diff --git a/LogisticRegression.ipynb b/LogisticRegression.ipynb new file mode 100644 index 000000000..2d8c1ee4c --- /dev/null +++ b/LogisticRegression.ipynb @@ -0,0 +1,484 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# used for mathematical operations of elements\n", + "import math\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "\n", + "# Optimization module in scipy\n", + "from scipy import optimize\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils\n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Load data\n", + "# The first two columns contains the exam scores and the third column\n", + "# contains the label.\n", + "data = np.loadtxt('ex2data1.txt', delimiter=',')\n", + "X, y = data[:, 0:2], data[:, 2]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def plotData(X, y):\n", + " \"\"\"\n", + " Plots the data points X and y into a new figure. Plots the data \n", + " points with * for the positive examples and o for the negative examples.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " An Mx2 matrix representing the dataset. \n", + " \n", + " y : array_like\n", + " Label values for the dataset. A vector of size (M, ).\n", + " \n", + " Instructions\n", + " ------------\n", + " Plot the positive and negative examples on a 2D plot, using the\n", + " option 'k*' for the positive examples and 'ko' for the negative examples. \n", + " \"\"\"\n", + " # Create New Figure\n", + " fig = pyplot.figure()\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " # Find Indices of Positive and Negative Examples\n", + " pos = y == 1\n", + " neg = y == 0\n", + " \n", + " pyplot.plot(X[neg,0],X[neg,1],'ko', mfc='y', ms=8, mec='k', mew=1)\n", + "\n", + " pyplot.plot(X[pos,0],X[pos,1],'k*', lw=2, ms=10)\n", + "\n", + " \n", + " # ============================================================" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plotData(X,y)\n", + "pyplot.xlabel('Exam 1 Score')\n", + "pyplot.ylabel('Exam 2 Score')\n", + "pyplot.legend(['Not Admitted','Admitted'])\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " \"\"\"\n", + " Compute sigmoid function given the input z.\n", + " \n", + " Parameters\n", + " ----------\n", + " z : array_like\n", + " The input to the sigmoid function. This can be a 1-D vector \n", + " or a 2-D matrix. \n", + " \n", + " Returns\n", + " -------\n", + " g : array_like\n", + " The computed sigmoid function. g has the same shape as z, since\n", + " the sigmoid is computed element-wise on z.\n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the sigmoid of each value of z (z can be a matrix, vector or scalar).\n", + " \"\"\"\n", + " # convert input to a numpy array\n", + " z = np.array(z)\n", + " \n", + " # You need to return the following variables correctly \n", + " g = np.zeros(z.shape)\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " g = 1/(1+np.exp((-z)))\n", + " \n", + " # =============================================================\n", + " return g" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "g( [0, 100] ) = [0.5 1. ]\n" + ] + } + ], + "source": [ + "# Test the implementation of sigmoid function here\n", + "z = [0,100]\n", + "g = sigmoid(z)\n", + "\n", + "print('g(', z, ') = ', g)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Setup the data matrix appropriately, and add ones for the intercept term\n", + "m, n = X.shape\n", + "\n", + "# Add intercept term to X\n", + "X = np.concatenate([np.ones((m, 1)), X], axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def costFunction(theta, X, y):\n", + " \"\"\"\n", + " Compute cost and gradient for logistic regression. \n", + " \n", + " Parameters\n", + " ----------\n", + " theta : array_like\n", + " The parameters for logistic regression. This a vector\n", + " of shape (n+1, ).\n", + " \n", + " X : array_like\n", + " The input dataset of shape (m x n+1) where m is the total number\n", + " of data points and n is the number of features. We assume the \n", + " intercept has already been added to the input.\n", + " \n", + " y : arra_like\n", + " Labels for the input. This is a vector of shape (m, ).\n", + " \n", + " Returns\n", + " -------\n", + " J : float\n", + " The computed value for the cost function. \n", + " \n", + " grad : array_like\n", + " A vector of shape (n+1, ) which is the gradient of the cost\n", + " function with respect to theta, at the current values of theta.\n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the cost of a particular choice of theta. You should set J to \n", + " the cost. Compute the partial derivatives and set grad to the partial\n", + " derivatives of the cost w.r.t. each parameter in theta.\n", + " \"\"\"\n", + " # Initialize some useful values\n", + " m = y.size # number of training examples\n", + "\n", + " # You need to return the following variables correctly \n", + " J = 0\n", + " grad = np.zeros(theta.shape)\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " z=theta.dot(X.transpose())\n", + " h=sigmoid(z)\n", + " \n", + " for i in range(m):\n", + " J=J+((-1*(y[i]*math.log(h[i])+(1-y[i])*math.log(1-h[i])))/m)\n", + " \n", + " for i in range(theta.shape[0]):\n", + " grad[i]=((h-y).dot(X[:,i]))/m\n", + "\n", + " # =============================================================\n", + " return J, grad" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cost at initial theta (zeros): 0.693\n", + "Expected cost (approx): 0.693\n", + "\n", + "Gradient at initial theta (zeros):\n", + "\t[-0.1000, -12.0092, -11.2628]\n", + "Expected gradients (approx):\n", + "\t[-0.1000, -12.0092, -11.2628]\n", + "\n", + "Cost at test theta: 0.218\n", + "Expected cost (approx): 0.218\n", + "\n", + "Gradient at test theta:\n", + "\t[0.043, 2.566, 2.647]\n", + "Expected gradients (approx):\n", + "\t[0.043, 2.566, 2.647]\n" + ] + } + ], + "source": [ + "# Initialize fitting parameters\n", + "initial_theta = np.zeros(n+1)\n", + "\n", + "cost, grad = costFunction(initial_theta, X, y)\n", + "\n", + "print('Cost at initial theta (zeros): {:.3f}'.format(cost))\n", + "print('Expected cost (approx): 0.693\\n')\n", + "\n", + "print('Gradient at initial theta (zeros):')\n", + "print('\\t[{:.4f}, {:.4f}, {:.4f}]'.format(*grad))\n", + "print('Expected gradients (approx):\\n\\t[-0.1000, -12.0092, -11.2628]\\n')\n", + "\n", + "# Compute and display cost and gradient with non-zero theta\n", + "test_theta = np.array([-24, 0.2, 0.2])\n", + "cost, grad = costFunction(test_theta, X, y)\n", + "\n", + "print('Cost at test theta: {:.3f}'.format(cost))\n", + "print('Expected cost (approx): 0.218\\n')\n", + "\n", + "print('Gradient at test theta:')\n", + "print('\\t[{:.3f}, {:.3f}, {:.3f}]'.format(*grad))\n", + "print('Expected gradients (approx):\\n\\t[0.043, 2.566, 2.647]')" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cost at theta found by optimize.minimize: 0.203\n", + "Expected cost (approx): 0.203\n", + "\n", + "theta:\n", + "\t[-25.161, 0.206, 0.201]\n", + "Expected theta (approx):\n", + "\t[-25.161, 0.206, 0.201]\n" + ] + } + ], + "source": [ + "# set options for optimize.minimize\n", + "options= {'maxiter': 400}\n", + "\n", + "# see documention for scipy's optimize.minimize for description about\n", + "# the different parameters\n", + "# The function returns an object `OptimizeResult`\n", + "# We use truncated Newton algorithm for optimization which is \n", + "# equivalent to MATLAB's fminunc\n", + "# See https://stackoverflow.com/questions/18801002/fminunc-alternate-in-numpy\n", + "res = optimize.minimize(costFunction,\n", + " initial_theta,\n", + " (X, y),\n", + " jac=True,\n", + " method='TNC',\n", + " options=options)\n", + "\n", + "# the fun property of `OptimizeResult` object returns\n", + "# the value of costFunction at optimized theta\n", + "cost = res.fun\n", + "\n", + "# the optimized theta is in the x property\n", + "theta = res.x\n", + "\n", + "# Print theta to screen\n", + "print('Cost at theta found by optimize.minimize: {:.3f}'.format(cost))\n", + "print('Expected cost (approx): 0.203\\n');\n", + "\n", + "print('theta:')\n", + "print('\\t[{:.3f}, {:.3f}, {:.3f}]'.format(*theta))\n", + "print('Expected theta (approx):\\n\\t[-25.161, 0.206, 0.201]')" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot Boundary\n", + "utils.plotDecisionBoundary(plotData, theta, X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def predict(theta, X):\n", + " \"\"\"\n", + " Predict whether the label is 0 or 1 using learned logistic regression.\n", + " Computes the predictions for X using a threshold at 0.5 \n", + " (i.e., if sigmoid(theta.T*x) >= 0.5, predict 1)\n", + " \n", + " Parameters\n", + " ----------\n", + " theta : array_like\n", + " Parameters for logistic regression. A vector of shape (n+1, ).\n", + " \n", + " X : array_like\n", + " The data to use for computing predictions. The rows is the number \n", + " of points to compute predictions, and columns is the number of\n", + " features.\n", + "\n", + " Returns\n", + " -------\n", + " p : array_like\n", + " Predictions and 0 or 1 for each row in X. \n", + " \n", + " Instructions\n", + " ------------\n", + " Complete the following code to make predictions using your learned \n", + " logistic regression parameters.You should set p to a vector of 0's and 1's \n", + " \"\"\"\n", + " m = X.shape[0] # Number of training examples\n", + "\n", + " # You need to return the following variables correctly\n", + " p = np.zeros(m)\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " for i in range(m):\n", + " if sigmoid(theta.dot(X.transpose()))[i]>=0.5 :\n", + " p[i]=1\n", + " else :\n", + " p[i]=0\n", + "\n", + " \n", + " # ============================================================\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "For a student with scores 45 and 85,we predict an admission probability of 0.776\n", + "Expected value: 0.775 +/- 0.002\n", + "\n", + "Train Accuracy: 89.00 %\n", + "Expected accuracy (approx): 89.00 %\n" + ] + } + ], + "source": [ + "# Predict probability for a student with score 45 on exam 1 \n", + "# and score 85 on exam 2 \n", + "prob = sigmoid(np.dot([1, 45, 85], theta))\n", + "print('For a student with scores 45 and 85,'\n", + " 'we predict an admission probability of {:.3f}'.format(prob))\n", + "print('Expected value: 0.775 +/- 0.002\\n')\n", + "\n", + "# Compute accuracy on our training set\n", + "p = predict(theta, X)\n", + "print('Train Accuracy: {:.2f} %'.format(np.mean(p == y) * 100))\n", + "print('Expected accuracy (approx): 89.00 %')\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/edit_assignment.py b/edit_assignment.py new file mode 100644 index 000000000..0b2b5e2d6 --- /dev/null +++ b/edit_assignment.py @@ -0,0 +1,33 @@ +import pandas as pd + +from matplotlib import pyplot as plt + +df=pd.read_csv('data.txt',delimiter='\t') + +plt.rcParams['figure.figsize']=(20,10) + +fig,ax=plt.subplots(nrows=5,ncols=9) + +r=c=0 + +list=[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[3,0],[3,1],[3,2],[3,3],[3,4],[3,5],[3,6],[3,7],[3,8],[4,0],[4,1],[4,2],[4,3],[4,4],[4,5],[4,6],[4,7],[4,8]] + +flag=-1 + +for i in range(1,10): + for j in range(i+1,11): + flag=flag+1 + r=list[flag][0] + c=list[flag][1] + for k in range(999): + if df['Label'][k]==1: + ax[r][c].scatter(df[str(i)][k],df[str(j)][k],color='r') + elif df['Label'][k]==2: + ax[r][c].scatter(df[str(i)][k],df[str(j)][k],color='b') + + ax[r][c].set_xlabel('feature '+str(i)) + ax[r][c].set_ylabel('feature '+str(j)) + ax[0][4].set_title('My Plot') + +# print(plt.rcParams['figure.figsize']) +plt.show() \ No newline at end of file diff --git a/ex1data1.txt b/ex1data1.txt new file mode 100644 index 000000000..0f88ccb61 --- /dev/null +++ b/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 diff --git a/ex1data2.txt b/ex1data2.txt new file mode 100644 index 000000000..79e9a807e --- /dev/null +++ b/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 diff --git a/ex2data1.txt b/ex2data1.txt new file mode 100644 index 000000000..3a5f95245 --- /dev/null +++ b/ex2data1.txt @@ -0,0 +1,100 @@ +34.62365962451697,78.0246928153624,0 +30.28671076822607,43.89499752400101,0 +35.84740876993872,72.90219802708364,0 +60.18259938620976,86.30855209546826,1 +79.0327360507101,75.3443764369103,1 +45.08327747668339,56.3163717815305,0 +61.10666453684766,96.51142588489624,1 +75.02474556738889,46.55401354116538,1 +76.09878670226257,87.42056971926803,1 +84.43281996120035,43.53339331072109,1 +95.86155507093572,38.22527805795094,0 +75.01365838958247,30.60326323428011,0 +82.30705337399482,76.48196330235604,1 +69.36458875970939,97.71869196188608,1 +39.53833914367223,76.03681085115882,0 +53.9710521485623,89.20735013750205,1 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+++ b/gradientdescentMulti.ipynb @@ -0,0 +1,456 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 177, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "from mpl_toolkits.mplot3d import Axes3D # needed to plot 3-D surfaces\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils \n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline\n" + ] + }, + { + "cell_type": "code", + "execution_count": 178, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " X[:,0] X[:, 1] y\n", + "--------------------------\n", + " 2104 3 399900\n", + " 1600 3 329900\n", + " 2400 3 369000\n", + " 1416 2 232000\n", + " 3000 4 539900\n", + " 1985 4 299900\n", + " 1534 3 314900\n", + " 1427 3 198999\n", + " 1380 3 212000\n", + " 1494 3 242500\n" + ] + } + ], + "source": [ + "# Load data\n", + "data = np.loadtxt('ex1data2.txt', delimiter=',')\n", + "X = data[:, :2]\n", + "y = data[:, 2]\n", + "m = y.size\n", + "\n", + "# print out some data points\n", + "print('{:>8s}{:>8s}{:>10s}'.format('X[:,0]', 'X[:, 1]', 'y'))\n", + "print('-'*26)\n", + "for i in range(10):\n", + " print('{:8.0f}{:8.0f}{:10.0f}'.format(X[i, 0], X[i, 1], y[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": 179, + "metadata": {}, + "outputs": [], + "source": [ + "def featureNormalize(X):\n", + " \"\"\"\n", + " Normalizes the features in X. returns a normalized version of X where\n", + " the mean value of each feature is 0 and the standard deviation\n", + " is 1. This is often a good preprocessing step to do when working with\n", + " learning algorithms.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The dataset of shape (m x n).\n", + " \n", + " Returns\n", + " -------\n", + " X_norm : array_like\n", + " The normalized dataset of shape (m x n).\n", + " \n", + " Instructions\n", + " ------------\n", + " First, for each feature dimension, compute the mean of the feature\n", + " and subtract it from the dataset, storing the mean value in mu. \n", + " Next, compute the standard deviation of each feature and divide\n", + " each feature by it's standard deviation, storing the standard deviation \n", + " in sigma. \n", + " \n", + " Note that X is a matrix where each column is a feature and each row is\n", + " an example. You needto perform the normalization separately for each feature. \n", + " \n", + " Hint\n", + " ----\n", + " You might find the 'np.mean' and 'np.std' functions useful.\n", + " \"\"\"\n", + " # You need to set these values correctly\n", + " X_norm = X.copy()\n", + " mu = np.zeros(X.shape[1])\n", + " sigma = np.zeros(X.shape[1])\n", + "\n", + " # =========================== YOUR CODE HERE =====================\n", + " for i in range(X.shape[1]):\n", + " sigma[i]=np.std(X[:,i])\n", + " mu[i]=np.sum(X[:,i])/X.shape[0]\n", + " \n", + " for j in range(X.shape[0]):\n", + " for k in range(X.shape[1]):\n", + " X_norm[j][k]=(X[j][k]-mu[k])/sigma[k]\n", + "\n", + " # ================================================================\n", + " return X_norm, mu, sigma" + ] + }, + { + "cell_type": "code", + "execution_count": 180, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computed mean: [2000.68085106 3.17021277]\n", + "Computed standard deviation: [7.86202619e+02 7.52842809e-01]\n" + ] + } + ], + "source": [ + "# call featureNormalize on the loaded data\n", + "X_norm, mu, sigma = featureNormalize(X)\n", + "\n", + "print('Computed mean:', mu)\n", + "print('Computed standard deviation:', sigma)" + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "metadata": {}, + "outputs": [], + "source": [ + "# Add intercept term to X\n", + "X = np.concatenate([np.ones((m, 1)), X_norm], axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 182, + "metadata": {}, + "outputs": [], + "source": [ + "def computeCostMulti(X, y, theta):\n", + " \"\"\"\n", + " Compute cost for linear regression with multiple variables.\n", + " Computes the cost of using theta as the parameter for linear regression to fit the data points in X and y.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The dataset of shape (m x n+1).\n", + " \n", + " y : array_like\n", + " A vector of shape (m, ) for the values at a given data point.\n", + " \n", + " theta : array_like\n", + " The linear regression parameters. A vector of shape (n+1, )\n", + " \n", + " Returns\n", + " -------\n", + " J : float\n", + " The value of the cost function. \n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the cost of a particular choice of theta. You should set J to the cost.\n", + " \"\"\"\n", + " # Initialize some useful values\n", + " m = y.shape[0] # number of training examples\n", + " \n", + " # You need to return the following variable correctly\n", + " J = 0\n", + " \n", + " # ======================= YOUR CODE HERE ===========================\n", + " H=theta.dot(X.transpose())\n", + " sum=0\n", + " for element in range(len(H.transpose()-y)):\n", + " sum=sum+((H.transpose()-y)[element]*(H.transpose()-y)[element])\n", + " \n", + " J=sum/(2*m) \n", + " \n", + " \n", + " # ==================================================================\n", + " return J" + ] + }, + { + "cell_type": "code", + "execution_count": 183, + "metadata": {}, + "outputs": [], + "source": [ + "def gradientDescentMulti(X, y, theta, alpha, num_iters):\n", + " \"\"\"\n", + " Performs gradient descent to learn theta.