Finished first part of task 1
This commit is contained in:
Sam Perry
@@ -0,0 +1,9 @@
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function hypothesis = calculate_hypothesis(X, theta, training_example)
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%CALCULATE_HYPOTHESIS This calculates the hypothesis for a given X,
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%theta and specified training example
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x0 = X(training_example, 1);
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x1 = X(training_example, 2);
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hypothesis = theta(1)*x0+theta(2)*x1;
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end
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@@ -0,0 +1,17 @@
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function J = compute_cost(X, y, theta)
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%COMPUTE_COST Compute cost for linear regression. Takes as input
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%matrix X of training examples, a parameter vector, theta, and an
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%output vector y
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J = 0.0; %cost
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m = size(y, 1); %number of training examples
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for i = 1:m
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hypothesis = calculate_hypothesis(X, theta, i);
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output = y(i);
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squared_error = (hypothesis - output) ^ 2;
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J = J + squared_error;
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end
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J = J * (1.0 / (2 * m));
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end
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@@ -0,0 +1,25 @@
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function J = compute_cost_regularised(X, y, theta, l)
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%COMPUTE_COST_REGULARISED Compute cost for regularised linear regression.
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%Takes as input matrix X of training examples, a parameter vector, theta,
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%lambda (l) and an output vector y
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total_squared_error = 0.0; %cost
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m = size(y, 1); %number of training examples
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for i = 1:m
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hypothesis = calculate_hypothesis(X, theta, i);
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output = y(i);
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squared_error = (hypothesis - output) ^ 2;
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total_squared_error = total_squared_error + squared_error;
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end
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total_regularised_error = 0.0;
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for i = 2:length(theta)
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total_regularised_error = total_regularised_error + theta(i) ^ 2;
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end
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total_regularised_error = total_regularised_error * l;
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J = (1.0 / (2 * m)) * (total_squared_error + total_regularised_error);
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end
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@@ -0,0 +1,97 @@
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6.1101,17.592
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5.5277,9.1302
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8.5186,13.662
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7.0032,11.854
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5.8598,6.8233
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8.3829,11.886
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7.4764,4.3483
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8.5781,12
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6.4862,6.5987
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5.0546,3.8166
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5.7107,3.2522
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14.164,15.505
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5.734,3.1551
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8.4084,7.2258
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5.6407,0.71618
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5.3794,3.5129
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6.3654,5.3048
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5.1301,0.56077
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6.4296,3.6518
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7.0708,5.3893
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6.1891,3.1386
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20.27,21.767
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5.4901,4.263
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6.3261,5.1875
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5.5649,3.0825
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18.945,22.638
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12.828,13.501
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10.957,7.0467
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13.176,14.692
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22.203,24.147
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5.2524,-1.22
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6.5894,5.9966
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9.2482,12.134
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5.8918,1.8495
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8.2111,6.5426
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7.9334,4.5623
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8.0959,4.1164
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5.6063,3.3928
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12.836,10.117
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6.3534,5.4974
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5.4069,0.55657
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6.8825,3.9115
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11.708,5.3854
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5.7737,2.4406
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7.8247,6.7318
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7.0931,1.0463
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5.0702,5.1337
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5.8014,1.844
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11.7,8.0043
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5.5416,1.0179
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7.5402,6.7504
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5.3077,1.8396
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7.4239,4.2885
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7.6031,4.9981
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6.3328,1.4233
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6.3589,-1.4211
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6.2742,2.4756
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5.6397,4.6042
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9.3102,3.9624
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9.4536,5.4141
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8.8254,5.1694
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5.1793,-0.74279
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21.279,17.929
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14.908,12.054
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18.959,17.054
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7.2182,4.8852
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8.2951,5.7442
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10.236,7.7754
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5.4994,1.0173
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20.341,20.992
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10.136,6.6799
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7.3345,4.0259
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6.0062,1.2784
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7.2259,3.3411
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5.0269,-2.6807
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6.5479,0.29678
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7.5386,3.8845
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5.0365,5.7014
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10.274,6.7526
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5.1077,2.0576
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5.7292,0.47953
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5.1884,0.20421
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6.3557,0.67861
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9.7687,7.5435
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6.5159,5.3436
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8.5172,4.2415
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9.1802,6.7981
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6.002,0.92695
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5.5204,0.152
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5.0594,2.8214
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5.7077,1.8451
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7.6366,4.2959
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5.8707,7.2029
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5.3054,1.9869
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8.2934,0.14454
