Finished first part of task 1

calculate_hypothesis.m

@@ -0,0 +1,9 @@
+function hypothesis = calculate_hypothesis(X, theta, training_example)
+    %CALCULATE_HYPOTHESIS This calculates the hypothesis for a given X,
+    %theta and specified training example
+    x0 = X(training_example, 1);
+    x1 = X(training_example, 2);
+
+    hypothesis = theta(1)*x0+theta(2)*x1;
+end
+

compute_cost.m

@@ -0,0 +1,17 @@
+function J = compute_cost(X, y, theta)
+    %COMPUTE_COST Compute cost for linear regression. Takes as input
+    %matrix X of training examples, a parameter vector, theta, and an
+    %output vector y
+
+    J = 0.0; %cost
+    m = size(y, 1); %number of training examples
+
+    for i = 1:m
+        hypothesis = calculate_hypothesis(X, theta, i);
+        output = y(i);
+        squared_error = (hypothesis - output) ^ 2;
+        J = J + squared_error;
+    end
+
+    J = J * (1.0 / (2 * m));
+end

compute_cost_regularised.m

@@ -0,0 +1,25 @@
+function J = compute_cost_regularised(X, y, theta, l)
+    %COMPUTE_COST_REGULARISED Compute cost for regularised linear regression.
+    %Takes as input matrix X of training examples, a parameter vector, theta, 
+    %lambda (l) and an output vector y
+
+    total_squared_error = 0.0; %cost
+    m = size(y, 1); %number of training examples
+
+    for i = 1:m
+        hypothesis = calculate_hypothesis(X, theta, i);
+        output = y(i);
+        squared_error = (hypothesis - output) ^ 2;
+        total_squared_error = total_squared_error + squared_error;
+    end
+
+    total_regularised_error = 0.0;
+
+    for i = 2:length(theta)
+        total_regularised_error = total_regularised_error + theta(i) ^ 2;
+    end
+
+    total_regularised_error = total_regularised_error * l;
+
+    J = (1.0 / (2 * m)) * (total_squared_error + total_regularised_error);
+end

ex1data1.txt

@@ -0,0 +1,97 @@
+6.1101,17.592
+5.5277,9.1302
+8.5186,13.662
+7.0032,11.854
+5.8598,6.8233
+8.3829,11.886
+7.4764,4.3483
+8.5781,12
+6.4862,6.5987
+5.0546,3.8166
+5.7107,3.2522
+14.164,15.505
+5.734,3.1551
+8.4084,7.2258
+5.6407,0.71618
+5.3794,3.5129
+6.3654,5.3048
+5.1301,0.56077
+6.4296,3.6518
+7.0708,5.3893
+6.1891,3.1386
+20.27,21.767
+5.4901,4.263
+6.3261,5.1875
+5.5649,3.0825
+18.945,22.638
+12.828,13.501
+10.957,7.0467
+13.176,14.692
+22.203,24.147
+5.2524,-1.22
+6.5894,5.9966
+9.2482,12.134
+5.8918,1.8495
+8.2111,6.5426
+7.9334,4.5623
+8.0959,4.1164
+5.6063,3.3928
+12.836,10.117
+6.3534,5.4974
+5.4069,0.55657
+6.8825,3.9115
+11.708,5.3854
+5.7737,2.4406
+7.8247,6.7318
+7.0931,1.0463
+5.0702,5.1337
+5.8014,1.844
+11.7,8.0043
+5.5416,1.0179
+7.5402,6.7504
+5.3077,1.8396
+7.4239,4.2885
+7.6031,4.9981
+6.3328,1.4233
+6.3589,-1.4211
+6.2742,2.4756
+5.6397,4.6042
+9.3102,3.9624
+9.4536,5.4141
+8.8254,5.1694
+5.1793,-0.74279
+21.279,17.929
+14.908,12.054
+18.959,17.054
+7.2182,4.8852
+8.2951,5.7442
+10.236,7.7754
+5.4994,1.0173
+20.341,20.992
+10.136,6.6799
+7.3345,4.0259
+6.0062,1.2784
+7.2259,3.3411
+5.0269,-2.6807
+6.5479,0.29678
+7.5386,3.8845
+5.0365,5.7014
+10.274,6.7526
+5.1077,2.0576
+5.7292,0.47953
+5.1884,0.20421
+6.3557,0.67861
+9.7687,7.5435
+6.5159,5.3436
+8.5172,4.2415
+9.1802,6.7981
+6.002,0.92695
+5.5204,0.152
+5.0594,2.8214
+5.7077,1.8451
+7.6366,4.2959
+5.8707,7.2029
+5.3054,1.9869
+8.2934,0.14454
+13.394,9.0551
+5.4369,0.61705

