xeonqq/logistic_regression.ipynb

## logistic_regression.ipynb
{
 "metadata": {
  "name": "",
  "signature": "sha256:0e106048bd091455c506746ba01dba2e60e9f484c9c324863fbf9e3686ba5129"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import load_iris\n",
      "import numpy as np\n",
      "from numpy import where\n",
      "from pylab import scatter, show, legend, xlabel, ylabel, plot\n",
      "from scipy.optimize import fmin_bfgs, fmin, fmin_cg\n",
      "%matplotlib inline\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 345
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris = load_iris()\n",
      "x = iris.data[:100,0:2]\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 346
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y  = iris.target[0:100]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 347
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pos = where(target == 1)\n",
      "neg = where(target == 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 348
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scatter(x[pos, 0], x[pos, 1], marker='o', c='b')\n",
      "scatter(x[neg, 0], x[neg, 1], marker='x', c='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 349,
       "text": [
        "<matplotlib.collections.PathCollection at 0x7f2699bdf510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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y5W7brVixQjp0uFIaNmwld9/9F0lNTa3kSKsufDRxWHtgBuZzbBDwH2AKcL/r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\n/h/qJjksU03asQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f2699c81fd0>"
       ]
      }
     ],
     "prompt_number": 349
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#append 1 for each row, because the theta0*x0+theta1*x1+theta2\n",
      "x = np.hstack((x, np.ones(100).reshape(1,-1).T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 350
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sigmoid(x):\n",
      "    return 1.0/(1.0+np.exp(-x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 351
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def h(x, theta):\n",
      "    assert len(theta) == x.shape[1]\n",
      "    return sigmoid(x.dot(theta))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 352
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cost_function(theta):\n",
      "    m = len(y)\n",
      "    j = -1.0/m*np.sum(y*np.log(h(x, theta)) + (1-y)*np.log(1-h(x, theta))) \n",
      "    return j"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 353
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cost_function_gradient(theta): \n",
      "    m = len(y)\n",
      "    dj = 1.0/m * np.sum(x*((h(x, theta)-y)[:,np.newaxis]), axis=0)\n",
      "    return dj"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 354
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theta0 = np.array([0,0,0])\n",
      "r1= fmin_bfgs(cost_function, theta0, cost_function_gradient)\n",
      "#r2 =  fmin_cg(cost_function, theta0, cost_function_gradient)\n",
      "#r3 = fmin(cost_function, theta0)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Warning: Desired error not necessarily achieved due to precision loss.\n",
        "         Current function value: nan\n",
        "         Iterations: 34\n",
        "         Function evaluations: 67\n",
        "         Gradient evaluations: 67\n"
       ]
      }
     ],
     "prompt_number": 356
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linx = np.linspace(min(x[:,0]),max(x[:,0]), 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 366
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "liny1 = -(r1[0]*linx+r1[2])/r1[1]\n",
      "#liny2 = -(r2[0]*linx+r2[2])/r2[1]\n",
      "#liny3 = -(r3[0]*linx+r3[2])/r3[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 367
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scatter(x[pos, 0], x[pos, 1], marker='o', c='b')\n",
      "scatter(x[neg, 0], x[neg, 1], marker='x', c='r')\n",
      "plot(linx, liny1)\n",
      "#plot(linx, liny2)\n",
      "#plot(linx, liny3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 368,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f26998846d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3ZQMWLszfJjvbbHIdHg7R0Wbz6+Rk388ZYA4HTJ4MrVqZyr7r1nneplWFprZt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\n5/4jcPgMbUJ+p9LS/g+kNMdfmmMHjd9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       "text": [
        "<matplotlib.figure.Figure at 0x7f26998efb10>"
       ]
      }
     ],
     "prompt_number": 368
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 368
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}