Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticRegression:\n",
    "    def __init__(self, lr=0.01, num_iter=100000):\n",
    "        self.lr = lr\n",
    "        self.num_iter = num_iter\n",
    "        \n",
    "    def __sigmoid(self, z):\n",
    "        return 1 / (1 + np.exp(-z))  \n",
    "    \n",
    "    def __loss(self, h, y):\n",
    "        return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        self.theta = np.zeros(X.shape[1])\n",
    "        for i in range(self.num_iter):\n",
    "            z = np.dot(X, self.theta)\n",
    "            h = self.__sigmoid(z)\n",
    "            gradient = np.dot(X.T, (h - y)) / y.size\n",
    "            self.theta -= self.lr * gradient\n",
    "\n",
    "    def predict_prob(self, X):\n",
    "        return self.__sigmoid(np.dot(X, self.theta))\n",
    "    \n",
    "    def predict(self, X, threshold):\n",
    "        return self.predict_prob(X) >= threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Linear Decision Boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_xls = pd.read_excel('ex2data1-logistic.xls', index_col=None)\n",
    "data_xls.to_csv('data1.csv', encoding='utf-8')\n",
    "data1 = pd.read_csv(\"data1.csv\") \n",
    "\n",
    "x1 = data1['x1']\n",
    "x2 = data1['x2']\n",
    "y = data1['y']\n",
    "\n",
    "x1 = (x1 - np.mean(x1))/np.std(x1)\n",
    "x2 = (x2 - np.mean(x2))/np.std(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression(lr=0.1, num_iter=100)\n",
    "\n",
    "x_input = np.c_[np.ones((len(x1),1)),x1,x2]\n",
    "\n",
    "xTrain, xTest, yTrain, yTest = train_test_split(x_input, y, test_size = 0.1, random_state = 0)\n",
    "theta = np.zeros((x_input.shape[1], 1))\n",
    "model.fit(xTrain, yTrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vv/wyDh06hLi4OEydOhW//PKLPgF5urKtvFG8JT1SfKPniJlekETuJSP0ytNDQEAAHnjgARQWFiI1NRVz5sxBTEwMNmzYoH0wnq5sq28Ub+n1ZCQzM0nJTRK5l5Tq2mzWC6atW7fGsmXLsGvXLjRu3BgpKSkYPHgwvtFyx3a1EWqS/uZCCWYpublqb1F7MnMbObP/1z4M1uzms8uXL/OcOXM4JCSEQ0JCeM6cOXz58mVtFl5zI4wda5gLUpoy0IU4SzLYwQq52GkcVrtgevz4cU5JSWEA3LVrV/7444/1DskeDJZkLMtAJ0t3iVyaVnRgkmY3j4WFheHdd99FZmYmfv75ZyQmJuL+++9HSUmJPgGZtd0K8C52k1yIc8lM28gM1xZcZXe1JymRm7xEXksJ5fz58zxlyhQOCgrili1b8tKlS7miokLb2MxaSvU2diMMbOYLM28jnUGaVozD1Puxh8Hn5+dzYmIiA+CEhAQ+cOCANvGZ+Szpbey19ac3cnu5kbaRgZpNPCGJ3GBMtv/8zouDsLKykpcvX86hoaEcGBjIkydP5rKyMnXjM2spldn72Ou6w9WopQOjbKO6CiUGPEglkQtl+HAQlpSU8KhRoxgAd+zYkdevX6/erf5GKu15y9cxxOsqmRuNUbZRbXEYtNosiVwow4+D8JNPPuHY2FgGwMnJyXzs2DHl4zPoAegRf2I3SinXE0bZRrWtM6OcbGqQRC6U4edBeOXKFZ43bx43atSIGzZsyLNnz+ZLly4pH6PBqsQe8zV2gyYet4ywjWpbZwY9MUoiF8pR4CD85ptv+I477mAAHB0dzTt27FA6SnsxSinXTGpbZwY9MaqayAEMAlAE4CiAqXV9XhK5qLJp0yaOiIhgAJyamspnzpzRO6SrGaH06AmzxGkk7taZQU+MqiVyAIEAvgJwHYD6APIA/Km2/5FErhwrHLu//PILT5s2jevVq8fNmzfnxYsXa9v3vDYGPaCFBgx4cKmZyPsA2Fzt78cBPF7b/0giV4bVcszhw4e5X79+DIB79erFubm5eodk2Cq2pRgwYRqVu0SuxC36HQB8W+3vYudrQmVmvkPblejoaGzfvh0rVqzAsWPH0KNHD0ycOBFlZWX6BWW18RSMZvVqIC0NOHHCcYo8ccLxt6+37Jvp1n8FKZHIXT0QkK/6EFEaEe0jon1nz55VYLHmoda+ZcUcQ0RITU1FUVER0tLSkJGRgaioKLz11ltVNT5tmWUYU7NSsjSi9EnBTFwV072ZIE0rtVKz+cNUtX4fq8+fffYZd+vWjQHwwIED+ejRo6qGeRWrtV8ZjZLd/Ex1QPgGKraRBwE4BiACv1/sjKntf+yUyNXct0yTYxToe/7f//6XmzRpwsHBwTxz5ky+ePGiykFXI2246lHyADFo328lqZbIHfPGrQCOwNF7Jb2uz9spkau9b5kixyh0sBYXF/PQoUMZAHfp0oW3bdumSrhCQ0qWRqREru1kp0Rug32rbgqfzT744AO+/vrrGQAPHz6cT506pXDAQlNKlUZMU0X1nSRynVhx3/L6uFPhbHbhwgWePn06169fn5s1a8YLFizg8vJyn+cnLMIUVVTfSSLXkZX2LZ9OTCqezYqKijgpKYkBcHx8PO/bt8/veQphVJLIhSJ8LlyreDarrKzk119/ndu1a8cBAQE8btw4/umnnxSbvxBG4S6Rk+M9bTlLTpovV/gvIMCRumsicjzSUE/nzp3DE088gYULF6Jt27aYP38+7rrrLhC5utVBCPMhohxmjq/5ujx8WXjFyPfHNGvWDC+++CKys7PRoUMHDB8+HAMGDMCXX36pd2hCqEoSufDKrFlASMgfXwsJcbxuFPHx8di7dy8WLFiA7OxsdO3aFTNmzMDFixf1Dk0IVUgiF14ZMQJYsgRo1er31xo21C8edwIDA/HQQw+hsLAQQ4YMwcyZM3HjjTdiy5Ytns/EpuN2CCcTbX9J5HUw0bbU1K+//v77Dz8Yd0iL9u3b4/XXX8fWrVsREBCAgQMHYtiwYTh58mTt/2jncTuE+ba/qyugak9m6bVixT7gSjDrTU4XL17kmTNncnBwMDdp0oQzMjL4ypUrrj9s1i8plGHQ7Q8Vh7G1LKsNE1sXT2sfZh11MTg4GE8++STy8/ORkJCACRMmoGfPnsjOzr76w2b9kkIZJtv+kshrYbJt6RdvapKK91zRuP2qc+fOeP/997F27VqcOXMGvXv3xtixY/Hjjz/+/iEjd88R6jPb9ndVTFd7MkvTikFrV6rw5rsq2uSkc/vVuXPneMKECRwQEMBt2rThlStXcmVlpe5xCZ0ZdPtD7uz0nkG3pSq8HddKsRs1DXK23L9/P/fs2ZMBcP/+/bmgoMBaYysI7xlw+0si95EBt6UqdMunBhpDury8nBctWsTNmzfnevXqcXp6Ol+