{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Chapter 9\n", "### This notebook and the figures below are made by Yeseul Lee, under the guidance of Steven Skiena." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math, random\n", "import pandas as pd\n", "\n", "from scipy.spatial import ConvexHull\n", "from scipy import stats\n", "from sklearn.metrics import mean_squared_error\n", "from matplotlib import cm\n", "from sklearn.linear_model import LogisticRegression\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.1 - Linear Regression graph" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.96908677 0.08064795]\n" ] }, { "data": { "text/plain": [ "(-4, 4.6)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create a random noise\n", "x1 = np.random.normal(size=200)\n", "xs = np.linspace(x1.min()-1, x1.max()+1, 100)\n", "x = xs\n", "y = 3*(np.random.normal(0, 1, 100)+x)\n", "plt.scatter(x, y , color='red')\n", "\n", "#Find the regression line\n", "regression = np.polyfit(x,y,1)\n", "print regression\n", "longerX = np.append(x, [5,-5])\n", "plt.plot(longerX, regression[0]*longerX + regression[1], color='black', linewidth='1.5')\n", "plt.xlim(-4, 4.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.2 - Point and line duality\n", "#### p = (a,b) -> p* = ax - b" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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KgM6dOxMXF0f16tUDEZpSSnnlxAl46CEz56hYEZYsgSZN7I5KeSszM5N58+Yx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\nhgcfdJd0CxZ//vknb7zxBpMmTeJ0Vm7DfffdR2x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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,4.5))\n", "\n", "plt.subplot(121)\n", "x = np.linspace(-10,16,500)\n", "y = 2*x\n", "y2 = -x+12\n", "plt.plot(x, y, 'k-', x, y2, 'b-', linewidth=2)\n", "plt.plot([0], [0], 'ko', [8],[16], 'ko', [-2], [14], 'bo', [15], [-3], 'bo', [4], [8], 'ro', markersize=12, markeredgewidth=0)\n", "plt.xlim(-4,16)\n", "plt.grid()\n", "\n", "plt.subplot(122)\n", "plt.plot(x, 0*x, 'k-', linewidth=2)\n", "plt.plot(x, 8*x-16, 'k-', linewidth=2)\n", "plt.plot([2], [0], 'ko', [-1], [-12], 'bo', markersize=12, markeredgewidth=0)\n", "plt.plot(x, -2*x-14, 'b-', x, 15*x+3, 'b-', x, 4*x-8, 'r-', linewidth=2)\n", "plt.xlim(-2.5,5)\n", "plt.ylim(-50,50)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.3 - Residual error" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 10, 100)\n", "y = 2*x+3\n", "#distance the dashed line is into the circle\n", "s = 0.4\n", "\n", "plt.plot(x, y)\n", "plt.plot([1, 1, 2, 3, 3, 4, 4, 5, 6, 7],[7, 3, 12, 5, 11, 15, 10, 15, 12, 19], 'yo', markersize=7)\n", "plt.plot([1, 1], [7-s, 5], 'b-', [1, 1], [3+s, 5], 'b-', \\\n", " [2, 2], [12-s, 7], 'b-', [3, 3], [5+s, 9], 'b-', \\\n", " [3, 3], [11-s, 9], 'b-', [4,4], [15-s, 11], 'b-', \\\n", " [4,4], [10+s, 11], 'b-', [5, 5], [15-s, 13], 'b-',\\\n", " [6, 6], [12+s+0.1, 15], 'b-', [7, 7], [19-s, 17], 'b-', linestyle='dashed')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.4 Regression line and outlier" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r2 = 0.91654158689\n", "r1 = 0.548282726023\n" ] }, { "data": { "image/png": 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grj766COZWTAQv/LKK6qsrCQQxxGuPgEgZc2dO1e5ubnHjD/66KN64oknlJ6e7kFVAJJN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\n1a1bN61du1aSdOWVV2r58uW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,4.5))\n", "\n", "#The right graph without an outlier.