ex1data2.txt

@@ -0,0 +1,47 @@
+2104,3,399900
+1600,3,329900
+2400,3,369000
+1416,2,232000
+3000,4,539900
+1985,4,299900
+1534,3,314900
+1427,3,198999
+1380,3,212000
+1494,3,242500
+1940,4,239999
+2000,3,347000
+1890,3,329999
+4478,5,699900
+1268,3,259900
+2300,4,449900
+1320,2,299900
+1236,3,199900
+2609,4,499998
+3031,4,599000
+1767,3,252900
+1888,2,255000
+1604,3,242900
+1962,4,259900
+3890,3,573900
+1100,3,249900
+1458,3,464500
+2526,3,469000
+2200,3,475000
+2637,3,299900
+1839,2,349900
+1000,1,169900
+2040,4,314900
+3137,3,579900
+1811,4,285900
+1437,3,249900
+1239,3,229900
+2132,4,345000
+4215,4,549000
+2162,4,287000
+1664,2,368500
+2238,3,329900
+2567,4,314000
+1200,3,299000
+852,2,179900
+1852,4,299900
+1203,3,239500

gradient_descent.m

@@ -0,0 +1,71 @@
+function theta = gradient_descent(X, y, theta, alpha, iterations, do_plot)
+    %GRADIENT_DESCENT do Gradient Descent for a given X, y, theta, alpha
+    %for a specified number of iterations
+
+    %if less than 6 arguments was given, then set do_plot to be false
+    if nargin < 6
+        do_plot = false;
+    end
+    if(do_plot)
+        plot_hypothesis(X, y, theta);
+        drawnow; pause(0.1); 
+    end
+
+    m = size(X, 1); %number of training examples
+    cost_vector = []; %will store the results of our cost function
+
+    for it = 1:iterations
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+        % gradient descent
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+        theta_0 = theta(1);
+        theta_1 = theta(2);
+
+        %update theta(1) and store in temporary variable theta_0
+        sigma = 0.0;
+
+        for i = 1:m
+            hypothesis = X(i, 1) * theta(1) + X(i, 2) * theta(2);
+            output = y(i);
+            sigma = sigma + (hypothesis - output);
+        end
+
+        theta_0 = theta_0 - ((alpha * 1.0) / m) * sigma;
+
+
+        %update theta(2) and store in temporary variable theta_1
+        sigma = 0.0;
+
+        for i = 1:m
+            hypothesis = X(i, 1) * theta(1) + X(i, 2) * theta(2);
+            output = y(i);
+            sigma = sigma + (hypothesis - output) * X(i, 2);
+        end
+
+        theta_1 = theta_1 - ((alpha * 1.0) / m) * sigma;
+
+        %update theta
+        theta = [theta_0, theta_1];
+
+        %update cost_vector
+        cost_vector = [cost_vector; compute_cost(X, y, theta)];
+
+        if do_plot
+            plot_hypothesis(X, y, theta);
+            drawnow; pause(0.1); 
+        end
+    end
+
+    disp 'Gradient descent is finished.'
+        
+    if do_plot
+        disp 'Press enter!'
+        pause;
+    end
+
+    plot_cost(cost_vector);
+        
+    disp 'Press enter!';
+    pause;
+end

hypothesis_to_vector.m

@@ -0,0 +1,7 @@
+function hypothesis_vec = hypothesis_to_vector(X, theta)
+    hypothesis_vec = [];
+
+    for i = 1:size(X, 1)
+        hypothesis_vec = [hypothesis_vec; calculate_hypothesis(X, theta, i)];
+    end
+end

load_data_ex1.m

@@ -0,0 +1,14 @@
+function [X, y] = load_data_ex1()
+%loads the data for excercise 1
+    
+    %read our data from a text file
+    data = dlmread('ex1data1.txt');
+
+    %load from the first column into X
+    X = data(:, 1);
+    %load from the second column into y
+    y = data(:, 2);
+
+    %add 1 to the input vector
+    X = [ones(size(X, 1), 1), X];
+end

