How to write back propagation code without using neural network toolbox?

%%HI, I am trying to write a back proagation code without the help of neural network toolbox. please suggest how to go about it

Answer 1

[Wei-An Yang]

function EBPTA2

input=[];

target=[];

out=[];

s=[];

y=[];

x1=[];

x2=[];

x3=[];

x4=[];

for i=1:1:600

x1=rand;

x2=rand;

x3=rand;

x4=rand;

s=[x1,x2,x3,x4];

input=[input;s];

y=0.8*x1*x2*x3*x4+x1.^2+x2.^2+x3.^3+x4.^2+x1+x2*0.7-x2.^2*x3.^2+0.5*x1*x4.^2+x4*x2.^3+(-x1)*x2+(x1*x2*x3*x4).^3+(x1-x2+x3-x4)+(x1*x4)-(x2*x3)-2;

target=[target;y];

end

outnet=[];

% initialize the weight matrix

outputmatrix=zeros(35,1);

for i=1:1:35

for j=1:1:1

outputmatrix(i,j)=rand;

end

end

hiddenmatrix=zeros(4,35);

for i=1:1:4

for j=1:1:35

hiddenmatrix(i,j)=rand;

end

end

RMSE1=zeros(100,1);

RMSE2=zeros(100,1);

% Training

for epoch=1:1:100

t1=[];

t2=[];

for iter=1:1:400

% forward «e¶Ç³¡¤À

% training

hiddensigma=input(iter,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma); %LOGSIG Logarithmic sigmoid transfer function.

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

% simalation ---> if you don't have enough data, this part can be ignored

if iter+400<=600 % take the first 400 as training samples, the remaining 200 as simulations

hsigma=input(iter+400,:)*hiddenmatrix;

hnet=logsig(hsigma);

osigma=hnet*outputmatrix;

onet=purelin(osigma);

mis=target(iter+400)-onet;

t2=[t2;mis.^2];

end

% backward part ­Ë¶Ç³¡¤À

% delta of outputmatrix ¿é¥X¼hªº delta

doutputnet=dpurelin(outputsigma);

deltaoutput=(target(iter)-outputnet)*doutputnet;

error=target(iter)-outputnet;

t1=[t1;error.^2];

% delta of hidden layer ÁôÂühªº delta

tempdelta=deltaoutput*outputmatrix;

transfer=dlogsig(hiddensigma,logsig(hiddensigma));

deltahidden=[];

for i=1:1:35

deltahidden=[deltahidden;tempdelta(i)*transfer(i)];

end

% output layer weight update ¿é¥X¼hÅv­«§ó·s

newoutputmatrix=outputmatrix+0.025*(deltaoutput*hiddennet)';

outputmatrix=newoutputmatrix;

% hidden layer ÁôÂühÅv­«§ó·s

newhiddenmatrix=hiddenmatrix;

for i=1:1:35

for j=1:1:4

newhiddenmatrix(j,i)=hiddenmatrix(j,i)+0.025*deltahidden(i)*input(iter,j);

end

end

hiddenmatrix=newhiddenmatrix;

end

RMSE1(epoch) = sqrt(sum(t1)/400);

RMSE2(epoch) = sqrt(sum(t2)/200);

fprintf('epoch %.0f: RMSE = %.3f\n',epoch, sqrt(sum(t1)/400));

end

% end of trainging

fprintf('\nTotal number of epochs: %g\n', epoch);

fprintf('Final RMSE: %g\n', RMSE1(epoch));

figure(1);

plot(1:epoch,RMSE1(1:epoch),1:epoch,RMSE2(1:epoch));

legend('Training','Simulation');

ylabel('RMSE');xlabel('Epoch');

Train_Correct=0;

for i=1:400

hiddensigma=input(i,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma);

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

out=[out;outputnet];

if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5

Train_Correct=Train_Correct+ 1;

end

end

Simu_Correct=0;

for i=401:length(input)

hiddensigma=input(i,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma);

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

outnet=[outnet;outputnet];

if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5

Simu_Correct=Simu_Correct+ 1;

end

end

figure(2);

plot(401:length(input),target(401:length(input)),401:length(input),outnet(1:200))

legend('Function','Simulation');

Train_Percent= (Train_Correct) / 400;

Simu_Percent= (Simu_Correct) / (length(input)-400);

Train_correct_percent=Train_Percent

Simu_correct_percent=Simu_Percent

figure(3)

[m,b,r]=postreg(out',target(1:400)');

