{"id":523,"date":"2015-04-03T23:09:57","date_gmt":"2015-04-04T05:09:57","guid":{"rendered":"http:\/\/mattdturner.com\/wordpress\/?p=523"},"modified":"2018-08-02T20:50:46","modified_gmt":"2018-08-03T02:50:46","slug":"coursera-machine-learning-in-python-exercise-1","status":"publish","type":"post","link":"http:\/\/mattdturner.com\/wordpress\/2015\/04\/coursera-machine-learning-in-python-exercise-1\/","title":{"rendered":"Coursera Machine Learning In Python (Exercise 1)"},"content":{"rendered":"

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I have previously done the Coursera Machine Learning exercises in Matlab. I thought, now that I am starting to get away from Matlab and use Python more, I should re-do the exercises in Python. This is exercise 1.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[447]:<\/div>\n
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%<\/span>matplotlib<\/span> inline\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> scipy<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 1: Create an eye matrix. While this is incredibly simple, I want to make sure that I go through each step and provide a resulting document that a novice can follow long and understand what is happening.<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[448]:<\/div>\n
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A<\/span> =<\/span> np<\/span>.<\/span>identity<\/span>(<\/span>5<\/span>)<\/span>\r\nprint<\/span> A<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[[ 1.  0.  0.  0.  0.]\r\n [ 0.  1.  0.  0.  0.]\r\n [ 0.  0.  1.  0.  0.]\r\n [ 0.  0.  0.  1.  0.]\r\n [ 0.  0.  0.  0.  1.]]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 2: Read in the data from ‘ex1data1.txt’ and plot it as a scatter plot<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[449]:<\/div>\n
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# Use the numpy genfromtext function to read the data<\/span>\r\ndata<\/span> =<\/span> np<\/span>.<\/span>genfromtxt<\/span>(<\/span>'\/Users\/matthewturner\/Desktop\/Coursera_machine_learning\/'<\/span>+<\/span>\r\n                     'machine-learning-ex1\/ex1\/ex1data1.txt'<\/span>,<\/span> delimiter<\/span>=<\/span>','<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[450]:<\/div>\n
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# Pull out the first column (theta0) into the variable X, and the 2nd column (theta1)<\/span>\r\n# into the variable y.  These variable names are consistent with the example.<\/span>\r\nX<\/span>,<\/span>y<\/span> =<\/span> data<\/span>[:,<\/span>0<\/span>],<\/span>data<\/span>[:,<\/span>1<\/span>]<\/span>\r\n\r\n# Set m = the length of y (i.e., the number of observations).<\/span>\r\nm<\/span> =<\/span> len<\/span>(<\/span>y<\/span>)<\/span>\r\ny<\/span> =<\/span> y<\/span>.<\/span>reshape<\/span>(<\/span>m<\/span>,<\/span>1<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[451]:<\/div>\n
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plt<\/span>.<\/span>scatter<\/span>(<\/span>X<\/span>,<\/span>y<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<matplotlib.collections.PathCollection at 0x1091f5d50><\/pre>\n<\/div>\n<\/div>\n
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Part 3: Gradient Descent<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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# Add a column of ones to the data<\/span>\r\nX<\/span> =<\/span> np<\/span>.<\/span>c_<\/span>[<\/span>np<\/span>.<\/span>ones<\/span>((<\/span>m<\/span>,<\/span>1<\/span>)),<\/span>X<\/span>]<\/span>\r\ntheta<\/span> =<\/span> np<\/span>.<\/span>zeros<\/span>((<\/span>2<\/span>,<\/span>1<\/span>))<\/span>\r\n\r\niterations<\/span> =<\/span> 1500<\/span>\r\nalpha<\/span> =<\/span> 0.01<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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def<\/span> costFuncIter<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>):<\/span>\r\n    cum_sum<\/span> =<\/span> 0<\/span>\r\n    for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>m<\/span>):<\/span>\r\n        h<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>[<\/span>i<\/span>],<\/span>theta<\/span>)<\/span> -<\/span> y<\/span>[<\/span>i<\/span>]<\/span>\r\n        cum_sum<\/span> +=<\/span> 1.0<\/span>\/<\/span>(<\/span>2<\/span>*<\/span>m<\/span>)<\/span> *<\/span> h<\/span> *<\/span> h<\/span>\r\n    return<\/span> cum_sum<\/span>\r\n        \r\nJ<\/span> =<\/span> costFuncIter<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>)<\/span>\r\nprint<\/span> J<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[ 32.07273388]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[454]:<\/div>\n