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13.394,9.0551
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5.4369,0.61705
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@@ -0,0 +1,47 @@
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2104,3,399900
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1600,3,329900
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2400,3,369000
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1416,2,232000
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3000,4,539900
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1985,4,299900
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1534,3,314900
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1427,3,198999
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1380,3,212000
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1494,3,242500
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1940,4,239999
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2000,3,347000
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1890,3,329999
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4478,5,699900
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1268,3,259900
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2300,4,449900
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1320,2,299900
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1236,3,199900
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2609,4,499998
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3031,4,599000
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1767,3,252900
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1888,2,255000
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1604,3,242900
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1962,4,259900
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3890,3,573900
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1100,3,249900
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1458,3,464500
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2526,3,469000
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2200,3,475000
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2637,3,299900
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1839,2,349900
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1000,1,169900
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2040,4,314900
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3137,3,579900
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1811,4,285900
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1437,3,249900
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1239,3,229900
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2132,4,345000
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4215,4,549000
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2162,4,287000
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1664,2,368500
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2238,3,329900
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2567,4,314000
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1200,3,299000
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852,2,179900
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1852,4,299900
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1203,3,239500
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@@ -0,0 +1,71 @@
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function theta = gradient_descent(X, y, theta, alpha, iterations, do_plot)
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%GRADIENT_DESCENT do Gradient Descent for a given X, y, theta, alpha
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%for a specified number of iterations
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%if less than 6 arguments was given, then set do_plot to be false
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if nargin < 6
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do_plot = false;
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end
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if(do_plot)
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plot_hypothesis(X, y, theta);
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drawnow; pause(0.1);
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end
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m = size(X, 1); %number of training examples
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cost_vector = []; %will store the results of our cost function
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for it = 1:iterations
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% gradient descent
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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theta_0 = theta(1);
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theta_1 = theta(2);
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%update theta(1) and store in temporary variable theta_0
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sigma = 0.0;
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for i = 1:m
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hypothesis = X(i, 1) * theta(1) + X(i, 2) * theta(2);
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output = y(i);
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sigma = sigma + (hypothesis - output);
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end
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theta_0 = theta_0 - ((alpha * 1.0) / m) * sigma;
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%update theta(2) and store in temporary variable theta_1
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sigma = 0.0;
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for i = 1:m
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hypothesis = X(i, 1) * theta(1) + X(i, 2) * theta(2);
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output = y(i);
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sigma = sigma + (hypothesis - output) * X(i, 2);
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end
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theta_1 = theta_1 - ((alpha * 1.0) / m) * sigma;
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%update theta
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theta = [theta_0, theta_1];
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%update cost_vector
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cost_vector = [cost_vector; compute_cost(X, y, theta)];
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if do_plot
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plot_hypothesis(X, y, theta);
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drawnow; pause(0.1);
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end
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end
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disp 'Gradient descent is finished.'
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if do_plot
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disp 'Press enter!'
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pause;
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end
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plot_cost(cost_vector);
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disp 'Press enter!';
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pause;
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end
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@@ -0,0 +1,7 @@
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function hypothesis_vec = hypothesis_to_vector(X, theta)
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hypothesis_vec = [];
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for i = 1:size(X, 1)
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hypothesis_vec = [hypothesis_vec; calculate_hypothesis(X, theta, i)];
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end
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end
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@@ -0,0 +1,14 @@
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function [X, y] = load_data_ex1()
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%loads the data for excercise 1
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%read our data from a text file
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data = dlmread('ex1data1.txt');
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%load from the first column into X
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X = data(:, 1);
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%load from the second column into y
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y = data(:, 2);
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%add 1 to the input vector
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X = [ones(size(X, 1), 1), X];
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end
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@@ -0,0 +1,11 @@
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function [X, y] = load_data_ex2()
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%loads the data for excercise 2
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%read our data from a text file
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data = dlmread('ex1data2.txt');
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%load from the first two columns into X
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X = data(:, 1:2);
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%load from the third column into y
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y = data(:, 3);
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end
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@@ -0,0 +1,14 @@
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%% This loads our data
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[X, y] = load_data_ex1();
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%% initialize
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theta = [0.0, 0.0]; %The weights of our model.