\n", + " Updates theta by taking num_iters gradient steps with learning rate alpha.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The dataset of shape (m x n+1).\n", + " \n", + " y : array_like\n", + " A vector of shape (m, ) for the values at a given data point.\n", + " \n", + " theta : array_like\n", + " The linear regression parameters. A vector of shape (n+1, )\n", + " \n", + " alpha : float\n", + " The learning rate for gradient descent. \n", + " \n", + " num_iters : int\n", + " The number of iterations to run gradient descent. \n", + " \n", + " Returns\n", + " -------\n", + " theta : array_like\n", + " The learned linear regression parameters. A vector of shape (n+1, ).\n", + " \n", + " J_history : list\n", + " A python list for the values of the cost function after each iteration.\n", + " \n", + " Instructions\n", + " ------------\n", + " Peform a single gradient step on the parameter vector theta.\n", + "\n", + " While debugging, it can be useful to print out the values of \n", + " the cost function (computeCost) and gradient here.\n", + " \"\"\"\n", + " # Initialize some useful values\n", + " m = y.shape[0] # number of training examples\n", + " \n", + " # make a copy of theta, which will be updated by gradient descent\n", + " theta = theta.copy()\n", + " \n", + " J_history = []\n", + " \n", + " for i in range(num_iters):\n", + " # ======================= YOUR CODE HERE ==========================\n", + " H=theta.dot(X.transpose())\n", + " \n", + " for j in range(theta.size):\n", + " theta[j]-=(alpha/m)*((H.transpose()-y).transpose()).dot(X[:,j])\n", + " \n", + " # =================================================================\n", + " \n", + " # save the cost J in every iteration\n", + " J_history.append(computeCostMulti(X, y, theta))\n", + " \n", + " return theta, J_history" + ] + }, + { + "cell_type": "code", + "execution_count": 184, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[340412.56301439 109370.05670466 -6500.61509507]\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "theta=np.zeros(X.shape[1])\n", + "alpha=0.01\n", + "num_iters=1500\n", + "theta,J_history=gradientDescentMulti(X, y, theta, alpha, num_iters)\n", + "print(theta)\n", + "pyplot.plot(np.arange(len(J_history)), J_history, lw=2) \n", + "pyplot.xlabel('Number of iterations')\n", + "pyplot.ylabel('Cost J')\n", + "pyplot.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Predicted price of a 1650 sq-ft, 3 br house (using gradient descent): $293098\n" + ] + } + ], + "source": [ + "# Estimate the price of a 1650 sq-ft, 3 br house\n", + "# ======================= YOUR CODE HERE ===========================\n", + "# Recall that the first column of X is all-ones. \n", + "# Thus, it does not need to be normalized.\n", + "sqft=1650\n", + "numhouse=3\n", + "\n", + "price = 0 # You should change this\n", + "\n", + "norm_sqft=(sqft-mu[0])/sigma[0]\n", + "norm_numhouse=(numhouse-mu[1])/sigma[1]\n", + "\n", + "price = theta[0] + (theta[1]*norm_sqft) + (theta[2]*norm_numhouse)\n", + "\n", + "# ===================================================================\n", + "\n", + "print('Predicted price of a 1650 sq-ft, 3 br house (using gradient descent): ${:.0f}'.format(price))" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "metadata": {}, + "outputs": [], + "source": [ + "# Load data\n", + "data = np.loadtxt('ex1data2.txt', delimiter=',')\n", + "X = data[:, :2]\n", + "y = data[:, 2]\n", + "m = y.size\n", + "X = np.concatenate([np.ones((m, 1)), X], axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "metadata": {}, + "outputs": [], + "source": [ + "def normalEqn(X, y):\n", + " \"\"\"\n", + " Computes the closed-form solution to linear regression using the normal equations.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The dataset of shape (m x n+1).\n", + " \n", + " y : array_like\n", + " The value at each data point. A vector of shape (m, ).\n", + " \n", + " Returns\n", + " -------\n", + " theta : array_like\n", + " Estimated linear regression parameters. A vector of shape (n+1, ).\n", + " \n", + " Instructions\n", + " ------------\n", + " Complete the code to compute the closed form solution to linear\n", + " regression and put the result in theta.\n", + " \n", + " Hint\n", + " ----\n", + " Look up the function `np.linalg.pinv` for computing matrix inverse.\n", + " \"\"\"\n", + " theta = np.zeros(X.shape[1])\n", + " \n", + " # ===================== YOUR CODE HERE ============================\n", + " \n", + " theta=((np.linalg.inv(((X.transpose()).dot(X)))).dot(X.transpose())).dot(y)\n", + "\n", + " \n", + " # =================================================================\n", + " return theta" + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Theta computed from the normal equations: [89597.9095428 139.21067402 -8738.01911233]\n", + "Predicted price of a 1650 sq-ft, 3 br house (using normal equations): $293081\n" + ] + } + ], + "source": [ + "# Calculate the parameters from the normal equation\n", + "theta = normalEqn(X, y);\n", + "\n", + "# Display normal equation's result\n", + "print('Theta computed from the normal equations: {:s}'.format(str(theta)));\n", + "\n", + "# Estimate the price of a 1650 sq-ft, 3 br house\n", + "# ====================== YOUR CODE HERE ======================\n", + "\n", + "price = 0 # You should change this\n", + "\n", + "sqft=1650\n", + "numhouse=3\n", + "\n", + "price = theta[0] + (theta[1]*sqft) + (theta[2]*numhouse)\n", + "\n", + "# ============================================================\n", + "\n", + "print('Predicted price of a 1650 sq-ft, 3 br house (using normal equations): ${:.0f}'.format(price))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/gradientdescentSingle.ipynb b/gradientdescentSingle.ipynb new file mode 100644 index 000000000..6530ab445 --- /dev/null +++ b/gradientdescentSingle.ipynb @@ -0,0 +1,388 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "from mpl_toolkits.mplot3d import Axes3D # needed to plot 3-D surfaces\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils \n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Read comma separated data\n", + "data = np.loadtxt('ex1data1.txt', delimiter=',')\n", + "X, y = data[:, 0], data[:, 1]\n", + "m = y.size # number of training examples" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Add a column of ones to X. The numpy function stack joins arrays along a given axis. \n", + "# The first axis (axis=0) refers to rows (training examples) \n", + "# and second axis (axis=1) refers to columns (features).