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# Compute and display the initial cost function<\/span>\r\ndef<\/span> costFunc<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>):<\/span>\r\n    h<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>,<\/span>theta<\/span>)<\/span>-<\/span>y<\/span>\r\n    h2<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>h<\/span>.<\/span>T<\/span>,<\/span>h<\/span>)<\/span>\r\n    J<\/span> =<\/span> 1.<\/span>\/<\/span>(<\/span>2<\/span>*<\/span>m<\/span>)<\/span> *<\/span> h2<\/span>\r\n    return<\/span> J<\/span>[<\/span>0<\/span>,<\/span>0<\/span>]<\/span>\r\n\r\nJ<\/span> =<\/span> costFunc<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>)<\/span>\r\nprint<\/span> J<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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32.0727338775\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[455]:<\/div>\n
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# Run the Gradient Descent Algorithm<\/span>\r\ndef<\/span> gradientDescent<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>,<\/span>alpha<\/span>,<\/span>iterations<\/span>):<\/span>\r\n    J_history<\/span> =<\/span> np<\/span>.<\/span>zeros<\/span>(<\/span>iterations<\/span>)<\/span>\r\n    \r\n    for<\/span> iter<\/span> in<\/span> range<\/span>(<\/span>iterations<\/span>):<\/span>\r\n        h<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>,<\/span>theta<\/span>)<\/span> -<\/span> y<\/span>\r\n        h_X<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>.<\/span>T<\/span>,<\/span>h<\/span>)<\/span>\r\n        \r\n        temp<\/span> =<\/span> theta<\/span>\r\n        \r\n        temp<\/span> -=<\/span> alpha<\/span> \/<\/span> m<\/span> *<\/span> h_X<\/span>\r\n        \r\n        theta<\/span> =<\/span> temp<\/span>\r\n        \r\n        J_history<\/span>[<\/span>iter<\/span>]<\/span> =<\/span> costFunc<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>)<\/span>\r\n        \r\n    return<\/span> theta<\/span>,<\/span>J_history<\/span>\r\n    \r\ntheta<\/span>,<\/span> J_history<\/span> =<\/span> gradientDescent<\/span>(<\/span>X<\/span>,<\/span>y<\/span>,<\/span>theta<\/span>,<\/span>alpha<\/span>,<\/span>iterations<\/span>)<\/span>\r\nprint<\/span> theta<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[[-3.63029144]\r\n [ 1.16636235]]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[456]:<\/div>\n
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# Plot the timeseries of cost function<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>J_history<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[<matplotlib.lines.Line2D at 0x109fcfd90>]<\/pre>\n<\/div>\n<\/div>\n
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# Plot the observations and the best fit line that we just solved for<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>X<\/span>[:,<\/span>1<\/span>],<\/span>y<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>X<\/span>[:,<\/span>1<\/span>],<\/span>np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>,<\/span>theta<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[<matplotlib.lines.Line2D at 0x10a108810>]<\/pre>\n<\/div>\n<\/div>\n
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# Make the 2 predictions<\/span>\r\npredict1<\/span> =<\/span> np<\/span>.<\/span>array<\/span>([<\/span>1<\/span>,<\/span>3.5<\/span>])<\/span>.<\/span>dot<\/span>(<\/span>theta<\/span>)<\/span>\r\npredict2<\/span> =<\/span> np<\/span>.<\/span>array<\/span>([<\/span>1<\/span>,<\/span>7<\/span>])<\/span>.<\/span>dot<\/span>(<\/span>theta<\/span>)<\/span>\r\nprint<\/span> predict1<\/span>\r\nprint<\/span> predict2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[ 0.45197679]\r\n[ 4.53424501]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 3: Now we do the multi variable exercise<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[490]:<\/div>\n