\n", "plt.subplot(122)\n", "# Create a random 15 points\n", "np.random.seed(7)\n", "x1 = np.random.normal(size=10)\n", "x = np.linspace(x1.min()-1, x1.max()+1, 15) \n", "y = 3*(np.random.normal(0, 1, 15)+x)\n", "plt.scatter(x, y , color='red')\n", "\n", "#Find the regression line\n", "regression = np.polyfit(x,y,1)\n", "longerX = np.append(x, [5,-5]) #this makes the regression line longer\n", "plt.plot(longerX, regression[0]*longerX + regression[1], color='black', linewidth='1.5')\n", "plt.xlim(-3.5,4.5)\n", "plt.ylim(-15, 20)\n", "#The correlation coefficient value r.\n", "r1 = stats.pearsonr(x, y)\n", "print 'r2 =', r1[0]\n", "\n", "#The left graph with an outlier\n", "plt.subplot(121)\n", "#plot the 15 points with an outlier.\n", "x1 = np.append(x, [4])\n", "y1 = np.append(y, [-10])\n", "plt.scatter(x1, y1 , color='red')\n", "\n", "#Find the regression line\n", "regression = np.polyfit(x1,y1,1)\n", "longerX = np.append(x1, [5,-5]) #this makes the regression line longer\n", "plt.plot(longerX, regression[0]*longerX + regression[1], color='black', linewidth='1.5')\n", "plt.xlim(-3.5,4.5)\n", "plt.ylim(-15, 20)\n", "#The correlation coefficient value r.\n", "r2 = stats.pearsonr(x1, y1)\n", "print 'r1 =', r2[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JyNvKC4gcDf9zpRkzxObnJ2eLF5cgkObNW8kPPxxzvzhzwNnJ/E+gbBbL5Pdz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\ntf5Xwl/UKVOHZ4Ke4ammT3F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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot a quadratic function x^2 - 2*x + 3\n", "x1 = np.linspace(-3,3,100)\n", "y1 = x1*x1 - 2*x1 + 3\n", "plt.plot(x1, y1, 'k-', linewidth=1.5)\n", "\n", "# Create random points\n", "np.random.seed(7)\n", "x = []\n", "y=[]\n", "for i in range(0,50):\n", " a = np.random.uniform(-3, 3)\n", " b = a*a - 2*a + 3\n", " c = np.random.uniform(-3,3)\n", " x.append(a)\n", " y.append(b+c)\n", "\n", "plt.scatter(x, y , color='blue')\n", "\n", "#Find the regression line mx + c and curve a*x*x + b*x + c\n", "regline = np.polyfit(x,y,1)\n", "plt.plot(x1, regline[0]*x1 + regline[1], 'g-', linewidth=1.5)\n", "regcurve = np.polyfit(x,y,2)\n", "plt.plot(x1, regcurve[0]*x1*x1 + regcurve[1]*x1 + regcurve[2], 'r-', linewidth=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.6 Left" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Summary of Fig 9.6\n", "1. Get the points (plot y = x line and make random points around the line by adding noise to the points.)\n", "2. Find the zscore of the points. (x-xmean/xstd, y-ymean/ystd)\n", "3. for angle 0 to 90, find the mean squared error of the line to the points.