Predict housing prices in Portland, Oregon..ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict housing prices in Portland, Oregon.\n",
    "#### Problem statement :\n",
    "Suppose you are selling your house and you want to know what a good market price would be. One way to do this is to first collect information on recent houses sold and make a model of housing prices.\n",
    "The file ex1data2.txt contains a training set of housing prices in Portland,Oregon. The first column is the size of the house (in square feet), the second column is the number of bedrooms and the third column is the price of the house.\n",
    "Dataset is like below :\n",
    "\n",
    "| Size of the house (in square feet) | Number of bedrooms | Price of the house |\n",
    "|------------------------------------|--------------------|--------------------|\n",
    "| 2104                               | 3                  | 399900             |\n",
    "| 1600                               | 3                  | 329900             |\n",
    "| 2400                               | 3                  | 369000             |\n",
    "\n",
    "Now we have to predict housing prices in Portland, Oregon.(including which is not mention in our example dataset).\n",
    "\n",
    "**Note:This problem statement and dataset is from coursera Andrew ng machine learning [Coursework](https://www.coursera.org/learn/machine-learning)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#supressing the scientific output\n",
    "np.set_printoptions(suppress=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   2104.,       3.,  399900.],\n",
       "       [   1600.,       3.,  329900.],\n",
       "       [   2400.,       3.,  369000.],\n",
       "       [   1416.,       2.,  232000.],\n",
       "       [   3000.,       4.,  539900.]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.loadtxt(\"ex1data2.txt\",dtype=np.float64,delimiter=\",\")\n",
    "data[:5,::] #dataset loaded demonstration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Break datasets into X and Y.\n",
    "X = data[::,0:2]\n",
    "Y = data[::,-1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABPQAAAFwCAYAAAA/oCUGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5fdfb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting example dataset\n",
    "plt.figure(figsize = (15,4),dpi=100)\n",
    "plt.subplot(121)\n",
    "plt.scatter(X[::,0:1],Y)\n",
    "plt.xlabel(\"Size of house (X1)\")\n",
    "plt.ylabel(\"Price (Y)\")\n",
    "plt.subplot(122)\n",
    "plt.scatter(X[::,-1:],Y)\n",
    "plt.xlabel(\"Number of Bedrooms (X2)\")\n",
    "plt.ylabel(\"Price (Y)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_bias = \n",
      "[[    1.  2104.     3.]\n",
      " [    1.  1600.     3.]\n",
      " [    1.  2400.     3.]\n",
      " [    1.  1416.     2.]\n",
      " [    1.  3000.     4.]]\n",
      "Y = \n",
      "[[ 399900.]\n",
      " [ 329900.]\n",
      " [ 369000.]\n",
      " [ 232000.]\n",
      " [ 539900.]]\n"
     ]
    }
   ],
   "source": [
    "# introduce weights of hypothesis (randomly initialize)\n",
    "Theta = np.random.rand(1,3)\n",
    "# m is total example set , n is number of features\n",
    "m,n = X.shape\n",
    "# add bias to input matrix by simple make X0 = 1 for all\n",
    "X_bias = np.ones((m,n+1))\n",
    "X_bias[::,1:] = X\n",
    "# output first 5 X_bias examples\n",
    "print \"X_bias = \\n\",X_bias[0:5,:]\n",
    "print \"Y = \\n\",Y[0:5,::]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.13141542, -0.22609337],\n",
       "       [ 1.        , -0.5096407 , -0.22609337],\n",
       "       [ 1.        ,  0.5079087 , -0.22609337],\n",
       "       [ 1.        , -0.74367706, -1.5543919 ],\n",
       "       [ 1.        ,  1.27107075,  1.10220517]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#feature scaling\n",
    "# it also protect program from overflow error\n",
    "mean_size = np.mean(X_bias[::,1:2])\n",
    "mean_bedroom = np.mean(X_bias[::,2:])\n",
    "size_std = np.std(X_bias[::,1:2])\n",
    "bedroom_std = np.std(X_bias[::,2:])\n",
    "X_bias[::,1:2] = (X_bias[::,1:2] - mean_size)/ (size_std) \n",
    "X_bias[::,2:] = (X_bias[::,2:] - mean_bedroom)/ (bedroom_std)\n",
    "X_bias[0:5,::]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#define function to find cost\n",
    "def cost(X_bias,Y,Theta):\n",
    "    np.seterr(over='raise')\n",
    "    m,n = X.shape\n",
    "    hypothesis = X_bias.dot(Theta.transpose())\n",
    "    return (1/(2.0*m))*((np.square(hypothesis-Y)).sum(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#function gradient descent algorithm from minimizing theta\n",
    "def gradientDescent(X_bias,Y,Theta,iterations,alpha):\n",
    "    count = 1\n",
    "    cost_log = np.array([])\n",
    "    while(count <= iterations):\n",
    "        hypothesis = X_bias.dot(Theta.transpose())\n",
    "        temp0 = Theta[0,0] - alpha*(1.0/m)*((hypothesis-Y)*(X_bias[::,0:1])).sum(axis=0)\n",
    "        temp1 = Theta[0,1] - alpha*(1.0/m)*((hypothesis-Y)*(X_bias[::,1:2])).sum(axis=0)\n",
    "        temp2 = Theta[0,2] - alpha*(1.0/m)*((hypothesis-Y)*(X_bias[::,-1:])).sum(axis=0)\n",
    "        Theta[0,0] = temp0\n",
    "        Theta[0,1] = temp1\n",
    "        Theta[0,2] = temp2\n",
    "        cost_log = np.append(cost_log,cost(X_bias,Y,Theta))\n",
    "        count = count + 1\n",
    "    plt.plot(np.linspace(1,iterations,iterations,endpoint=True),cost_log)\n",
    "    plt.title(\"Iteration vs Cost graph \")\n",
    "    plt.xlabel(\"Number of iteration\")\n",
    "    plt.ylabel(\"Cost of Theta\")\n",
    "    plt.show()\n",
    "    return Theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x61e8070>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 340412.65957447   72655.84621595   59125.40416724]]\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.3\n",
    "iterations = 100\n",
    "Theta = gradientDescent(X_bias,Y,Theta,iterations,alpha)\n",
    "print Theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of house with 1650 sq ft and 3 bedroom is  [ 294637.10371537]\n"
     ]
    }
   ],
   "source": [
    "# predict the price of a house with 1650 square feet and 3 bedrooms\n",
    "# add bias unit 1.0\n",
    "X_predict = np.array([1.0,1650.0,3]) \n",
    "#feature scaling the data first\n",
    "X_predict[1] = (X_predict[1] - mean_size)/ (size_std) \n",
    "X_predict[2] = (X_predict[2]- mean_bedroom)/ (bedroom_std)\n",
    "hypothesis = X_predict.dot(Theta.transpose())\n",
    "print \"Cost of house with 1650 sq ft and 3 bedroom is \",hypothesis\n"
   ]
  }
 ],
 "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}