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# Use the numpy genfromtext function to read the data<\/span>\r\ndata2<\/span> =<\/span> np<\/span>.<\/span>genfromtxt<\/span>(<\/span>'\/Users\/matthewturner\/Desktop\/Coursera_machine_learning\/'<\/span>+<\/span>\r\n                     'machine-learning-ex1\/ex1\/ex1data2.txt'<\/span>,<\/span> delimiter<\/span>=<\/span>','<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[491]:<\/div>\n
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# Pull out the first column (theta0) into the variable X, and the 2nd column (theta1)<\/span>\r\n# into the variable y.  These variable names are consistent with the example.<\/span>\r\nX2<\/span>,<\/span>y2<\/span> =<\/span> data2<\/span>[:,<\/span>0<\/span>:<\/span>2<\/span>],<\/span>data2<\/span>[:,<\/span>2<\/span>]<\/span>\r\n\r\n# Set m = the length of y (i.e., the number of observations).<\/span>\r\nm2<\/span> =<\/span> len<\/span>(<\/span>y2<\/span>)<\/span>\r\ny2<\/span> =<\/span> y2<\/span>.<\/span>reshape<\/span>(<\/span>m2<\/span>,<\/span>1<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 3.1: Feature Normalization<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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def<\/span> featureNormalize<\/span>(<\/span>X<\/span>):<\/span>\r\n    mu<\/span> =<\/span> np<\/span>.<\/span>mean<\/span>(<\/span>X<\/span>,<\/span>axis<\/span>=<\/span>0<\/span>)<\/span>\r\n    sigma<\/span> =<\/span> np<\/span>.<\/span>std<\/span>(<\/span>X<\/span>,<\/span>axis<\/span>=<\/span>0<\/span>)<\/span>\r\n    X_norm<\/span> =<\/span> (<\/span> X<\/span> -<\/span> mu<\/span> )<\/span> \/<\/span> sigma<\/span>\r\n    return<\/span> X_norm<\/span>,<\/span> mu<\/span>,<\/span> sigma<\/span>\r\n    \r\nX_norm<\/span>,<\/span> mu<\/span>,<\/span> sigma<\/span> =<\/span> featureNormalize<\/span>(<\/span>X2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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# Add the column of ones to X2<\/span>\r\nX2<\/span> =<\/span> np<\/span>.<\/span>c_<\/span>[<\/span>np<\/span>.<\/span>ones<\/span>((<\/span>m2<\/span>,<\/span>1<\/span>)),<\/span>X_norm<\/span>]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 3.2: Gradient Descent<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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def<\/span> gradientDescentMulti<\/span>(<\/span>X2<\/span>,<\/span>y2<\/span>,<\/span>theta2<\/span>,<\/span>alpha2<\/span>,<\/span>iterations2<\/span>):<\/span>\r\n    J_history2<\/span> =<\/span> np<\/span>.<\/span>zeros<\/span>(<\/span>iterations2<\/span>)<\/span>\r\n    \r\n    max1<\/span> =<\/span> np<\/span>.<\/span>shape<\/span>(<\/span>X2<\/span>)[<\/span>1<\/span>]<\/span>\r\n    alpha_over_m<\/span> =<\/span> alpha2<\/span> \/<\/span> m2<\/span>\r\n    for<\/span> iter<\/span> in<\/span> range<\/span>(<\/span>iterations2<\/span>):<\/span>\r\n        temp2<\/span> =<\/span> theta2<\/span>\r\n        h2<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X2<\/span>,<\/span>temp2<\/span>.<\/span>reshape<\/span>(<\/span>max1<\/span>,<\/span>1<\/span>))<\/span>-<\/span>y2<\/span>\r\n        h3<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X2<\/span>.<\/span>T<\/span>,<\/span>h2<\/span>)<\/span>\r\n        temp2<\/span> =<\/span> temp2<\/span>.<\/span>reshape<\/span>(<\/span>max1<\/span>,<\/span>1<\/span>)<\/span> -<\/span> alpha_over_m<\/span> *<\/span> h3<\/span>\r\n        theta2<\/span> =<\/span> temp2<\/span>\r\n        \r\n        J_history2<\/span>[<\/span>iter<\/span>]<\/span> =<\/span> costFunc<\/span>(<\/span>X2<\/span>,<\/span>y2<\/span>,<\/span>theta2<\/span>)<\/span>\r\n        \r\n    return<\/span> theta2<\/span>,<\/span>J_history2<\/span>\r\n    \r\ntheta2<\/span> =<\/span> np<\/span>.<\/span>zeros<\/span>(<\/span>np<\/span>.<\/span>shape<\/span>(<\/span>X2<\/span>)[<\/span>1<\/span>])<\/span>\r\nalpha2<\/span> =<\/span> 0.1<\/span>\r\niterations2<\/span> =<\/span> 400<\/span>\r\n    \r\ntheta2<\/span>,<\/span> J_history2<\/span> =<\/span> gradientDescentMulti<\/span>(<\/span>X2<\/span>,<\/span>y2<\/span>,<\/span>theta2<\/span>,<\/span>alpha2<\/span>,<\/span>iterations2<\/span>)<\/span>\r\nprint<\/span> theta2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[[ 340412.65957447]\r\n [ 109447.79558639]\r\n [  -6578.3539709 ]]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[518]:<\/div>\n
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plt<\/span>.<\/span>plot<\/span>(<\/span>J_history2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Part 3.3: Normal Equation<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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def<\/span> normalEqn<\/span>(<\/span>X<\/span>,<\/span>y<\/span>):<\/span>\r\n    pinv_X<\/span> =<\/span> np<\/span>.<\/span>linalg<\/span>.<\/span>pinv<\/span>(<\/span>np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>.<\/span>T<\/span>,<\/span>X<\/span>))<\/span>\r\n    X_y<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>X<\/span>.<\/span>T<\/span>,<\/span>y<\/span>)<\/span>\r\n    theta<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>pinv_X<\/span>,<\/span>X_y<\/span>)<\/span>\r\n    return<\/span> np<\/span>.<\/span>linalg<\/span>.<\/span>inv<\/span>(<\/span>X<\/span>.<\/span>T<\/span>.<\/span>dot<\/span>(<\/span> X<\/span> ))<\/span>.<\/span>dot<\/span>(<\/span> X<\/span>.<\/span>T<\/span> )<\/span>.<\/span>dot<\/span>(<\/span> y<\/span> )<\/span>\r\n    \r\ntheta3<\/span> =<\/span> normalEqn<\/span>(<\/span>X2<\/span>,<\/span>y2<\/span>)<\/span>\r\nprint<\/span> theta3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[[ 340412.65957447]\r\n [ 109447.79646964]\r\n [  -6578.35485416]]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[527]:<\/div>\n
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# Predict proce of 1650 sq foot house with 3 bedrooms<\/span>\r\nx_predict<\/span> =<\/span> [<\/span>1650<\/span>,<\/span>3<\/span>]<\/span>\r\nnormalized_predict<\/span> =<\/span> (<\/span>x_predict<\/span> -<\/span> mu<\/span>)<\/span>\/<\/span>sigma<\/span>\r\nnormalized_predict<\/span> =<\/span> np<\/span>.<\/span>insert<\/span>(<\/span>normalized_predict<\/span>,<\/span>0<\/span>,<\/span>1<\/span>)<\/span>\r\npredict3<\/span> =<\/span> np<\/span>.<\/span>dot<\/span>(<\/span>normalized_predict<\/span>,<\/span>theta2<\/span>)<\/span>\r\n\r\nprint<\/span> predict3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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[ 293081.46452917]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
  I have previously done the Coursera Machine Learning exercises in Matlab. I thought, now that I am starting to get away from Matlab and use Python more, I should re-do the exercises in Python. This is exercise 1. In\u00a0[447]: %matplotlib inline import matplotlib.pyplot as plt import numpy as np import scipy Part 1: Create […]<\/p>\n","protected":false},"author":1,"featured_media":532,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[3,235,233,20],"tags":[249,240,250,248,80],"class_list":["post-523","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-command-line","category-data-science","category-python","category-scripting","tag-coursera","tag-data-science","tag-ipython","tag-machine-learning","tag-python"],"_links":{"self":[{"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/posts\/523"}],"collection":[{"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/comments?post=523"}],"version-history":[{"count":6,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/posts\/523\/revisions"}],"predecessor-version":[{"id":6131,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/posts\/523\/revisions\/6131"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/media\/532"}],"wp:attachment":[{"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/media?parent=523"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/categories?post=523"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/mattdturner.com\/wordpress\/wp-json\/wp\/v2\/tags?post=523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}