Back propagation algorithm of Neural Network : XOR training

c=0;

wih = .1*ones(nh,ni+1);

who = .1*ones(no,nh+1);

 while(c<3000)
     c=c+1;
     for i = 1:length(x(1,:))

        for j = 1:nh
            netj(j) = wih(j,1:end-1)*double(x(:,i))+wih(j,end)*1;
            outj(j) = 1./(1+exp(-1*netj(j)));
        end

% hidden to output layer

        for k = 1:no

            netk(k) = who(k,1:end-1)*outj'+who(k,end)*1;
            outk(k) = 1./(1+exp(-1*netk(k)));
            delk(k) = outk(k)*(1-outk(k))*(t(k,i)-outk(k));

        end

% back proagation for j = 1:nh s=0; for k = 1:no s = s+who(k,j)*delk(k); end

            delj(j) = outj(j)*(1-outj(j))*s; 

            s=0;
        end

        for k = 1:no
            for l = 1:nh
                who(k,l)=who(k,l)+.5*delk(k)*outj(l);
            end
            who(k,l+1)=who(k,l+1)+1*delk(k)*1;
        end

        for j = 1:nh
            for ii = 1:ni
                wih(j,ii)=wih(j,ii)+.5*delj(j)*double(x(ii,i));
            end
            wih(j,ii+1)=wih(j,ii+1)+1*delj(j)*1;

        end

    end

end

// The code above, I have written it to implement back propagation neural network, x is input , t is desired output, ni , nh, no number of input, hidden and output layer neuron. I am testing this for different functions like AND, OR, it works fine for these. But XOR is not working.

// Training x = [0 0 1 1; 0 1 0 1] // Training t = [0 1 1 0]

// who -> weight matrix from hidden to output layer

// wih -> weight matrix from input to hidden layer

// Can you help ?

[Greg Heath]

It would help immensely if you posted a code that could be cut, pasted, run, and yield a numerical answer. Then we could begin by matching our results with yours.

It would also help immensely if you replaced the loops with vectorized code.

Greg

[Greg Heath]

If you initialized weights randomly, you could see if it is

an initialization problem.

Have you noticed the loop accidentally included in the backpropagation comment?

Greg

[sultana albanhar]

how this code work XOR?

Answer 1

[Greg Heath]

close all, clear all, clc

x = [0 0 1 1; 0 1 0 1]

t = [0 1 1 0]

[ni N] = size(x)

[no N] = size(t)

nh = 2

% wih = .1*ones(nh,ni+1);

% who = .1*ones(no,nh+1);

wih = 0.01*randn(nh,ni+1);

who = 0.01*randn(no,nh+1);

 c = 0;

 while(c < 3000)

     c = c+1;

% %for i = 1:length(x(1,:))

     for i = 1:N    

        for j = 1:nh

            netj(j) = wih(j,1:end-1)*x(:,i)+wih(j,end);

% %outj(j) = 1./(1+exp(-netj(j)));

            outj(j) = tansig(netj(j));

        end

        % hidden to output layer

        for k = 1:no            

           netk(k) = who(k,1:end-1)*outj' + who(k,end);

           outk(k) = 1./(1+exp(-netk(k))); 

           delk(k) = outk(k)*(1-outk(k))*(t(k,i)-outk(k)); 

        end

         % back propagation 

        for j = 1:nh

            s=0; 

            for k = 1:no 

               s = s + who(k,j)*delk(k); 

            end

            delj(j) = outj(j)*(1-outj(j))*s;

% %s=0;

        end 

        for k = 1:no

            for l = 1:nh

                who(k,l) = who(k,l)+.5*delk(k)*outj(l);

            end

            who(k,l+1) = who(k,l+1)+1*delk(k)*1;

        end  

        for j = 1:nh

            for ii = 1:ni

                wih(j,ii) = wih(j,ii)+.5*delj(j)*x(ii,i);

            end

            wih(j,ii+1) = wih(j,ii+1)+1*delj(j)*1;

         end    

      end

   end

h = tansig(wih*[x;ones(1,N)])

y = logsig(who*[h;ones(1,N)])

e = t-round(y)

Hope this helps.

Greg

[Ashikur]

Hi Greg, Thank you so much for the effort and time you have put on this. I am really grateful to you.

But the problems still remains, your modification (basically random initialization of weights and using tan sigmoid for hidden layer) sometimes works sometimes not. And I must know your motivation for not using logsig everywhere. Are there any explanations?