\n", + "X = np.stack([np.ones(m), X], axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def computeCost(X, y, theta):\n", + " \"\"\"\n", + " Compute cost for linear regression. Computes the cost of using theta as the\n", + " parameter for linear regression to fit the data points in X and y.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The input dataset of shape (m x n+1), where m is the number of examples,\n", + " and n is the number of features. We assume a vector of one's already \n", + " appended to the features so we have n+1 columns.\n", + " \n", + " y : array_like\n", + " The values of the function at each data point. This is a vector of\n", + " shape (m, ).\n", + " \n", + " theta : array_like\n", + " The parameters for the regression function. This is a vector of \n", + " shape (n+1, ).\n", + " \n", + " Returns\n", + " -------\n", + " J : float\n", + " The value of the regression cost function.\n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the cost of a particular choice of theta. \n", + " You should set J to the cost.\n", + " \"\"\"\n", + " \n", + " # initialize some useful values\n", + " m = y.size # number of training examples\n", + "\n", + " # You need to return the following variables correctly\n", + " J = 0\n", + "\n", + " # ====================== YOUR CODE HERE =====================\n", + " H=theta.dot(X.transpose())\n", + " sum=0\n", + " for element in range(len(H.transpose()-y)):\n", + " sum=sum+((H.transpose()-y)[element]*(H.transpose()-y)[element])\n", + " \n", + " J=sum/(2*m) \n", + "\n", + " # ===========================================================\n", + " return J\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# J = computeCost(X, y, theta=np.array([0.0, 0.0]))\n", + "# print('With theta = [0, 0] \\nCost computed = %.2f' % J)\n", + "# print('Expected cost value (approximately) 32.07\\n')\n", + "\n", + "# # further testing of the cost function\n", + "# J = computeCost(X, y, theta=np.array([-1, 2]))\n", + "# print('With theta = [-1, 2]\\nCost computed = %.2f' % J)\n", + "# print('Expected cost value (approximately) 54.24')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def gradientDescent(X, y, theta, alpha, num_iters):\n", + " \"\"\"\n", + " Performs gradient descent to learn `theta`. Updates theta by taking `num_iters`\n", + " gradient steps with learning rate `alpha`.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " The input dataset of shape (m x n+1).\n", + " \n", + " y : arra_like\n", + " Value at given features. A vector of shape (m, ).\n", + " \n", + " theta : array_like\n", + " Initial values for the linear regression parameters. \n", + " A vector of shape (n+1, ).\n", + " \n", + " alpha : float\n", + " The learning rate.\n", + " \n", + " num_iters : int\n", + " The number of iterations for gradient descent. \n", + " \n", + " Returns\n", + " -------\n", + " theta : array_like\n", + " The learned linear regression parameters. A vector of shape (n+1, ).\n", + " \n", + " J_history : list\n", + " A python list for the values of the cost function after each iteration.\n", + " \n", + " Instructions\n", + " ------------\n", + " Peform a single gradient step on the parameter vector theta.\n", + "\n", + " While debugging, it can be useful to print out the values of \n", + " the cost function (computeCost) and gradient here.\n", + " \"\"\"\n", + " # Initialize some useful values\n", + " m = y.shape[0] # number of training examples\n", + " \n", + " # make a copy of theta, to avoid changing the original array, since numpy arrays\n", + " # are passed by reference to functions\n", + " theta = theta.copy()\n", + " \n", + " J_history = [] # Use a python list to save cost in every iteration\n", + " \n", + " for i in range(num_iters):\n", + " # ==================== YOUR CODE HERE =================================\n", + " H=theta.dot(X.transpose())\n", + " temp1=(alpha/m)*((H.transpose()-y).transpose()).dot(X[:,0])\n", + " temp2=(alpha/m)*((H.transpose()-y).transpose()).dot(X[:,1])\n", + " theta[0]-=temp1\n", + " theta[1]-=temp2\n", + " # =====================================================================\n", + " \n", + " # save the cost J in every iteration\n", + " J_history.append(computeCost(X, y, theta))\n", + " \n", + " return theta, J_history" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Theta found by gradient descent: -3.6303, 1.1664\n", + "Expected theta values (approximately): [-3.6303, 1.1664]\n" + ] + } + ], + "source": [ + "# initialize fitting parameters\n", + "theta = np.zeros(2)\n", + "\n", + "# some gradient descent settings\n", + "iterations = 1500\n", + "alpha = 0.01\n", + "\n", + "theta, J_history = gradientDescent(X ,y, theta, alpha, iterations)\n", + "print('Theta found by gradient descent: {:.4f}, {:.4f}'.format(*theta))\n", + "print('Expected theta values (approximately): [-3.6303, 1.1664]')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def plotData(x, y):\n", + " \"\"\"\n", + " Plots the data points x and y into a new figure. Plots the data \n", + " points and gives the figure axes labels of population and profit.\n", + " \n", + " Parameters\n", + " ----------\n", + " x : array_like\n", + " Data point values for x-axis.