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alpha = 0.01; %The step size for gradient descent.
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iterations = 50;
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%do plotting
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do_plot = true;
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%% run gradient descent
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t = gradient_descent(X, y, theta, alpha, iterations, do_plot);
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@@ -0,0 +1,18 @@
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%% This loads our data
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[X, y] = load_data_ex2();
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%% Normalise and initialize.
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[X, mean_vec, std_vec] = normalise_features(X);
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%after normalising we add the bias
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X = [ones(size(X, 1), 1), X];
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%initialise theta
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theta = [0.0, 0.0, 0.0];
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alpha = 0.1;
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iterations = 100;
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%%
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t = gradient_descent(X, y, theta, alpha, iterations);
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disp 'Press enter to exit!';
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pause;
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@@ -0,0 +1,60 @@
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function mllab3()
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% load input data
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X = [-0.99768; -0.69574; -0.40373; -0.10236; 0.22024; 0.47742; 0.82229];
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% load output data
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y = [2.0885; 1.1646; 0.3287; 0.46013; 0.44808; 0.10013; -0.32952];
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% insert the bias into the input data
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X = [ones(size(X, 1), 1), X];
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% perform a polynomial expansion to the fifth order
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for j = 2:5
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X = [X, X(:, 2) .^ j];
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end
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% initialise theta
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theta = [1.0, 1.0, 1.0, 1.0, 1.0];
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alpha = 0.01;
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l = 0.0;
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iterations = 1000;
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do_plot = false;
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% run gradient descent
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% you will need to modify the gradient_descent function to accept an
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% additional argument lambda (l).
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theta = gradient_descent(X, y, theta, alpha, iterations, l, do_plot)
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% plot the original data
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original_x = [-0.99768; -0.69574; -0.40373; -0.10236; 0.22024; 0.47742; 0.82229];
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figure(1);
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plot(original_x, y, 'x');
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hold on;
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x = linspace(-1, 1, 1000);
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y = [];
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for index = 1:1000
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y = [y, get_hypothesis(x(index), theta)];
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end
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plot(x, y,'-');
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disp 'Press enter to exit.';
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pause;
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close(1);
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end
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function hypothesis = get_hypothesis(x, theta)
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% helper function which we will use to calculate the
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% hypothesis for a given x and theta
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hypothesis = 0.0;
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for t = 1:length(theta)
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hypothesis = hypothesis + theta(t) * (x ^ (t - 1));
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end
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end
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@@ -0,0 +1,14 @@
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function [N, mean_vector, std_vector] = normalise_features(X)
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%NORMALISE_FEATURES Normalise our features by subtracting the mean and
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%dividing by the standard deviation
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num_rows = size(X, 1);
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mean_vector = mean(X);
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std_vector = std(X);
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%subtract column mean
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N = X - ones(num_rows, 1) * mean_vector;
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%divide each element by column standard deviation
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N = N ./ (ones(num_rows, 1) * std_vector);
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end
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@@ -0,0 +1,8 @@
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function plot_cost(J)
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figure(2);
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plot(J);
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xlabel('itarations');
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ylabel('cost');
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end
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@@ -0,0 +1,10 @@
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function plot_hypothesis(X, y, theta)
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figure(1);
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clf(1);
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plot(X(:, 2), y, 'rx');
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hold on;
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plot(X(:, 2), hypothesis_to_vector(X, theta));
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xlabel('x'); ylabel('y=f(x)');
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end
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Reference in New Issue
Block a user