load_data_ex2.m

@@ -0,0 +1,11 @@
+function [X, y] = load_data_ex2()
+%loads the data for excercise 2
+
+    %read our data from a text file
+    data = dlmread('ex1data2.txt');
+
+    %load from the first two columns into X
+    X = data(:, 1:2);
+    %load from the third column into y
+    y = data(:, 3);
+end

mllab1.m

@@ -0,0 +1,14 @@
+%% This loads our data
+[X, y] = load_data_ex1();
+
+%% initialize
+theta = [0.0, 0.0]; %The weights of our model.
+
+alpha = 0.01; %The step size for gradient descent.
+iterations = 50;
+
+%do plotting
+do_plot = true;
+
+%% run gradient descent
+t = gradient_descent(X, y, theta, alpha, iterations, do_plot);

mllab2.m

@@ -0,0 +1,18 @@
+%% This loads our data
+[X, y] = load_data_ex2();
+
+%% Normalise and initialize.
+[X, mean_vec, std_vec] = normalise_features(X);
+
+%after normalising we add the bias
+X = [ones(size(X, 1), 1), X];
+
+%initialise theta
+theta = [0.0, 0.0, 0.0];
+alpha = 0.1;
+iterations = 100;
+
+%% 
+t = gradient_descent(X, y, theta, alpha, iterations);
+disp 'Press enter to exit!';
+pause;

mllab3.m

@@ -0,0 +1,60 @@
+function mllab3()
+    % load input data
+    X = [-0.99768; -0.69574; -0.40373; -0.10236; 0.22024;  0.47742;  0.82229];
+
+    % load output data
+    y = [2.0885; 1.1646; 0.3287; 0.46013; 0.44808; 0.10013; -0.32952];
+
+    % insert the bias into the input data
+    X = [ones(size(X, 1), 1), X];
+
+    % perform a polynomial expansion to the fifth order
+    for j = 2:5
+        X = [X, X(:, 2) .^ j];
+    end
+
+    % initialise theta
+    theta = [1.0, 1.0, 1.0, 1.0, 1.0];
+
+    alpha = 0.01;
+    l = 0.0;
+    iterations = 1000;
+    do_plot = false;
+
+    % run gradient descent
+    % you will need to modify the gradient_descent function to accept an
+    % additional argument lambda (l).
+    theta = gradient_descent(X, y, theta, alpha, iterations, l, do_plot)
+
+    % plot the original data
+    original_x = [-0.99768; -0.69574; -0.40373; -0.10236; 0.22024;  0.47742;  0.82229];
+
+    figure(1);
+    plot(original_x, y, 'x');
+    hold on;
+        
+    x = linspace(-1, 1, 1000);
+    y = [];
+
+    for index = 1:1000
+        y = [y, get_hypothesis(x(index), theta)];
+    end
+
+    plot(x, y,'-');
+
+    disp 'Press enter to exit.';
+    pause;
+
+    close(1);
+end
+
+function hypothesis = get_hypothesis(x, theta)
+% helper function which we will use to calculate the
+% hypothesis for a given x and theta
+
+    hypothesis = 0.0;
+    
+    for t = 1:length(theta)
+        hypothesis = hypothesis + theta(t) * (x ^ (t - 1));
+    end
+end

normalise_features.m

@@ -0,0 +1,14 @@
+function [N, mean_vector, std_vector] = normalise_features(X)
+    %NORMALISE_FEATURES Normalise our features by subtracting the mean and
+    %dividing by the standard deviation
+
+    num_rows = size(X, 1);
+
+    mean_vector = mean(X);
+    std_vector = std(X);
+
+    %subtract column mean
+    N = X - ones(num_rows, 1) * mean_vector;
+    %divide each element by column standard deviation
+    N = N ./ (ones(num_rows, 1) * std_vector);
+end

plot_cost.m

@@ -0,0 +1,8 @@
+function plot_cost(J)
+    figure(2);
+
+    plot(J);
+    
+    xlabel('itarations');
+    ylabel('cost');
+end

plot_hypothesis.m

@@ -0,0 +1,10 @@
+function plot_hypothesis(X, y, theta)
+    figure(1);
+    
+    clf(1);
+    plot(X(:, 2), y, 'rx');
+
+    hold on;
+    plot(X(:, 2), hypothesis_to_vector(X, theta));
+    xlabel('x'); ylabel('y=f(x)');
+end