I want to share the whole code which is now in better shape. And you are right about the vectorization, I will do that once the code is working.

Here is two functions one for training and another for simulation.

You can try to run like this, and see sometimes it works sometimes not, I have added your suggestion in code.

>> net = biasBackProp(2,3,1,1,0.0001,[0 0 1 1;0 1 0 1],[0 1 1 0])

>> bpSim([0;1],net)

>> bpSim([1;1],net)

>> bpSim([1;0],net)

>> bpSim([0;0],net)

The functions can be copied from here,

https://docs.google.com/document/d/18kGXAgeVP1kOlJHZJ2KmV_mkxY61f255LQjPcr6uwnI/edit

https://docs.google.com/document/d/13YVWHUXug6XrngQD3a52IgzPxMH2M9sgECkb7peRckA/edit

Once again thank you and please be in touch, I will accept your answer later.

[Aya Ahmed]

Greg Heath , Thank you so much for the effort on this.

i want to ask you plz .. how can i use Multilayer perceptron to make classification to some images ??

my teature told me to make first XOR gate to make sure that the algorithm working .

and when i research i found your code , is that code suitable to what i want to do ??

cause i try to research alot about matlab code ?

how can i use it ??

[Aya Ahmed]

this code using one hidden layer , how can i use 2 or 3 hidden layer to make xor ?

[Shantanu Arya]

Greg Heath, Why Doesn't this code work for 3 input XOR ?? If I replace the X and Y with 3 inputs then the error does not converge to 0 !!

[Greg Heath]

1. I ALWAYS use the bipolar tanh in hidden layers. It ALWAYS works.
2. What are x and t for 3 input XOR???

Greg

Answer 2

[Greg Heath]

It is well known that successful deterministic training depends on a lucky choice of initial weights. The most common approach is to use a loop and create Ntrial (e.g., 10 or more) nets from different random initial weights. Then choose the best net.

It is also well known that an odd bounded monotonically increasing activation function like TANSIG is the choice of preference for hidden layers because it does not restrict the polarity of the layer variables. It works even better when the input is shifted to have zero mean.

You can check the superiority of TANSIG and zero-mean yourself. You can also search the comp.ai.neural-nets FAQ and archives to find both agreement and numerical experiments.

For most real world problems the best choice for number of hidden nodes, H, is not known apriori. That is why I have posted many examples using a double loop: An outer loop over H and an inner loop over Ntrials random weight initializations. For examples, search the newsgroup using the keywords

heath clear Ntrials

Hope this helps.

Greg

[Ashikur]

Thanks, you are awesome :)

[Imran Babar]

Thank you very much a nice example of MLP BP NN and very easy to understand. Though I am a novice in this field but I am now clear in the programming idea

[Havot Albeyboni]

can anyone please explain this line ???

netj(j) = wih(j,1:end-1)*x(:,i)+wih(j,end);

shouldnt it be i.e ->> Y3=sigmoid(X1W13+ X2W23 - θ3 )

rgrds

Answer 3

[Imran Babar]

Dear sir I want to use the same code for the following data set

Input dataset=[1 1 1 2;1 1 2 2;1 2 2 2; 2 2 2 2] Output=[5 6 7 8]

but it is always generating output as given below

1 1 1 1

I tried my best but unable to understand how may I get these results

[Greg Heath]

Your outputs are not within the range of logsig.

Either normalize your outputs to fit in {0,1)

or

change your output activation function (e.g., 'purelin')

Answer 4

[Sohel Ahammed]

Ok. If i Want to test it, how i have to change. Ex: input : 1 0 expected output : 1 (From learing).

Answer 5

[dsmalenb]

Am I missing something here but I don't see any bias neurons. Maybe this is why you are getting some inputs to work and others not?

[Greg Heath]

Biases are included in my equations (see the "ones")

Greg

[dsmalenb]

Ah! But why are they 1's? Should they now vary as well?

[Greg Heath]

The ones are multiplied by the bias weights which are automatically learned with the others.

[dsmalenb]

I'm sorry but that statement does not make much sense to me. Biases are added to shift the values within the activation function. Multiplying by 1 does nothing.

[Greg Heath]

The 1 is a placeholder which is multiplied by a learned weight.

Hmm, I've been using that notation for decades and this is the 1st question re that that I can remember.

Greg

Answer 6

[sultana albanhar]