4cEHzOIRwx10ilzbyOowYARw/7rj9/Phxx99WpNuNPgZqiwwMDMSYMWNQWFiIu+66C7NmzUJMTAyysrI0j0UIb0giFwB+v9EnLMwxbkpYmONv1U9cBrxVtG3btlixYgW2b9+O4OBgJCcnY8iQISguLtYtJiFqI4lc/EaX2oduZ5C69e/fH3l5eZg1axaysrIQHR2N+fPno7y8XO/QjEPumDMEGf1QCA98/fXXGDduHLKyshAbG4vFixejT58+eoelr6o+q9VvtggJMcyJ2Ipk9EOLk4KRuiIiIrBx40a8/fbbKC0tRUJCAtLS0lBaWqp3aNpwtYPZ7Y45I3N1BVTtyUy9VszATt0kjaCsrIwnT57MgYGBHBoayq+++qqj77lVudvBXPU20qnHkV1Aeq1YlxSMtNW4cWM8//zz2L9/P2644Qbcd9996NevHw4dOqR3aOpwt4MFBrr+vFHvfrQwSeQWYKehBIwkNjYWu3fvxtKlS5Gfn4+4uDhMnToVv/zyi96hKcvdjlRRYbgeR3YlidwCDNQV23YCAgIwatQoFBYW4p577sGcOXMQExODDRs26B2actztSFU9jAzY48huJJFbgAG7YttO69atsXz5cuzatQuNGzdGSkoKBg8ejG+sUC2qbQezyx1zBieJ3AIM3BXbdhITE5Gbm4s5c+Zg69atiI6Oxty5c3HlyhW9Q/Od7GCGJ/3IhVDJiRMn8PDDD2PDhg3o2rUrFi1ahJtuuknvsISJST9yITQWFhaGzMxMZGZm4ueff0ZiYiLuv/9+lJSU6B2asBhJ5EL4w4M7sW6//XYcPnwYjz32GFauXInIyEi88sorqKys1DxcYU2SyIVqLH+3qRePVWrUqBHmzJmD3NxcxMTEYNSoUUhMTMTBgwd1CFxYjSRyoUrC1fMh5JqdQHy4E6tr16746KOPsHz5chw5cgTdunXDo48+ivPnz6sUpLAFV7d7qj3JLfrGodbt/Xo9qELT4Qr8fChGSUkJjxo1igFwx44def369da+1V/4DW5u0ZdeKzYXHu4oLdcUFuboFuyrgABHVquJyNHlWC1qfR81F/bJJ59g7NixOHjwIJKTk/Hiiy8iIiJCsTCFdUivFeGSWrf363W3qabDFSh0J1bfvn2Rk5OD559/Hjt37kRMTAyeeeYZXL58WcFghZVJIrc5tRKuHnebrl7tqAm4osoJRMEbZerVq4fJkyejoKAAt9xyC6ZNm4a4uDjs3LlT+biF9bhqb1F7kjZy41CzTVnLB1e7+h5mHtJ348aNHB4ezgA4NTWVz5w5o3dIwgBgt2FsLd/1TSHuCpWA/+tPy2E4XHUgARwjrZrxbvLk5GQcOnQI06ZNwxtvvIHIyEi89NJL0vdcuOYqu6s9qV0ilwct+MeM68/PDiSGdvjwYe7Xrx8D4F69enFubq7eIQmdwE4lcnnQgn/crb8JE/SJxxNWHso3Ojoa27dvx4oVK3Ds2DH06NEDEydORFlZmd6hCYOwZCKXBy34x916+uEH4zZRWX0oXyJCamoqioqKMHr0aGRkZCAqKgrr1q0Dq9mFWNoozcFVMd3TCcCdAA4BqAQQ7+n/qd20otfNKFbhbv0ZfR1qeXFVb5999hnHxcUxAB40aBAfPXpU+YWYsY3N4uCmacXfRB4NIBLATiMlctn//LNqlftEboU2Z6u48tpr/N8WLbgJwA2IeOaQIXzx4kXlFiAlIsNxl8j9alph5gJmLvJnHmqQcfD9M2IE0KqV6/es0OZsCatXI2jsWEz48UcUALiNGdPffhux4eH48MMPlVmGtFGahiXbyAF1ur7ZqbkwI+PqNud69YDz5+3x/Q2v2hXpDgDWAngfQEVJCW6++WaMGDECp0+f9m8ZVr6CbDWuiunVJwDbAOS7mFKqfWYn6mhaAZAGYB+AfZ06ddKuLqIQOzbXVG9zbtWKuX59e33/mjRvg69tgW76W14AePr06Vy/fn1u1qwZL1iwgMvLy31fvt12eoODGm3kv83EYG3karB7c6Hdv7/mOa2uBdaxQYqKijgpKYkBsHOQOt/jsMsVZBOQRO4nK99wUhe5+KnDiayuBXpwZqmsrOTXX3+d27ZtywEBATxu3Dj+6aefVArYQCx88lElkQP4J4BiAJcAnAGw2ZP/M2Mit2uJtLYxTOzw/atofiL3ZIEeJqwff/yRH3roISYibteuHa9Zs8ZY454rmXgt3hykaonc28mMidzi+4dbtfUpt8P3r2K4ErkPPv/8c+4REcEA+GaAj1xzjf4bUOkDy+IlLknkCrBwjc0tdwVDwB7fv4rh2sh9nGd5w4a8AOCmANcHeHpQEP+6bJlycXtL6cRr8TZQSeQ+sGPirsniBRyvGKrXii+qbcyTAN8NMADuHBTEmzdvViBgHyideC2+w9oykftzHNi1KaUmWQ8W4iJpbgX4BmdCHzp0KH/33XfaxqR04rX4Dmu7RO7N9nSV8C1+YveK1Ewsws1O/WunTvzUU09xcHAwN2nShDMyMvjKlSuu56H0zuDqQK064fg6fwvvsLZL5J4mYncJ3127sEWa2oQXLJMX6ijdfPnllzxgwAAGwN26deO9e/d69f9+xVV1wNasNVioNK0E2yVyT5ve3CX8wEApkRuZVsnVcjX1OlbcypWVHBr6JgPtGSBOShrDpaWljjfVrqZKNbhOtkvknu4TtfXKsNQBbCFaJlc75ZY/rtdzDExgIICbNm3DK1eu5Eq1q6kW73GiBHeJ3LKDZnn6oAF34/9UjZgoIygaj5ZPgLLTAIB/XK9NAfwXwD5cvBiO1NRUJAUHo9DVPyo1iJYM0uU7V9ld7clIvVYsV3W2AS0LbnqVyPVol3dfOy3nRYsWcfOQEK4HcDocg3MpfrDIwVgn2K1pxRuWuZhlE1okVz2vv+mVz+par6dPn+Z7+vZlABwB8KY2bZQPSg7GWkkiF5ahdqJTo0ecN/SsBdQcqrh+/au/7/bt2zkqKooB8JAhQ/jbb79VNzDxG3eJ3LJt5MK61H4ClKs2eGbHcpR6SElt9GyXZ679bwDo378/8vLyMGvWLGzatAnR0dGYP38+ysvL1Q9QuETsakupzDk+subLFcITAQGuExiR44lTagsPB06cuPr1qhOJkZZ77NgxjB8/HllZWYiNjcXixYvRp08f9YK0OSLKYeb4mq9LiVyIGvTuPOFpjyul+VITuO6667Bx40a8/fbbKC0tRUJCAtLS0lBaWqpOkMIlSeRCc0Z/9qleibSKXg8P9/UERkS44447cPjwYUyaNAnLli1DZGQkXnvtNehR47clVw3nak9ysdO+zNLDzI6dJ5TaNnl5edynTx8GwH/96185Pz9flVjttn2YpdeKMAg73SlpRkolyIqKCl6yZAm3aNGCg4KCeMqUKXz+/HnFYvTmhGOlpC+JXBiC3IVtL99//z3fd999DIDDwsJ4w4YNfs/Tm8KAWWqAnnKXyKWNXGhK7wuJQlutW7fG8uXLsWvXLjRu3Bi33347Bg8ejG/86EvpzUVZLYdz0JMkcqEpvS8kCn0kJiZi//79ePbZZ7FlyxZER0dj7ty5uHLlitfz8qYwYJexciSRC03p1SND6K9+/fqYMmUKCgoKcPPNN2PKlCno3r07du/e7dV8vCkM2KUGKIlcaG7ECMcNJpWV2twpKYwlLCwMmZmZePvuaq0AAAtESURBVPfdd/Hzzz8jMTER999/P0pKSjz6f28KA3apAUoiF0LoIiUlBYcPH8Zjjz2GlStXIjIyEq+88goqPbh91tPCgF1qgJLIhSaMfhOQ0EejRo0wZ84c5Obm4k9/+hNGjRqFxMREHDx4ULFl2KEGKIlcqG71aiAtzTGOB7PjZ1qaJHPxu65du+Kjjz7CsmXLUFRUhG7duuHRRx/F+fPn9Q7NFCSRC9XZpQuY8E9AQABGjhyJoqIijBw5EvPmzUN0dDTeeecdudW/DpLIhers0gVMKKNVq1ZYunQpdu/ejRYtWuCOO+7Abbfdhq+//lrv0AxLErlQnV26gAll9e3bFzk5OXj++eexc+dOxMTE4JlnnsHly5f1Ds1wJJEL1dmlC5hQXr169TB58mQUFBRg0KBBmDZtGuLi4vDRRx/pHZqhSCIXqrNLFzChnmuvvRbr16/Hxo0b8euvv6Jfv36499578f333+sdmiHIE4KEEKZy4cIFzJo1C8899xwaN26MZ555BqNHj0ZAgPXLpfKEICGEJYSEhGDWrFnIy8tDbGwsxowZg4SEBHzxxRd6h6YbSeRCCFOKjo7Gjh07sGLFChw7dgw9evTAxIkTUVZWpndompNELoQwLSJCamoqioqKMHr0aGRkZCAqKgrr1q2zVd9zSeRCCNNr0aIFFi9ejD179qBNmza48847ceutt+Krr77SOzRNSCIXQlhG79698fnnn+OFF17A7t270bVrV/znP//BpUuX9A5NVZLIhTAoGWjMN0FBQXjkkUdQWFiI2267DdOnT0dsbCy2b9+ud2iqkUQuhAHJQGP+69ChA9auXYv3338f5eXlSEpKwogRI3D69Gm9Q1OcJHIhDEgGGlPOoEGDkJ+fjyeffBLr1q1DVFQUFi5ciIqKCr1DU4xfiZyIniOiQiI6QETvEFFzpQITws5koDFlNWzYEDNnzsSBAwcQHx+PcePGoXfv3sjJydE7NEX4WyLfCqArM8cCOALgcf9DEkLIQGPqiIyMxNatW7F69Wp8++236NmzJ8aPH49z587pHZpf/ErkzLyFmcudf34GoKP/IQkhZKAx9RARhg8fjsLCQowdOxYLFy5EVFQU3njjDdP2PVeyjfx+AO+7e5OI0ohoHxHtO3v2rIKLFcJ6ZKAx9TVv3hwLFizA3r170aFDB9x9990YMGAAvvzyS71D81qdg2YR0TYA7Vy8lc7Mmc7PpAOIB3AHe3BKk0GzhBBGUlFRgUWLFiE9PR0XL17E1KlT8fjjj6NBgwZ6h/YH7gbN8nv0QyK6F8AYAEnMfKGuzwOSyIUQxnTq1ClMmjQJb7zxBjp37oyFCxdiwIABeof1G1VGPySiQQCmALjd0yQuhBBG1b59e6xZswZbtmwBEWHgwIEYNmwYTp48qXdotfK3jXwBgCYAthLRF0S0WIGYhBBCV//4xz9w4MABPPXUU8jMzERUVBT+97//oby8vO5/1oG/vVY6M/O1zBznnMYoFZgQQuipQYMGmD59OvLz89GnTx9MmDABPXv2RHZ2tt6hXUXu7BRCiFp07twZH3zwAd58802cPn0avXv3xoMPPoiffvpJ79B+I4lcCCHqQEQYOnQoCgsLMX78eLz00kuIjIzEqlWrDNH3XBK5EEJ4qGnTpsjIyMDnn3+O8PBwpKamIikpCYWFhbrGJYlcCCG81L17d+zZsweLFi1Cbm4uYmNj8cQTT+DXX3/VJR5J5EII4YPAwECMGTMGhYWFGDZsGGbNmoWYmBhkZWVpHoskciGE8EPbtm2xcuVKfPjhh6hfvz6Sk5Pxr3/9C8XFxZrFIIlcCCEU8Pe//x15eXl4+umnsWnTJkRHR2P+/Pma9D2XRC6EEAoJDg5Geno6Dh06hMTEREyePBnx8fH49NNPVV2uJHIhhFDYddddh02bNmHdunUoKSlBQkIC0tLSUFpaqsryJJELIYQKiAhDhgxBQUEBJk2ahGXLliEyMhI7duxQfFmSyIUQQkVNmjTBvHnzkJOTg+7du6NLly6KLyNI8TkKIYS4yp///Gds3rxZlXlLiVwIIUxOErkQQpicJHIhhDA5SeRCCGFyksiFEMLkJJELIYTJSSIXQgiTk0QuhBAmR3o8poiIzgI44eO/hwIoUTAcpUhc3pG4vCNxeceocQH+xRbGzK1rvqhLIvcHEe1j5ni946hJ4vKOxOUdics7Ro0LUCc2aVoRQgiTk0QuhBAmZ8ZEvkTvANyQuLwjcXlH4vKOUeMCVIjNdG3kQggh/siMJXIhhBDVGD6RE9FzRFRIRAeI6B0iau7mc4OIqIiIjhLRVA3iupOIDhFRJRG5vQJNRMeJ6CARfUFE+wwUl9brqyURbSWiL50/W7j5XIVzXX1BRBtUjKfW709EwUT0pvP9vUQUrlYsXsZ1HxGdrbaORmkU1zIi+p6I8t28T0T0P2fcB4iou0Hi6kdE56qtr+kaxHQtEe0gogLnsTjBxWeUXV/MbOgJwAAAQc7f5wCY4+IzgQC+AnAdgPoA8gD8SeW4ogFEAtgJIL6Wzx0HEKrh+qozLp3W11wAU52/T3W1HZ3vnddgHdX5/QE8CGCx8/e7ALxpkLjuA7BAq/2p2nL/CqA7gHw3798K4H0ABKA3gL0GiasfgI0ar6v2ALo7f28C4IiL7ajo+jJ8iZyZtzBzufPPzwB0dPGxngCOMvMxZr4M4A0AKSrHVcDMRWouwxcexqX5+nLO/zXn768BGKzy8mrjyfevHu86AElERAaISxfMvAtAbU8OTgGwgh0+A9CciNobIC7NMfMpZt7v/L0MQAGADjU+puj6Mnwir+F+OM5iNXUA8G21v4tx9YrTCwPYQkQ5RJSmdzBOeqyvtsx8CnDs6ADauPlcAyLaR0SfEZFayd6T7//bZ5wFiXMAWqkUjzdxAcAQZ3V8HRFdq3JMnjLyMdiHiPKI6H0iitFywc4muW4A9tZ4S9H1ZYhndhLRNgDtXLyVzsyZzs+kAygHsNrVLFy85nd3HE/i8kBfZj5JRG0AbCWiQmcpQs+4NF9fXsymk3N9XQdgOxEdZOav/I2tBk++vyrrqA6eLPM9AGuY+RIRjYGj1vB3lePyhB7ryxP74bit/TwR3QrgXQA3aLFgImoM4G0AjzDzzzXfdvEvPq8vQyRyZr65tveJ6F4A/wdAEjsbmGooBlC9ZNIRwEm14/JwHiedP78nonfgqD77lcgViEvz9UVEZ4ioPTOfclYhv3czj6r1dYyIdsJRmlE6kXvy/as+U0xEQQCaQf0qfJ1xMfMP1f5cCsd1IyNQZZ/yV/UEysxZRPT/iCiUmVUdh4WI6sGRxFcz83oXH1F0fRm+aYWIBgGYAuB2Zr7g5mOfA7iBiCKIqD4cF6dU6/HgKSJqRERNqn6H48Kty6vrGtNjfW0AcK/z93sBXFVzIKIWRBTs/D0UQF8Ah1WIxZPvXz3efwHY7qYQoWlcNdpRb4ej/dUINgD4v87eGL0BnKtqStMTEbWrurZBRD3hyHk/1P5ffi+TALwCoICZ57v5mLLrS8uruT5eAT4KR1vSF86pqifBNQCyalwFPgJH6S1dg7j+CcdZ9RKAMwA214wLjt4Hec7pkFHi0ml9tQLwIYAvnT9bOl+PB/Cy8/cEAAed6+sggAdUjOeq7w9gJhwFBgBoAOAt5/6XDeA6tdeRh3E949yX8gDsABClUVxrAJwCcMW5fz0AYAyAMc73CcBCZ9wHUUtPLo3jGldtfX0GIEGDmG6Co5nkQLW8daua60vu7BRCCJMzfNOKEEKI2kkiF0IIk5NELoQQJieJXAghTE4SuRBCmJwkciGEMDlJ5EIIYXKSyIUQwuT+PwsDm0Ipj1fNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = model.theta\n",
    "\n",
    "xval = np.linspace(-2,2,1000)\n",
    "yval = ((-t[0] - t[1]*xval)/t[2])  \n",
    "\n",
    "plt.plot(xval,yval,'black')\n",
    "\n",
    "for i in range(len(x1)):\n",
    "    if(y[i]==1):\n",
    "        plt.scatter(x1[i],x2[i],color='red')\n",
    "    else:\n",
    "        plt.scatter(x1[i],x2[i],color='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on Train Dataset: 90.0 %\n",
      "Accuracy on Test Dataset : 80.0 %\n"
     ]
    }
   ],
   "source": [
    "preds = model.predict(xTrain,0.5)\n",
    "print(\"Accuracy on Train Dataset:\",(preds == yTrain).mean()*100,\"%\")\n",
    "\n",
    "preds = model.predict(xTest,0.5)\n",
    "print(\"Accuracy on Test Dataset :\",(preds == yTest).mean()*100,\"%\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Non-Linear Decision Boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_xls = pd.read_excel('ex2data2-logistic.xls', index_col=None)\n",
