Modifying Existing Neural Network for multiclass classification

I have come across some matlab code that seems to make a neural network for m hidden nodes. I want to extend it to make a neural network for m hidden nodes and 10 outputs for multi-class classification, and any amount of hidden layers.

I have one big question about it though, it seems to make a weight matrix based on the number of samples, which seems completely wrong. Can anyone explain what is going on exactly? And how i might modify this for multi-class classification?

Here is the code, it is broken into two functions

One that simply calls the training of the neural net until it seems to have low error:

function BackPropAlgo(Input, Output) %% Credits to: Anoop.V.S & Lekshmi B G %% http://anoopacademia.wordpress.com/2013/09/29/back-propagation-algorithm-using-matlab/ %STEP 1 : Normalize the Input %Checking whether the Inputs needs to be normalized or not if (max(Input(:))< 1 || max(Input(:))>-1) %Need to normalize Norm_Input = Input / max(Input(:)); else Norm_Input = Input; end %Checking Whether the Outputs needs to be normalized or not if(max(Output(:)) < 1 || max(Output(:))>-1) %Need to normalize Norm_Output = Output / max(Output(:)); else Norm_Output = Output; end %Assigning the number of hidden neurons in hidden layer m = 2; %Find the size of Input and Output Vectors [l,b] = size(Input); [n,a] = size(Output); %Initialize the weight matrices with random weights V = rand(l,m); % Weight matrix from Input to Hidden W = rand(m,n); % Weight matrix from Hidden to Output %Setting count to zero, to know the number of iterations count = 0; %Calling function for training the neural network [errorValue, delta_V, delta_W] = trainNeuralNet(Norm_Input,Norm_Output,V,W); %Checking if error value is greater than 0.1. If yes, we need to train the %network again. User can decide the threshold value while errorValue > 0.05 %incrementing count count = count + 1; %Store the error value into a matrix to plot the graph Error_Mat(count)=errorValue; %Change the weight metrix V and W by adding delta values to them W=W+delta_W; V=V+delta_V; %Calling the function with another overload. %Now we have delta values as well. count [errorValue, delta_V, delta_W]=trainNeuralNet(Norm_Input,Norm_Output,V,W,delta_V,delta_W); end %This code will be executed when the error value is less than 0.1 if errorValue < 0.05 %Incrementing count variable to know the number of iteration count=count+1; %Storing error value into matrix for plotting the graph Error_Mat(count)=errorValue; end %Calculating error rate Error_Rate=sum(Error_Mat)/count; figure; %setting y value for plotting graph y=[1:count]; %Plotting graph plot(y, Error_Mat); end 

And another that actually performs the updates of the weights in the neural net:

function [errorValue, delta_V, delta_W] = trainNeuralNet(Input, Output, V, W, delta_V, delta_W) %% Credits to: Anoop.V.S & Lekshmi B G %% http://anoopacademia.wordpress.com/2013/09/29/back-propagation-algorithm-using-matlab/ %Description : Function to train the network %Function for calculation (steps 4 - 16) %To train the Neural Network %Calculating the Output of Input Layer %No computation here. %Output of Input Layer is same as the Input of Input Layer Output_of_InputLayer = Input; %Calculating Input of the Hidden Layer %Here we need to multiply the Output of the Input Layer with the %synaptic weight. That weight is in the matrix V. Input_of_HiddenLayer = V' * Output_of_InputLayer; %Calculate the size of Input to Hidden Layer [m n] = size(Input_of_HiddenLayer); %Now, we have to calculate the Output of the Hidden Layer %For that, we need to use Sigmoidal Function Output_of_HiddenLayer = 1./(1+exp(-Input_of_HiddenLayer)); %Calculating Input to Output Layer %Here we need to multiply the Output of the Hidden Layer with the - %synaptic weight. That weight is in the matrix W Input_of_OutputLayer = W'*Output_of_HiddenLayer; %Clear varables clear m n; %Calculate the size of Input of Output Layer [m n] = size(Input_of_OutputLayer); %Now, we have to calculate the Output of the Output Layer %For that, we need to use Sigmoidal Function Output_of_OutputLayer = 1./(1+exp(-Input_of_OutputLayer)); %Now we need to calculate the Error using Root Mean Square method difference = Output - Output_of_OutputLayer; square = difference.*difference; errorValue = sqrt(sum(square(:))); %Calculate the matrix 'd' with respect to the desired output %Clear the variable m and n clear m n [n a] = size(Output); for i = 1:n for j = 1:a d(i,j) =(Output(i,j)-Output_of_OutputLayer(i,j))*Output_of_OutputLayer(i,j)*(1-Output_of_OutputLayer(i,j)); end end %Now, calculate the Y matrix Y = Output_of_HiddenLayer * d; %STEP 11 %Checking number of arguments. We are using function overloading %On the first iteration, we don't have delta V and delta W %So we have to initialize with zero. The size of delta V and delta W will %be same as that of V and W matrix respectively (nargin - no of arguments) if nargin == 4 delta_W=zeros(size(W)); delta_V=zeros(size(V)); end %Initializing etta with 0.6 and alpha with 1 etta=0.6; alpha=1; %Calculating delta W delta_W= alpha.*delta_W + etta.*Y;%STEP 12 %STEP 13 %Calculating error matrix error = W*d; %Calculating d* clear m n [m n] = size(error); for i = 1:m for j = 1:n d_star(i,j)= error(i,j)*Output_of_HiddenLayer(i,j)*(1-Output_of_HiddenLayer(i,j)); end end %Now find matrix, X (Input * transpose of d_star) X = Input * d_star'; %STEP 14 %Calculating delta V delta_V=alpha*delta_V+etta*X; end