3006-NEURAL COMPUTING
ASSIGNMENT 2 GROUP 09

NAME G.D.P.M. Perera A.A. Vidura H.P.S.S. Kumara G.M.T.C. Galahena

INDEX No 10001352 10000909 10000552 10000437

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Part 1
Introduction
In the part 1, we have to classify the given four English Characters into known four different classes. As the output classes are known we used Feed Forward Back Propagation method to train the artificial neural network. Here is a brief description of a supervised training network.

Consider the network output Y which is usually denoted by NET, When the network is trained for a specific Target, this training process is called Supervised Training. In supervised training, when the network is being trained it is required to produce the expected target. Training is carried out in such a way that, weights of the network are trained (or adjusted or updated or modified) until the network produces the expected target.

Basic steps of supervised training
     Weights are randomly set. Target (Expected or Desired output) is identified. Input is applied to the Network. Network Actual Output (Weighted Sum of Input) is calculated. Calculate the Error (Error = Target ~ Actual Output).  Weights are updated until the Error is minimized

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Dalta Rule

   

– Wnew - Wold η – Learning rate parameter δ – Error (target – actual output) x – input

In a feed forward back propagation network the signals are traveled on the forward direction and inputs have no feedback from the output. And the error is propagated backwards from the output nodes to the input nodes. There can be hidden layers as well and the output of a layer is weighted and given to the next layer. Here are the abstract steps of the neural network.

Build the network (newff)

Train the Network (train)

Test the Network (sim)

Inputs for the Neural Network
We have been given 25 images for each character. The task of ANN is classifying these characters correctly. We used first 25 images for the training and rest of 10 images for testing.

Preprocessing
As the inputs are formed in different scales first we have to scale them into acceptable size. This will help to ANN to generate correct output. We decided to scale down all the inputs to the size of the data set which was 40x40 pixels. To do that we used the “imresize” function available in image processing toolbox in matlab. After resizing the image convert it to grayscale image because the scanned images may be in rgb or different color formats. Convert it to a binary image. Detect the edges of the character image.Perform the image dilation and image filling on the image

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% Reading the First Input(character "o") folder = '.\images\trainnig\o\'; a = dir('.\images\trainnig\o\*.jpg'); size_o = size(a) for m=1:1:size_o(1) I = imread(strcat(folder,a(m).name)); I1 = rgb2gray(I); I1 = imresize(I1,[40,40]); I1 = im2bw(I1,graythresh(I1)); I1 = edge(uint8(I1)); sem = strel('square',2); I1 = imdilate(I1, sem); I1= imfill(I1,'holes'); char1(m).im = I1; end

After processing the image, the input image again resize in to 13*13 pixels to reduce the number of input nodes. for k=1:25 mat1(k).im mat2(k).im mat3(k).im mat4(k).im end =imresize(p.char1(k).im,[13 =imresize(p.char2(k).im,[13 =imresize(p.char3(k).im,[13 =imresize(p.char4(k).im,[13 13]); 13]); 13]); 13]);

The input image should be converting into a column vector of 169x1 in order to create the input vector for the ANN. for k=1:25 mat11(k).im mat12(k).im mat13(k).im mat14(k).im end

= = = =

mat1(k).im(:); mat2(k).im(:); mat3(k).im(:); mat4(k).im(:);

After that those reshaped combined together and made the 169*25*4 input vector for the ANN.

Declaring the targets
In supervised training we have to set the target for the ANN. We used following binary pattern. Classification for target 1000 – for the target of the “o” 0100 – for the target of the “q” 0010 – for the target of the “a” 0001 – for the target of the “c”

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Training the network
Matlab command ‘newff’ creates a Feed Forward Back Propagation artificial neural network. Syntax net = newff(minmax(alphabet),[S1 S2],{'logsig' 'logsig'},'traingdx'); Description alphabet(PR) - R x 2 matrix of min and max values for R input elements. S1 - Size of the 1st hidden layer. S2 – Size of the output layer. 'logsig' - Transfer function of ith layer. 'logsig' - Backprop network training function. 'traingdx' - Backprop weight/bias learning function.

Testing the Neural Network
10 images of each character are used to test the ANN that we have already created. Following Matlab command ‘sim’ used to test and simulate the results in the code. Syntax fout = round(sim(net,test)); Description SIM simulates neural networks. net - Neural Network. test - Network inputs for testing. and returns: fout - Network outputs.

Sample output

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Conclusion
    probability to classify the character “o” is 100%. probability to classify the character “q” is 90%. probability to classify the character “a” is 80%. probability to classify the character “o” is 100%.

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Part 2
Unsupervised Networks - Self-Organizing Maps (SOMs) In a way similar to the self-learning process of the human brain, a neural network can be designed for Unsupervised Learning. In this case, the network does not have a target for the given input. Instead, the network decides the most appropriate class for the given input by selecting the most relevant (output) node in the hidden layer. Steps followed in unsupervised network training are:
      

Set Weights Randomly. Apply Input Vector X . Calculate the Strength (i.e. Weighted Sum) of Each Node. Determine the Node i with the Highest Response. Declare the Node i as the Winner. (i has the Weights most similar to X) Train Weights of i to make them even more similar to X. Go to step 2 above until end-of-input.

Generating the random real numbers within the four given ranges
Followings are the ranges

Class 1 15.7-16.0

Class 2 16.2-16.5

Class 3 16.7-17.0

Class 4 17.2-17.5

To generate random numbers rand function is being used. Training set has 400 inputs 100 from each range all insert into a matrix.Each range is given as a row in the train set matrix.Given below are the command’s for creating the train set.

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% training set X_1= [p1 q1 r1 s1 ;q1 r1 s1 p1 ;r1 s1 p1 q1 ;s1 p1 q1 r1 ]; p2 q2 r2 s2 = = = = 15.7 16.2 16.7 17.2 + + + + (15.7-16) * rand(1,25); (16.2-16.5) * rand(1,25); (16.7-17) * rand(1,25); (17.2-17.5) * rand(1,25);

% testing set X_2= [p2 q2 r2 s2 ;q2 r2 s2 p2 ;r2 s2 p2 q2 ;s2 p2 q2 r2 ];

Training the Network
Initializing the Network netsom=newsom([ 15.7 17.5;15.7 17.5;15.7 17.5;15.7 17.5],4); netsom.inputWeights{1}.initFcn = 'randnc'; netsom.trainParam.epochs = 10

Training the Network
We create column vectors (X11, X22) . X11 is for input vector and X22 for train vector.
X11=zeros(4,100); for i=1:400 X11(:,i)= X_1(:,i); end X22 = zeros(4,25); for i=1:100 X22(:, i) = X_2(:, i); end

To train the network the function train is being used . For this we use trainSet that has being obtained earlier.
% Training SOM netsom = train(netsom,X11);

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Geting the Output we can use sim function to get output result_1 = sim(netsom,X11); result_2 = sim(netsom,X22);

Sample output

Conclusion
Every instance the error rate is very close to the 0%

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