\n", + "\n", + " y : array_like\n", + " Data point values for y-axis. Note x and y should have the same size.\n", + " \n", + " Instructions\n", + " ------------\n", + " Plot the training data into a figure using the \"figure\" and \"plot\"\n", + " functions. Set the axes labels using the \"xlabel\" and \"ylabel\" functions.\n", + " Assume the population and revenue data have been passed in as the x\n", + " and y arguments of this function. \n", + " \n", + " Hint\n", + " ----\n", + " You can use the 'ro' option with plot to have the markers\n", + " appear as red circles. Furthermore, you can make the markers larger by\n", + " using plot(..., 'ro', ms=10), where `ms` refers to marker size. You \n", + " can also set the marker edge color using the `mec` property.\n", + " \"\"\"\n", + " fig = pyplot.figure() # open a new figure\n", + " \n", + " # ====================== YOUR CODE HERE ======================= \n", + " pyplot.plot(x, y, 'ro',ms=10, mec='k')\n", + " pyplot.ylabel('Profit in $10,000')\n", + " pyplot.xlabel('Population of City in 10,000s')\n", + "\n", + " # =============================================================" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the linear fit\n", + "plotData(X[:, 1], y)\n", + "pyplot.plot(X[:, 1], np.dot(X, theta), '-')\n", + "pyplot.legend(['Training data', 'Linear regression']);" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "For population = 35,000, we predict a profit of 4519.77\n", + "\n", + "For population = 70,000, we predict a profit of 45342.45\n", + "\n" + ] + } + ], + "source": [ + "# Predict values for population sizes of 35,000 and 70,000\n", + "predict1 = np.dot([1, 3.5], theta)\n", + "print('For population = 35,000, we predict a profit of {:.2f}\\n'.format(predict1*10000))\n", + "\n", + "predict2 = np.dot([1, 7], theta)\n", + "print('For population = 70,000, we predict a profit of {:.2f}\\n'.format(predict2*10000))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# grid over which we will calculate J\n", + "theta0_vals = np.linspace(-10, 10, 100)\n", + "theta1_vals = np.linspace(-1, 4, 100)\n", + "\n", + "# initialize J_vals to a matrix of 0's\n", + "J_vals = np.zeros((theta0_vals.shape[0], theta1_vals.shape[0]))\n", + "\n", + "# Fill out J_vals\n", + "for i, theta0 in enumerate(theta0_vals):\n", + " for j, theta1 in enumerate(theta1_vals):\n", + " J_vals[i][j] = computeCost(X, y, np.array([theta0, theta1]))\n", + " \n", + "# Because of the way meshgrids work in the surf command, we need to\n", + "# transpose J_vals before calling surf, or else the axes will be flipped\n", + "J_vals = J_vals.T\n", + "\n", + "# surface plot\n", + "fig = pyplot.figure(figsize=(12, 5))\n", + "ax = fig.add_subplot(121, projection='3d')\n", + "ax.plot_surface(theta0_vals, theta1_vals, J_vals, cmap='viridis')\n", + "pyplot.xlabel('theta0')\n", + "pyplot.ylabel('theta1')\n", + "pyplot.title('Surface')\n", + "\n", + "# contour plot\n", + "# Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100\n", + "ax = pyplot.subplot(122)\n", + "pyplot.contour(theta0_vals, theta1_vals, J_vals, linewidths=2, cmap='viridis', levels=np.logspace(-2, 3, 20))\n", + "pyplot.xlabel('theta0')\n", + "pyplot.ylabel('theta1')\n", + "pyplot.plot(theta[0], theta[1], 'ro', ms=10, lw=2)\n", + "pyplot.title('Contour, showing minimum')\n", + "pass" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/introduction_to_matrix.ipynb b/introduction_to_matrix.ipynb new file mode 100644 index 000000000..f92f097c1 --- /dev/null +++ b/introduction_to_matrix.ipynb @@ -0,0 +1,102 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "from mpl_toolkits.mplot3d import Axes3D # needed to plot 3-D surfaces\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils \n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def warmUpExercise():\n", + " \"\"\"\n", + " Example function in Python which computes the identity matrix.\n", + " \n", + " Returns\n", + " -------\n", + " A : array_like\n", + " The 5x5 identity matrix.\n", + " \n", + " Instructions\n", + " ------------\n", + " Return the 5x5 identity matrix.\n", + " \"\"\" \n", + " # ======== YOUR CODE HERE ======\n", + " A = [] # modify this line\n", + " A=np.eye(5)\n", + " \n", + " # ==============================\n", + " return A" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0., 0., 0., 0.],\n", + " [0., 1., 0., 0., 0.],\n", + " [0., 0., 1., 0., 0.],\n", + " [0., 0., 0., 1., 0.],\n", + " [0., 0., 0., 0., 1.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "warmUpExercise()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/plotData.ipynb b/plotData.ipynb new file mode 100644 index 000000000..c4f11e1cb --- /dev/null +++ b/plotData.ipynb @@ -0,0 +1,136 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "from mpl_toolkits.mplot3d import Axes3D # needed to plot 3-D surfaces\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils \n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Read comma separated data\n", + "data = np.loadtxt('ex1data1.txt', delimiter=',')\n", + "X, y = data[:, 0], data[:, 1]\n", + "\n", + "m = y.size # number of training examples" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def plotData(x, y):\n", + " \"\"\"\n", + " Plots the data points x and y into a new figure. Plots the data \n", + " points and gives the figure axes labels of population and profit.\n", + " \n", + " Parameters\n", + " ----------\n", + " x : array_like\n", + " Data point values for x-axis.\n", + "\n", + " y : array_like\n", + " Data point values for y-axis. Note x and y should have the same size.\n", + " \n", + " Instructions\n", + " ------------\n", + " Plot the training data into a figure using the \"figure\" and \"plot\"\n", + " functions. Set the axes labels using the \"xlabel\" and \"ylabel\" functions.