    "data_xls.to_csv('data2.csv', encoding='utf-8')\n",
    "data2 = pd.read_csv(\"data2.csv\") \n",
    "\n",
    "x1 = data2['x1']\n",
    "x2 = data2['x2']\n",
    "y = data2['y']\n",
    "\n",
    "x1 = (x1 - np.mean(x1))/np.std(x1)\n",
    "x2 = (x2 - np.mean(x2))/np.std(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression(lr=0.1, num_iter=100)\n",
    "\n",
    "x_input = np.c_[np.ones((len(x1),1)),x1,x2,x1**2,x2**2, x1*x2]\n",
    "\n",
    "xTrain, xTest, yTrain, yTest = train_test_split(x_input, y, test_size = 0.1, random_state = 0)\n",
    "\n",
    "theta = np.zeros((x_input.shape[1], 1))\n",
    "model.fit(x_input, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jui/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \n",
      "/home/jui/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: RuntimeWarning: invalid value encountered in sqrt\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "t = model.theta\n",
    "\n",
    "xval = np.linspace(-2,2,1000)\n",
    "c = t[0] + t[2]*xval + t[4]*xval*xval\n",
    "b = t[1]*(1 + xval)\n",
    "a = t[3]\n",
    "D = (b*b) - (4*a*c)\n",
    "yval1 = (-b + (D)**(0.5))/(2*a)\n",
    "yval2 = (-b - (D)**(0.5))/(2*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xval,yval1,'black')\n",
    "plt.plot(xval,yval2,'black')\n",
    "\n",
    "for i in range(len(x1)):\n",
    "    if(y[i]==1):\n",
    "        plt.scatter(x1[i],x2[i],color='red')\n",
    "    else:\n",
    "        plt.scatter(x1[i],x2[i],color='blue')\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on Train Dataset: 80.18867924528303 %\n",
      "Accuracy on Test Dataset : 83.33333333333334 %\n"
     ]
    }
   ],
   "source": [
    "preds = model.predict(xTrain,0.4)\n",
    "print(\"Accuracy on Train Dataset:\",(preds == yTrain).mean()*100,\"%\")\n",
    "\n",
    "preds = model.predict(xTest,0.4)\n",
    "print(\"Accuracy on Test Dataset :\",(preds == yTest).mean()*100,\"%\")\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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}