neural network - matlab

Question

I am trying to write a code for error back-propagation for neural network but my code is taking really long time to execute. I know that training of Neural network takes long time but it is taking long time for a single iteration as well.
Multi-class classification problem!
Total number of training set = 19978
Number of inputs = 513
Number of hidden units = 345
Number of classes = 10
Below is my entire code:
X=horzcat(ones(19978,1),inputMatrix); %Adding bias
M=floor(0.66*(513+10)); %Taking two-third of imput+output
Wji=rand(513,M);
aj=X*Wji;
zj=tanh(aj); %Hidden Layer output
Wkj=rand(M,10);
ak=zj*Wkj;
akTranspose = ak';
ykTranspose=softmax(akTranspose); %For multi-class classification
yk=ykTranspose'; %Final output
error=0;
%Initializing target variables
t = zeros(19978,10);
t(1:2000,1)=1;
t(2001:4000,2)=1;
t(4001:6000,3)=1;
t(6001:8000,4)=1;
t(8001:10000,5)=1;
t(10001:12000,6)=1;
t(12001:14000,7)=1;
t(14001:16000,8)=1;
t(16001:18000,9)=1;
t(18001:19778,10)=1;
errorArray=zeros(100000,1); %Stroing error values to keep track of error iteration
errorDiff=zeros(100000,1);
for nIterations=1:5
errorOld=error;
aj=X*Wji; %Forward propagating in each iteration
zj=tanh(aj);
ak=zj*Wkj;
akTranspose = ak';
ykTranspose=softmax(akTranspose);
yk=ykTranspose';
error=0;
%Calculating error
for n=1:19978 %for 19978 training samples
for k=1:10 %for 10 classes
error = error + t(n,k)*log(yk(n,k)); %using cross entropy function
end
end
error=-error;
Ediff = error-errorOld;
errorArray(nIterations,1)=error;
errorDiff(nIterations,1)=Ediff;
%Calculating dervative of error wrt weights wji
derEWji=zeros(513,345);
derEWkj=zeros(345,10);
for i=1:513
for j=1:M;
derErrorTemp=0;
for k=1:10
for n=1:19978
derErrorTemp=derErrorTemp+Wkj(j,k)*(yk(n,k)-t(n,k));
Calculating derivative of E wrt Wkj%
derEWkj(j,k) = derEWkj(j,k)+(yk(n,k)-t(n,k))*zj(n,j);
end
end
for n=1:19978
Calculating derivative of E wrt Wji
derEWji(i,j) = derEWji(i,j)+(1-(zj(n,j)*zj(n,j)))*derErrorTemp;
end
end
end
eta = 0.0001; %learning rate
Wji = Wji - eta.*derEWji; %updating weights
Wkj = Wkj - eta.*derEWkj;
end

Answer 1

for-loop is very time-consuming in Matlab even with the help of JIT. Try to modify your code by vectorize them rather than organizing them in a 3-loop or even 4-loop. For example,
for n=1:19978 %for 19978 training samples
for k=1:10 %for 10 classes
error = error + t(n,k)*log(yk(n,k)); %using cross entropy function
end
end
can be changed to:
error = sum(sum(t.*yk)); % t and yk are both n*k arrays that you construct
You may try to do similar jobs for the rest of your code. Use dot product or multiplication operations on arrays for different cases.