Answer 2

[Miljan Jeremic]

function EBPTA2

input=[];

target=[];

out=[];

s=[];

y=[];

x1=[];

x2=[];

x3=[];

x4=[];

for i=1:1:600

x1=rand;

x2=rand;

x3=rand;

x4=rand;

s=[x1,x2,x3,x4];

input=[input;s];

y=0.8*x1*x2*x3*x4+x1.^2+x2.^2+x3.^3+x4.^2+x1+x2*0.7-x2.^2*x3.^2+0.5*x1*x4.^2+x4*x2.^3+(-x1)*x2+(x1*x2*x3*x4).^3+(x1-x2+x3-x4)+(x1*x4)-(x2*x3)-2;

target=[target;y];

end

outnet=[];

% initialize the weight matrix

outputmatrix=zeros(35,1);

for i=1:1:35

for j=1:1:1

outputmatrix(i,j)=rand;

end

end

hiddenmatrix=zeros(4,35);

for i=1:1:4

for j=1:1:35

hiddenmatrix(i,j)=rand;

end

end

RMSE1=zeros(100,1);

RMSE2=zeros(100,1);

% Training

for epoch=1:1:100

t1=[];

t2=[];

for iter=1:1:400

% forward «e¶Ç³¡¤À

% training

hiddensigma=input(iter,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma); %LOGSIG Logarithmic sigmoid transfer function.

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

% simalation ---> if you don't have enough data, this part can be ignored

if iter+400<=600 % take the first 400 as training samples, the remaining 200 as simulations

hsigma=input(iter+400,:)*hiddenmatrix;

hnet=logsig(hsigma);

osigma=hnet*outputmatrix;

onet=purelin(osigma);

mis=target(iter+400)-onet;

t2=[t2;mis.^2];

end

% backward part ­Ë¶Ç³¡¤À

% delta of outputmatrix ¿é¥X¼hªº delta

doutputnet=dpurelin(outputsigma);

deltaoutput=(target(iter)-outputnet)*doutputnet;

error=target(iter)-outputnet;

t1=[t1;error.^2];

% delta of hidden layer ÁôÂühªº delta

tempdelta=deltaoutput*outputmatrix;

transfer=dlogsig(hiddensigma,logsig(hiddensigma));

deltahidden=[];

for i=1:1:35

deltahidden=[deltahidden;tempdelta(i)*transfer(i)];

end

% output layer weight update ¿é¥X¼hÅv­«§ó·s

newoutputmatrix=outputmatrix+0.025*(deltaoutput*hiddennet)';

outputmatrix=newoutputmatrix;

% hidden layer ÁôÂühÅv­«§ó·s

newhiddenmatrix=hiddenmatrix;

for i=1:1:35

for j=1:1:4

newhiddenmatrix(j,i)=hiddenmatrix(j,i)+0.025*deltahidden(i)*input(iter,j);

end

end

hiddenmatrix=newhiddenmatrix;

end

RMSE1(epoch) = sqrt(sum(t1)/400);

RMSE2(epoch) = sqrt(sum(t2)/200);

fprintf('epoch %.0f: RMSE = %.3f\n',epoch, sqrt(sum(t1)/400));

end

% end of trainging

fprintf('\nTotal number of epochs: %g\n', epoch);

fprintf('Final RMSE: %g\n', RMSE1(epoch));

figure(1);

plot(1:epoch,RMSE1(1:epoch),1:epoch,RMSE2(1:epoch));

legend('Training','Simulation');

ylabel('RMSE');xlabel('Epoch');

Train_Correct=0;

for i=1:400

hiddensigma=input(i,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma);

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

out=[out;outputnet];

if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5

Train_Correct=Train_Correct+ 1;

end

end

Simu_Correct=0;

for i=401:length(input)

hiddensigma=input(i,:)*hiddenmatrix;

hiddennet=logsig(hiddensigma);

outputsigma=hiddennet*outputmatrix;

outputnet=purelin(outputsigma);

outnet=[outnet;outputnet];

if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5

Simu_Correct=Simu_Correct+ 1;

end

end

figure(2);

plot(401:length(input),target(401:length(input)),401:length(input),outnet(1:200))

legend('Function','Simulation');

Train_Percent= (Train_Correct) / 400;

Simu_Percent= (Simu_Correct) / (length(input)-400);

Train_correct_percent=Train_Percent

Simu_correct_percent=Simu_Percent

figure(3)

[m,b,r]=postreg(out',target(1:400)');