Air quality prediction .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df=pd.read_csv('Train.csv')\n",
    "dft=pd.read_csv('Test.csv')\n",
    "vt=dft.values\n",
    "v=df.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of feature of data set is 5\n"
     ]
    }
   ],
   "source": [
    "x=v[:,:-1]\n",
    "y=v[:,-1:]\n",
    "x_test=vt[:,:-1]\n",
    "y_test=vt[:,-1:]\n",
    "print(\"Number of feature of data set is\",x.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X=(x-x.mean())/x.std()\n",
    "X_test=(x_test-x_test.mean())/x_test.std()\n",
    "Y =y\n",
    "Y_test=y_test\n",
    "X=np.insert(X,0,1,axis=1)\n",
    "X_test=np.insert(X_test,0,1,axis=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-103-8b4a44857c58>, line 19)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-103-8b4a44857c58>\"\u001b[1;36m, line \u001b[1;32m19\u001b[0m\n\u001b[1;33m    m=X.shape[0]\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "def hypothesis(X, theta):\n",
    "    return  np.dot(X,theta.T)\n",
    "def cost(X,Y,theta):\n",
    "    m=X.shape[0]\n",
    "    hp=hypothesis(X,theta)\n",
    "    c=(hp-Y)**2\n",
    "    return np.sum(c)/(2*m)\n",
    "def gradient_desent(X,Y , learning_rate=0.01):\n",
    "    theta=np.zeros((1,X.shape[1]))\n",
    "    m=X.shape[0]\n",
    "    cost_list= np.zeros(1000)\n",
    "    for i in range(1000):\n",
    "        hp=hypothesis(X,theta)\n",
    "        theta = theta - (learning_rate/m) * np.sum(X * (hp - Y), axis=0)\n",
    "        cost_list[i] = cost(X, Y, theta)\n",
    "    return theta, cost_list\n",
    "def stochastic_gradient_descent(X,Y, learning_rate=0.001):\n",
    "    theta=np.zeros((1,X.shape[1])\n",
    "    m=X.shape[0]\n",
    "    cost_list= np.zeros(X.shape[0])\n",
    "    for i in range(X.shape[0]):\n",
    "        hp=hypothesis(X[i,:],theta)\n",
    "        theta = theta - (learning_rate/m) * np.sum(X[i,:] * (hp - Y[i,:]), axis=0)\n",
    "        cost_list[i] = cost(X, Y, theta)\n",
    "    \n",
    "    return theta, cost_list  \n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_theta , cost_list= gradient_desent(X,Y)\n",
    "final_cost=cost(X,Y,final_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final hypothesis is 509.200570463\n"
     ]
    }
   ],
   "source": [
    "hp=hypothesis(X,final_theta)\n",
    "print(\"final hypothesis is\",np.sum(hp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "207.776673737\n"
     ]
    }
   ],
   "source": [
    "print(final_cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7m4TBzsMKABGJPgVAmll5OSytKuZNBYCIxIAC4AJXz9edQCISDwqAC3xwwRyOdJ6m5cTp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2abff0e4e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.49074643,  29.8408354 ,  93.16196034,   8.32269365,\n",
       "         45.00820867,   2.53129205]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bfinal_theta , bcost_list= stochastic_gradient_descent(X,Y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BiUjI2vHDYXr+7Rv2HswGoG6VeEZe1YZ29Sv7nCy0FXUvIBUAEQlph7NzefaL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\nB7s6C7FOCQNxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2abff231898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(bcost_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficients of theta- [ 29.8408354   93.16196034   8.32269365  45.00820867   2.53129205]\n",
      "intercept of theta- 1.49074642538\n",
      "hypothesis function [[ -57.87084727]\n",
      " [ -89.45473064]\n",
      " [  53.95018198]\n",
      " ..., \n",
      " [-115.65900246]\n",
      " [ -64.27841029]\n",
      " [-116.10771024]]\n"
     ]
    }
   ],
   "source": [
    "print(\"coefficients of theta-\",final_theta[0,1:])\n",
    "print(\"intercept of theta-\",final_theta[0,0])\n",
    "print(\"hypothesis function\",hypothesis(X,final_theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Coefficient_of_Determination(Y,X,final_theta):\n",
    "    Y_predict=hypothesis(X, final_theta)\n",
    "    m=X.shape[0]\n",
    "    re=np.sum((Y-Y_predict)**2)\n",
    "    sre=np.sum((Y-Y.mean())**2)\n",
    "    r= 1- (re/sre)\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score using Traning data 0.966093964393\n",
      "score using Test data 0.968528055101\n"
     ]
    }
   ],
   "source": [
    "r= Coefficient_of_Determination(Y,X,final_theta)\n",
    "print(\"score using Traning data\",r)\n",
    "rt=Coefficient_of_Determination(Y_test,X_test,final_theta)\n",
    "print(\"score using Test data\",rt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score of test data is better\n",
      "[[ -8.61204418e+01]\n",
      " [ -1.63939206e+01]\n",
      " [ -6.73801809e+01]\n",
      " [ -2.41157407e+02]\n",
      " [ -2.85455633e+01]\n",
      " [ -1.77447216e+02]\n",
      " [ -1.58110724e+02]\n",
      " [  1.89121515e+01]\n",
      " [ -1.03163108e+01]\n",
      " [ -6.25798862e+01]\n",
      " [  1.06234502e+02]\n",
      " [  2.04391380e+01]\n",
      " [  1.60808023e+02]\n",
      " [ -9.51495587e+01]\n",
      " [  4.70567821e+01]\n",
      " [  3.26618048e+01]\n",
      " [  1.31868001e+02]\n",
      " [  1.09515652e+02]\n",
      " [  4.48100255e+01]\n",
      " [  2.84382460e+01]\n",
      " [  6.57859600e+01]\n",
      " [  3.47991490e+01]\n",
      " [  6.44101023e+01]\n",
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      " [  4.52749112e+01]\n",
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      " [ -1.23686059e+02]\n",
      " [  4.19295293e+01]\n",
      " [  1.69699045e+01]\n",
      " [  8.81742358e+00]\n",
      " [  2.39994365e+02]\n",
      " [  1.56899909e+02]\n",
      " [ -7.47530650e+01]\n",
      " [  6.09558901e+01]\n",
      " [ -2.87813021e+01]\n",
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      " [ -2.30973215e+02]\n",
      " [ -1.08190494e+02]\n",
      " [ -2.92077224e+01]\n",
      " [  2.36202439e+01]\n",
      " [ -2.07332660e+00]\n",
      " [ -3.38834941e+01]\n",
      " [ -8.44850627e+01]\n",
      " [ -6.12897593e+00]\n",
      " [ -1.52159794e+00]\n",
      " [ -2.30039562e+01]\n",
      " [  5.54642355e+01]\n",
      " [  6.35818106e+01]\n",
      " [ -2.18357911e+02]\n",
      " [ -8.53413504e+01]\n",
      " [ -1.14368591e+01]\n",
      " [ -1.28889988e+02]\n",
      " [ -4.66711503e+01]\n",
      " [ -6.43262024e+01]\n",
      " [  1.11852242e+02]\n",
      " [ -1.23364383e+02]]\n"
     ]
    }
   ],
   "source": [
    "print(\"score of test data is better\")\n",
    "Y_predict=hypothesis(X_test, final_theta)\n",
    "print(Y_predict) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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