\n", "4. plot (angle, error)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Make Points\n", "\n", "np.random.seed(7)\n", "x = np.linspace(0,10, 100)\n", "y = np.random.normal(0,1, 100)+x\n", "\n", "xmean = np.mean(x)\n", "xstd = np.std(x)\n", "ymean = np.mean(y)\n", "ystd = np.std(y)\n", "\n", "## Compute the zscores\n", "xz = []\n", "yz = []\n", "for i, j in zip(x, y):\n", " xz.append((i-xmean)/float(xstd))\n", " yz.append((j-ymean)/float(ystd))\n", " \n", "plt.figure(figsize=(5,5))\n", "\n", "plt.plot(xz, yz, 'bo', markersize=5)\n", "regline = np.polyfit(xz, yz, 1)\n", "plt.plot(xz, [k*regline[0] for k in xz], 'r-', linewidth=3)\n", "\n", "plt.grid(linewidth=1.2)\n", "plt.xticks([-2,-1,0,1,2], ['-2','-1','0','1', '2'])\n", "plt.yticks([-2,-1,0,1,2], ['-2','-1','0','1', '2'])\n", "plt.xlabel(\"x\", fontsize=14)\n", "plt.ylabel(\"y\", fontsize=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.6 Right" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "errorlst = []\n", "label = []\n", "#for angle 0 ~ 89 bc when a = 90, it is a vertical line.\n", "for a in range(0,90, 1):\n", " # slope = y/x\n", " slope = math.sin(math.radians(a))/float(math.cos(math.radians(a)))\n", " label.append(slope)\n", " error = mean_squared_error(yz, [ slope*k for k in xz])\n", " errorlst.append(error)\n", "\n", "#Slope vs. errorlst\n", "plt.figure(figsize=(5,5))\n", "plt.plot(label, errorlst, 'b-', linewidth=2)\n", "plt.plot([1,1],[0,1], '--')\n", "plt.xlim(0,2)\n", "plt.ylim(0,1)\n", "plt.xlabel(r\"$w_1$\", fontsize=14)\n", "plt.ylabel(r\"$J(0,w_1)$\", fontsize=14)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.7\n", "#### Made with the help of this tutorial: http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PPPMMNm3ahOnpaZx66qnYvn07tm3bhrGxMTcEO+Hxxx/Hm9/8Znzve9/D7t27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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.arange(-10, 10, 0.1)\n", "Y = np.arange(-10, 10, 0.1)\n", "X, Y = np.meshgrid(X, Y)\n", "R = 1*((X**2)/(1) + (Y**2)/1)\n", "Z = R\n", "\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.rainbow,\n", " linewidth=0, antialiased=False)\n", "ax.set_zlim(0,400)\n", "ax.set_zticks(np.arange(0,450,50))\n", "ax.set_xlabel(r\"$w_0$\")\n", "ax.set_ylabel(r\"$w_1$\")\n", "ax.set_zlabel(r\"$J(w_0, w_1)$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.8\n", "The tangent line approximates the derivative." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1,2,100)\n", "y = 0.7*np.sin(x)\n", "plt.plot(x,y, linewidth='1.7')\n", "\n", "#the tangent line\n", "x0 = 0.0\n", "x1 = 1.0\n", "slope=(0.7*np.sin(x1)-0.7*np.sin(x0))/(x1-x0)\n", "xline = np.linspace(x0-0.5, x1+0.5, 100)\n", "plt.plot(xline, slope*xline, 'r-', linewidth='1.9')\n", "\n", "#the points\n", "plt.scatter([x0,x1],[0.7*np.sin(x0), 0.7*np.sin(x1)], s=40, color='black')\n", "plt.text(x0-0.05, 0.7*np.sin(x0)+0.05, 'A')\n", "plt.text(x1, 0.7*np.sin(x1)+0.05, 'B')\n", "\n", "#the triangle\n", "plt.plot([x0,x1,x1,x0], [0.7*np.sin(x0), 0.7*np.sin(x1),0.7*np.sin(x0), 0.7*np.sin(x0)], color='black')\n", "plt.text(x0+0.5, 0.7*np.sin(x0)-0.1, r'$\\Delta x$', fontsize=14)\n", "plt.text(x1+0.05, 0.7*np.sin(x1)-0.3, r'$\\Delta y$', fontsize=14)\n", "plt.text(x0+0.25, 0.7*np.sin(x0)-0.5, r'slope = $\\frac{\\Delta y}{\\Delta x}$', fontsize=14)\n", "\n", "plt.xlim(-1,2)\n", "\n", "#Hide the x and y axis.