(Solved Homework): Computer exercises Several of the exercises use the data in the following table.

% Loading the dataset

dataSet = load(‘DataSet.txt’);

% Storing the values in seperate matrices

W1 = dataSet(:, 1);

w3 = dataSet(:, 2);

% Do you want feature normalization?

normalization = true;

% Applying mean normalization to our dataset

if (normalization)

    maxX = max(W1);

    minX = min(W1);

   W1= (W1 - maxX) / (maxX - minX);

End

% Running gradient descent on the data

% 'w1' is our input matrix

% 'w3' is our output matrix

% 'parameters' is a matrix containing our initial theta and slope

parameters = [0; 0];

learningRate = 0.1;

iteration = 1500;

[parameters, criterionHistory] = gradient(w1, w3, parameters, learningRate, iteration);

% Plotting our final hypothesis

figure;

plot(min(w1 (:, 2)):max(w1 (:, 2)), parameters(1) + parameters(2) * (min(w1 (:, 2)):max(w1 (:, 2))));

hold on;

% Plotting our criterion function on a different figure to see how we did

figure;

plot(criterionHistory, 1:iteration);

% Finally predicting the output of the provided input

input = 120;

if (normalization)

    input = (input - maxX) / (maxX - minX);

end

output = parameters(1) + parameters(2) * input;

disp(output);

gradient.m

function [ parameters, criterionHistory ] = gradient(w1, w3, parameters, learningRate, iteration )

% Getting the length of our dataset

m = length(w3);

% Creating a matrix of zeros for storing our criterion function history

criterionHistory = zeros(iteration, 1); 

% Running gradient descent

for i = 1:iteration

% Calculating the transpose of our hypothesis

h = (w1* parameters – w3′;

% Updating the parameters

parameters(1) = parameters(1) – learningRate * (1/m) * h * w1(:, 1);

parameters(2) = parameters(2) – learningRate * (1/m) * h * w1 (:, 2);

% Keeping track of the criterion function

criterionHistory(i) = criterion(w1, w3, parameters);

end

criterion.m

parameters(1) = parameters(1) - learningRate * (1/m) * h * w1(:, 1);

parameters(2) = parameters(2) - learningRate * (1/m) * h * w1(:, 2);

function [ criterion ] = criterion( w1, w3, parameters )

    %   Calculates the criterion function

    criterion = (w1 * parameters – w3)' * (w1 * parameters – w3) / (2 * length(w3));    

end