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Assignment Description

CSCI 410 Pattern Recognition

Assignment Four

by Denton Bobeldyk



1.       Using Matlab, create a multi-layer perceptron with 3 layers: input layer, hidden layer, output layer (using a sigmoid function).

2.       Define the learning rate and total iterations learningRate = 0.5; totalIterations = 500;


3.       Define the size of the input layer and the hidden layer:

inputLayerNumber = 2; hiddenLayerNumber = 2;


4.       Define the input and hidden layer:

inputLayer = zeros(inputLayerNumber, 1);

hiddenLayer = zeros(hiddenLayerNumber, 1);



5.       Add the bias to the input and hidden layer:

inputLayerWithBias = zeros(inputLayerNumber + 1, 1); hiddenLayerWithBias = zeros(hiddenLayerNumber + 1, 1);


6.       Define the output layer:

outputLayer = 0;

7.       Randomly assign the weights to the input and hidden layer: inputLayerWeights = rand( (inputLayerNumber + 1) ,hiddenLayerNumber) - .5 ; hiddenLayerWeights = rand( (hiddenLayerNumber + 1), 1) - .5;

8.       Define the input data:

inputLayer = [0 0; 0 1; 1 0; 1 1];


9.       Define the target output for the input layer: ANDtargetOutput = [0; 0; 0; 1]; targetOutput = ANDtargetOutput;

10.   Define the variable `m’ as the number of samples:

m = size(targetOutput, 1);


11.   Create a for loop, that will step through each of the samples one at a time (Note: this is known as online learning)


for iter=1:totalIterations


     for i = 1:m;


        hiddenLayerActivation = inputLayerWithBias(i, :) * inputLayerWeights;         hiddenLayer = sigmoid(hiddenLayerActivation);


        %Add the bias to the hiddenLayer         hiddenLayerWithBias = [1, hiddenLayer];


        outputLayer = sigmoid(hiddenLayerWithBias * hiddenLayerWeights);


%Calculate the error:

deltaOutput = targetOutput(i) - outputLayer;

        deltaHidden(1) = (deltaOutput * hiddenLayerWeights(1)) .* ((hiddenLayerWithBias(1) * (1.0 - hiddenLayerWithBias(1))));         deltaHidden(2) = (deltaOutput * hiddenLayerWeights(2)) .* ((hiddenLayerWithBias(2) * (1.0 - hiddenLayerWithBias(2))));         deltaHidden(3) = (deltaOutput * hiddenLayerWeights(3)) .*

((hiddenLayerWithBias(3) * (1.0 - hiddenLayerWithBias(3)))); 

        % Fixed Step Gradient Descent - Update the weights

        hiddenLayerWeights(1) = hiddenLayerWeights(1) + (learningRate *

(deltaOutput * hiddenLayerWithBias(1)));

        hiddenLayerWeights(2) = hiddenLayerWeights(2) + (learningRate *

(deltaOutput * hiddenLayerWithBias(2)));

        hiddenLayerWeights(3) = hiddenLayerWeights(3) + (learningRate *

(deltaOutput * hiddenLayerWithBias(3)));


        %update each weight according to the part that they played         inputLayerWeights(1,1) = inputLayerWeights(1,1) + (learningRate * deltaHidden(2) * inputLayerWithBias(i, 1));

        inputLayerWeights(1,2) = inputLayerWeights(1,2) + (learningRate * deltaHidden(3) * inputLayerWithBias(i, 1));


        inputLayerWeights(2,1) = inputLayerWeights(2,1) + (learningRate * deltaHidden(2) * inputLayerWithBias(i, 2));

        inputLayerWeights(2,2) = inputLayerWeights(2,2) + (learningRate * deltaHidden(3) * inputLayerWithBias(i, 2));


        inputLayerWeights(3,1) = inputLayerWeights(3,1) + (learningRate * deltaHidden(2) * inputLayerWithBias(i, 3));

        inputLayerWeights(3,2) = inputLayerWeights(3,2) + (learningRate * deltaHidden(3) * inputLayerWithBias(i, 3));  







12.   Create the sigmoid function:


function a = sigmoid(z)


a = 1.0 ./ (1.0 + exp(-z));




13.   Create the cost function:

% This function will only work for NN with just one output (k = 1) function [averageCost] = costFunction(inputLayerWithBias, inputLayerWeights, hiddenLayerWeights, targetOutput)

%Sum of square errors cost function m = 4;

hiddenLayer = sigmoid(inputLayerWithBias * inputLayerWeights);


hiddenLayerWithBias = [ones(m,1) hiddenLayer];


outputLayer = sigmoid(hiddenLayerWithBias * hiddenLayerWeights);



% Step through all of the samples and calculate the cost at each one for i=1:m

    cost(i) = (1/2) * ((outputLayer(i) - targetOutput(i)) .^ 2); end


%Sum up all of the individual costs totalCost = sum(cost);


%average them out

averageCost = totalCost * (1/m);






14. Create a function that will summarize the output of the 4 samples:

 function outputSummary(inputLayerWithBias, inputLayerWeights, hiddenLayerWeights, targetOutput, totalIterations)


cost = costFunction(inputLayerWithBias, inputLayerWeights, hiddenLayerWeights, targetOutput);


hiddenLayer = sigmoid(inputLayerWithBias * inputLayerWeights);


%we have multiple samples, so we need to add the bias to each of them hiddenLayerWithBias = [ones(size(targetOutput,1),1) hiddenLayer];


actualOutput = sigmoid(hiddenLayerWithBias * hiddenLayerWeights);



fprintf('========================================= '); fprintf('Output Summary (after %d iterations): ', totalIterations); fprintf('Total Cost: [%f] ', cost);

    for i=1:length(actualOutput)     if(actualOutput(i) > 0.5)         thresholdedValue = 1;     else

        thresholdedValue = 0;     end     

    if(thresholdedValue == targetOutput(i))

        fprintf('Sample[%d]: Target = [%f] Thresholded Value = [%f] Actual= [%f] ', i, targetOutput(i), thresholdedValue, actualOutput(i));     else  % else print the error in red

        fprintf(2,'Sample[%d]: Target = [%f] Thresholded Value = [%f] Actual= [%f] ', i, targetOutput(i), thresholdedValue, actualOutput(i));     end          end   










15.   Attempt to learn the following target outputs:

ANDtargetOutput = [0; 0; 0; 1];

ORtargetOutput = [0; 1; 1; 1];

NANDtargetOutput = [1; 1; 1; 0];

NORtargetOutput = [1; 0; 0; 0];

XORtargetOutput = [0; 1; 1; 0];


16.   Which of the above target outputs does it have the hardest time learning and why?





1.       A single matlab script that performs the above tasks.

2.       The answer to question 16 output using ‘fprintf’ commands in the above script.

3.       A word document containing the copy and pasted output of the script execution. Please make sure there are no line wrappings (decrease the font if necessary).













Andrew NG, Machine Learning course from Coursera

Bishop, Christopher M. Neural networks for pattern recognition. Oxford university press, 1995.


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