\n", "plt.gca().axes.get_xaxis().set_ticks([])\n", "plt.gca().axes.get_yaxis().set_ticks([])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.11 - Bumpy surface" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ,\n", " ,\n", " ]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GM5WyUCjgui6xWIx0Oo1lWZvmYWtwPhdF435eyEUhQ5/S1N+BWwSgkO2metsYxs4eVDyO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\nq0gkQnd39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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.arange(-2, 2, 0.1)\n", "Y = np.arange(-2, 2, 0.1)\n", "X, Y = np.meshgrid(X, Y)\n", "R = np.sin(X) + np.cos(Y)\n", "R = ((np.cos(X))**4+(np.cos(Y))**4-2*((np.cos(X))**2)*((np.cos(Y))**2))\n", "Z = R\n", "#Equation from http://stackoverflow.com/questions/24045379/matplotlib-3d-surface-of-bumpy-function-does-not-work\n", "\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "p = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.rainbow, linewidth=0)\n", "ax.set_zlim(-1.1,1.1)\n", "ax.set_xlabel(r\"$w_0$\")\n", "ax.set_ylabel(r\"$w_1$\")\n", "ax.set_zlabel(r\"$J(w_0, w_1)$\")\n", "ax.set_xticks(np.arange(-2,2.1,1))\n", "ax.set_yticks(np.arange(-2,2.1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.12" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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L5uXZuHEjx44ds7s0r3H9c9MDeuavVBWyaNEiBg8ezNGjR2ncuDGxsbH89a9/tbssZQPN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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(1,1,1)\n", "\n", "x = [-14,-12, -10, -8, -7, -4]\n", "x1 = [ 3, 5, 7, 10, 12, 13]\n", "y = [0]*len(x)\n", "y1 = [1]*len(x1)\n", "regline = np.polyfit(x+x1,y+y1,1)\n", "\n", "plt.plot(x,y, 'bo', x1,y1,'ro')\n", "plt.plot(x+x1, [regline[0]*i + regline[1] for i in x+x1], 'k-', linewidth=2)\n", "plt.plot([0,0],[1.2,-0.2], 'g-', linewidth=2)\n", "plt.plot([-15,15],[0.5,0.5], 'k--')\n", "\n", "plt.ylim(-0.2, 1.2)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.15 - The logit function " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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m9qmZ/b0u/12T76hpkJ6+gw3jgGlmNtfMLg87mDRxoHOuGMA59zWwW1fz6gIb\nxGRmbwGdYk/h/5Bvcc69GtTnZKK9/WyBx4A7nHPOzP4I/BkY3fhRiux0qnNutZkdALxlZvnR1qgE\np9aeMIEld+fcT+rxy4qAg2KOu0fPSYw4frZP4MccSN0VAQfHHOs72EDOudXRfYmZTcaXvpTcG6bY\nzDo554rNrDPwTW2/IIyyTGx9eAow0syyzKwHcASgp+txiP5BVzkHyAsrlhS1c5BedOrqkfjvpdSD\nmbUyszbR162Bweg7WR/G7rny0ujrXwCv1HaDRlmsw8zOAh4G9gemmtmnzrkznHOfm9nzwOdAOfAr\nzQkct/8xs774HgrLgCvDDSe17GmQXshhpbJOwOToVCPNgAnOuekhx5RSzOxZIAJ0NLPl+Bl37wEm\nmdl/AYX4XoZ7v49yqYhI+gm7t4yIiCSAkruISBpSchcRSUNK7iIiaUjJXUQkDSm5i4ikISV3EZE0\npOQuIpKG/g9fkXJGjP1HqQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c = 1\n", "x = np.linspace(-10,10,100)\n", "y = 1/(1+np.exp(-c*x))\n", "\n", "plt.plot(x,y, linewidth='1.7')\n", "plt.ylim(-0.001,1.01)\n", "plt.text(2, 0.7, r'$\\frac{1}{1+e^{-x}}$', fontsize=26, fontweight='bold')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.16" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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XcBA4jAxCu9BaG5BlwkKimsjT/Plwyy3SzfS//5VvgVIqqmRny8CytWulB9HK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\n2Fjo3Vtaca++Grp0kW49hX7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vI6XChiYDpZRSWk2klFJKk4FSSik0GSillEKTgVJKKTQZ\nKKWUQpOBUkop4P8DPwqkSebdi/wAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.01,0.99, 100)\n", "y1 = -np.log(x)\n", "y2 = -np.log(1-x)\n", "\n", "plt.plot(x, y1, 'r-', label=r\"$-\\log(h_0(x))$, $y=1$\", linewidth=2)\n", "plt.plot(x, y2, 'b-', label=r\"$-\\log(1-h_0(x))$, $y=0$\", linewidth=2)\n", "\n", "plt.xlabel(r'$h_0(x)$')\n", "plt.ylabel(r\"$Cost(h_0(x), y)$\")\n", "plt.legend(loc=\"upper center\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 9.17\n", "#### The source of the data set https://www.statcrunch.com/app/index.php?dataid=1406047\n", "You can look at figure 10.11, which is another version of this figure but using K-means." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[80.839583333333337, 167.02430555555554]\n", "0.479287717168\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fLOrAQQelRVtXxHMLuXH7JOtaiueGSdWl5qafXymkfu1CWNVSiHfvhmbN4JJL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\n776DAw/ce231aopbdnJ2gzmVFImlqx/puW4ZMwb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "path = \"/home/yeseul/practice-notebook/weight.xls\"\n", "csv_data = pd.ExcelFile(path).parse('Sheet1')\n", "female = csv_data[(csv_data['Gender'] == 0) & (csv_data['Age'] >=800) & (csv_data['Age'] <=900)] #Age is by the number of months. 20~40\n", "male = csv_data[(csv_data['Gender'] == 1) & (csv_data['Age'] >=800) & (csv_data['Age'] <= 900)]\n", "y = np.append(female[\"Height\"], male[\"Height\"])\n", "x = np.append(female[\"Weight\"], male[\"Weight\"])\n", "z = [[i,j] for i,j in zip(x,y)]\n", "\n", "plt.figure(figsize=(6,4))\n", "\n", "#Log Reg\n", "f = [0]*len(female)\n", "m = [1]*len(male)\n", "k = np.append(f,m)\n", "reg = LogisticRegression()\n", "reg.fit(z,k)\n", "label = reg.predict(z)\n", "\n", "#Draw the convex hull.\n", "division1 = [i for i,c in zip(z, label) if c == 1]\n", "division1= np.array(division1)\n", "division2 = [i for i,c in zip(z, label) if c == 0]\n", "division2 = np.array(division2)\n", "hull1 = ConvexHull(division1)\n", "hull2 = ConvexHull(division2)\n", "\n", "# to make the line come back to the first point, I appended the first vertice to it at last.\n", "plt.plot(np.append(division1[hull1.vertices, 0], division1[hull1.vertices[0],0]), \\\n", " np.append(division1[hull1.vertices,1], division1[hull1.vertices[0],1]),'b-', linewidth=1.5)\n", "plt.plot(np.append(division2[hull2.vertices, 0], division2[hull2.vertices[0],0]), \\\n", " np.append(division2[hull2.vertices,1], division2[hull2.vertices[0],1]),'r-', linewidth=1.5)\n", "plt.scatter(female['Weight'], female['Height'], c='red', s=10, lw=0)\n", "plt.scatter(male['Weight'], male['Height'], c='blue', s=10, lw=0)\n", "\n", "#Find the perpendicular bisector\n", "#first find the centroids\n", "cx1 = np.sum(division1[:,0])/len(division1)\n", "cy1 = np.sum(division1[:,1])/len(division1)\n", "cx2 = np.sum(division2[:,0])/len(division1)\n", "cy2 = np.sum(division2[:,1])/len(division1)\n", "\n", "midpoint = [(cx1+cx2)/2.0, (cy1+cy2)/2.0]\n", "print midpoint\n", "lineslope = (cy2-cy1)/(cx2-cx1)\n", "print lineslope\n", "perslope = -1/lineslope\n", "perx = [20,120]\n", "pery = perslope*(perx - midpoint[0]) + midpoint[1]\n", "\n", "#Line separating the two\n", "plt.plot([26,118], [200,140], 'k-')\n", "\n", "plt.xlim(20,160)\n", "plt.ylim(140,200)\n", "plt.xlabel(\"Weight (kg)\")\n", "plt.ylabel(\"Height (cm)\")\n", "plt.title(\"Logistic Regression\", fontsize=16)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }