LogisticRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LogisticRegression:\n",
    "    def __init__(self, lrate=0.0001, n_iter=50):\n",
    "        self.lrate = lrate\n",
    "        self.n_iter = n_iter\n",
    "    \n",
    "    def fit(self, X, Y):\n",
    "        self.theta = np.zeros(1 + X.shape[1])\n",
    "        self.cost_ = []\n",
    "        \n",
    "        for _ in range(self.n_iter):\n",
    "            error = self.hypothesis(X) - Y\n",
    "            t = self.lrate/X.shape[0]\n",
    "            self.theta[1:] -= t * np.dot(error,X)\n",
    "            self.theta[0] -= t * error.sum()\n",
    "    \n",
    "    def hypothesis(self, X):\n",
    "        return np.where(self.predict(X) >= 0.5, 1, -1)\n",
    "                \n",
    "    def predict(self, X):\n",
    "        return 1/(1 + 2.71 ** (-1 * (np.dot(X,self.theta[1:]) + self.theta[0])))\n",
    "        \n",
    "         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "irisData = pd.read_csv('Iris.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = irisData.iloc[0:25,4].values \n",
    "Y = np.append(Y,irisData.iloc[50:75,4].values)\n",
    "Y = np.where(Y == 'Iris-setosa',1,-1)\n",
    "t = np.unique(Y)\n",
    "len(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 2)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.append(irisData.iloc[0:25, [0, 2]].values,irisData.iloc[50:75, [0, 2]].values,axis=0)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
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uvlX6WEjlJZ4UzKynmf3OzB5rZ93hZvaIma03s+fMrCHpeETyVbqHcJLF47j7VuljIelQ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\njpKCiIjk/H85PtaVjv+maQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd150f79390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:25,0], X[:25,1], color = 'red', marker='o', label='setosa')\n",
    "plt.scatter(X[25:50,0], X[25:50,1], color='blue', marker='x', label='versicolor')\n",
    "plt.xlabel('sepal length')\n",
    "plt.ylabel('petal length')\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lRegress = LogisticRegression(lrate=0.000001, n_iter=50)\n",
    "lRegress.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.24000000e-06,   3.50400000e-06,  -5.97200000e-06])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lRegress.theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,\n",
       "        1,  1,  1,  1,  1,  1,  1,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lRegress.hypothesis(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(1)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lRegress.hypothesis(irisData.iloc[30, [0, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}