\n", + " Assume the population and revenue data have been passed in as the x\n", + " and y arguments of this function. \n", + " \n", + " Hint\n", + " ----\n", + " You can use the 'ro' option with plot to have the markers\n", + " appear as red circles. Furthermore, you can make the markers larger by\n", + " using plot(..., 'ro', ms=10), where `ms` refers to marker size. You \n", + " can also set the marker edge color using the `mec` property.\n", + " \"\"\"\n", + " fig = pyplot.figure() # open a new figure\n", + " \n", + " # ====================== YOUR CODE HERE ======================= \n", + " pyplot.plot(x, y, 'ro',ms=10, mec='k')\n", + " pyplot.ylabel('Profit in $10,000')\n", + " pyplot.xlabel('Population of City in 10,000s')\n", + "\n", + " # =============================================================" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plotData(X, y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/regularisedLogisticRegression.ipynb b/regularisedLogisticRegression.ipynb new file mode 100644 index 000000000..29006e75c --- /dev/null +++ b/regularisedLogisticRegression.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# used for manipulating directory paths\n", + "import os\n", + "\n", + "# used for mathematical operations of elements\n", + "import math\n", + "\n", + "# Scientific and vector computation for python\n", + "import numpy as np\n", + "\n", + "# Plotting library\n", + "from matplotlib import pyplot\n", + "\n", + "# Optimization module in scipy\n", + "from scipy import optimize\n", + "\n", + "# library written for this exercise providing additional functions for assignment submission, and others\n", + "import utils\n", + "\n", + "# define the submission/grader object for this exercise\n", + "grader = utils.Grader()\n", + "\n", + "# tells matplotlib to embed plots within the notebook\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Load Data\n", + "# The first two columns contains the X values and the third column\n", + "# contains the label (y).\n", + "data = np.loadtxt('ex2data2.txt', delimiter=',')\n", + "X = data[:, :2]\n", + "y = data[:, 2]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " \"\"\"\n", + " Compute sigmoid function given the input z.\n", + " \n", + " Parameters\n", + " ----------\n", + " z : array_like\n", + " The input to the sigmoid function. This can be a 1-D vector \n", + " or a 2-D matrix. \n", + " \n", + " Returns\n", + " -------\n", + " g : array_like\n", + " The computed sigmoid function. g has the same shape as z, since\n", + " the sigmoid is computed element-wise on z.\n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the sigmoid of each value of z (z can be a matrix, vector or scalar).\n", + " \"\"\"\n", + " # convert input to a numpy array\n", + " z = np.array(z)\n", + " \n", + " # You need to return the following variables correctly \n", + " g = np.zeros(z.shape)\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " g = 1/(1+np.exp((-z)))\n", + " \n", + " # =============================================================\n", + " return g" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def plotData(X, y):\n", + " \"\"\"\n", + " Plots the data points X and y into a new figure. Plots the data \n", + " points with * for the positive examples and o for the negative examples.\n", + " \n", + " Parameters\n", + " ----------\n", + " X : array_like\n", + " An Mx2 matrix representing the dataset. \n", + " \n", + " y : array_like\n", + " Label values for the dataset. A vector of size (M, ).\n", + " \n", + " Instructions\n", + " ------------\n", + " Plot the positive and negative examples on a 2D plot, using the\n", + " option 'k*' for the positive examples and 'ko' for the negative examples. \n", + " \"\"\"\n", + " # Create New Figure\n", + " fig = pyplot.figure()\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " # Find Indices of Positive and Negative Examples\n", + " pos = y == 1\n", + " neg = y == 0\n", + " \n", + " pyplot.plot(X[neg,0],X[neg,1],'ko',mfc='y', ms=8, mec='k', mew=1)\n", + "\n", + " pyplot.plot(X[pos,0],X[pos,1],'k*',lw=2, ms=10)\n", + "\n", + " \n", + " # ============================================================" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plotData(X, y)\n", + "# Labels and Legend\n", + "pyplot.xlabel('Microchip Test 1')\n", + "pyplot.ylabel('Microchip Test 2')\n", + "\n", + "# Specified in plot order\n", + "pyplot.legend(['y = 1', 'y = 0'], loc='upper right')\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Note that mapFeature also adds a column of ones for us, so the intercept\n", + "# term is handled\n", + "X = utils.mapFeature(X[:, 0], X[:, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def costFunctionReg(theta, X, y, lambda_):\n", + " \"\"\"\n", + " Compute cost and gradient for logistic regression with regularization.\n", + " \n", + " Parameters\n", + " ----------\n", + " theta : array_like\n", + " Logistic regression parameters. A vector with shape (n, ). n is \n", + " the number of features including any intercept. If we have mapped\n", + " our initial features into polynomial features, then n is the total \n", + " number of polynomial features. \n", + " \n", + " X : array_like\n", + " The data set with shape (m x n). m is the number of examples, and\n", + " n is the number of features (after feature mapping).\n", + " \n", + " y : array_like\n", + " The data labels. A vector with shape (m, ).\n", + " \n", + " lambda_ : float\n", + " The regularization parameter. \n", + " \n", + " Returns\n", + " -------\n", + " J : float\n", + " The computed value for the regularized cost function. \n", + " \n", + " grad : array_like\n", + " A vector of shape (n, ) which is the gradient of the cost\n", + " function with respect to theta, at the current values of theta.\n", + " \n", + " Instructions\n", + " ------------\n", + " Compute the cost `J` of a particular choice of theta.\n", + " Compute the partial derivatives and set `grad` to the partial\n", + " derivatives of the cost w.r.t. each parameter in theta.\n", + " \"\"\"\n", + " # Initialize some useful values\n", + " m = y.size # number of training examples\n", + "\n", + " # You need to return the following variables correctly \n", + " J = 0\n", + " grad = np.zeros(theta.shape)\n", + "\n", + " # ===================== YOUR CODE HERE ======================\n", + " z=theta.dot(X.transpose())\n", + " h=sigmoid(z)\n", + " \n", + " for i in range(m):\n", + " J=J+((-1*(y[i]*math.log(h[i])+(1-y[i])*math.log(1-h[i])))/m)\n", + " \n", + " for i in range(1,theta.shape[0]):\n", + " J=J+(lambda_*theta[i]*theta[i])/(2*m)\n", + " \n", + " \n", + " for i in range(theta.shape[0]):\n", + " grad[i]=(((h-y).dot(X[:,i]))/m) \n", + " \n", + " for i in range(1,theta.shape[0]):\n", + " grad[i]=grad[i]+(lambda_*theta[i])/m\n", + " \n", + " # =============================================================\n", + " return J, grad" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cost at initial theta (zeros): 0.693\n", + "Expected cost (approx) : 0.693\n", + "\n", + "Gradient at initial theta (zeros) - first five values only:\n", + "\t[0.0085, 0.0188, 0.0001, 0.0503, 0.0115]\n", + "Expected gradients (approx) - first five values only:\n", + "\t[0.0085, 0.0188, 0.0001, 0.0503, 0.0115]\n", + "\n", + "------------------------------\n", + "\n", + "Cost at test theta : 3.16\n", + "Expected cost (approx): 3.16\n", + "\n", + "Gradient at initial theta (zeros) - first five values only:\n", + "\t[0.3460, 0.1614, 0.1948, 0.2269, 0.0922]\n", + "Expected gradients (approx) - first five values only:\n", + "\t[0.3460, 0.1614, 0.1948, 0.2269, 0.0922]\n" + ] + } + ], + "source": [ + "# Initialize fitting parameters\n", + "initial_theta = np.zeros(X.shape[1])\n", + "\n", + "# Set regularization parameter lambda to 1\n", + "# DO NOT use `lambda` as a variable name in python\n", + "# because it is a python keyword\n", + "lambda_ = 1\n", + "\n", + "# Compute and display initial cost and gradient for regularized logistic\n", + "# regression\n", + "cost, grad = costFunctionReg(initial_theta, X, y, lambda_)\n", + "\n", + "print('Cost at initial theta (zeros): {:.3f}'.format(cost))\n", + "print('Expected cost (approx) : 0.693\\n')\n", + "\n", + "print('Gradient at initial theta (zeros) - first five values only:')\n", + "print('\\t[{:.4f}, {:.4f}, {:.4f}, {:.4f}, {:.4f}]'.format(*grad[:5]))\n", + "print('Expected gradients (approx) - first five values only:')\n", + "print('\\t[0.0085, 0.0188, 0.0001, 0.0503, 0.0115]\\n')\n", + "\n", + "\n", + "# Compute and display cost and gradient\n", + "# with all-ones theta and lambda = 10\n", + "test_theta = np.ones(X.shape[1])\n", + "cost, grad = costFunctionReg(test_theta, X, y, 10)\n", + "\n", + "print('------------------------------\\n')\n", + "print('Cost at test theta : {:.2f}'.format(cost))\n", + "print('Expected cost (approx): 3.16\\n')\n", + "\n", + "print('Gradient at initial theta (zeros) - first five values only:')\n", + "print('\\t[{:.4f}, {:.4f}, {:.4f}, {:.4f}, {:.4f}]'.format(*grad[:5]))\n", + "print('Expected gradients (approx) - first five values only:')\n", + "print('\\t[0.3460, 0.1614, 0.1948, 0.2269, 0.0922]')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def predict(theta, X):\n", + " \"\"\"\n", + " Predict whether the label is 0 or 1 using learned logistic regression.\n", + " Computes the predictions for X using a threshold at 0.5 \n", + " (i.e., if sigmoid(theta.T*x) >= 0.5, predict 1)\n", + " \n", + " Parameters\n", + " ----------\n", + " theta : array_like\n", + " Parameters for logistic regression. A vector of shape (n+1, ).\n", + " \n", + " X : array_like\n", + " The data to use for computing predictions. The rows is the number \n", + " of points to compute predictions, and columns is the number of\n", + " features.\n", + "\n", + " Returns\n", + " -------\n", + " p : array_like\n", + " Predictions and 0 or 1 for each row in X. \n", + " \n", + " Instructions\n", + " ------------\n", + " Complete the following code to make predictions using your learned \n", + " logistic regression parameters.You should set p to a vector of 0's and 1's \n", + " \"\"\"\n", + " m = X.shape[0] # Number of training examples\n", + "\n", + " # You need to return the following variables correctly\n", + " p = np.zeros(m)\n", + "\n", + " # ====================== YOUR CODE HERE ======================\n", + " for i in range(m):\n", + " if sigmoid(theta.dot(X.transpose()))[i]>=0.5 :\n", + " p[i]=1\n", + " else :\n", + " p[i]=0\n", + "\n", + " \n", + " # ============================================================\n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Train Accuracy: 83.1 %\n", + "Expected accuracy (with lambda = 1): 83.1 % (approx)\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Initialize fitting parameters\n", + "initial_theta = np.zeros(X.shape[1])\n", + "\n", + "# Set regularization parameter lambda to 1 (you should vary this)\n", + "lambda_ = 1\n", + "\n", + "# set options for optimize.minimize\n", + "options= {'maxiter': 100}\n", + "\n", + "res = optimize.minimize(costFunctionReg,\n", + " initial_theta,\n", + " (X, y, lambda_),\n", + " jac=True,\n", + " method='TNC',\n", + " options=options)\n", + "\n", + "# the fun property of OptimizeResult object returns\n", + "# the value of costFunction at optimized theta\n", + "cost = res.fun\n", + "\n", + "# the optimized theta is in the x property of the result\n", + "theta = res.x\n", + "\n", + "utils.plotDecisionBoundary(plotData, theta, X, y)\n", + "pyplot.xlabel('Microchip Test 1')\n", + "pyplot.ylabel('Microchip Test 2')\n", + "pyplot.legend(['y = 1', 'y = 0'])\n", + "pyplot.grid(False)\n", + "pyplot.title('lambda = %0.2f' % lambda_)\n", + "\n", + "# Compute accuracy on our training set\n", + "p = predict(theta, X)\n", + "\n", + "print('Train Accuracy: %.1f %%' % (np.mean(p == y) * 100))\n", + "print('Expected accuracy (with lambda = 1): 83.1 % (approx)\\n')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}