Step3_remove_price_outliers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3. Remove outliers based on the price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The price value of the raw data has a very large range, as it is shown in the figure below. \n",
    "In this section we want to find and remove price outliers in order to be able to properly train our regressor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "%matplotlib inline\n",
    "\n",
    "import MAD_functions as mad\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cross_validation import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('raw/step2_output.csv',sep=\";\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#reassign the index to have the surviving row correctly indexed (needed if one wants to drop other rows before the price analisis)\n",
    "data.index = range(data.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6nI49O9a4TTYG0ouINGnuXi147nPWPkmDZ20UQEWk2fNy58b2N1ZLP/ZPx9ZpvykFUDNr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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd2999e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(5,4))\n",
    "ax = fig1.add_subplot(111)\n",
    "a=plt.semilogy(np.sort(data.loc[:,('price')].values),'purple', Linewidth=3)\n",
    "#b=plt.plot(np.sort(y_test),'k',Linewidth=3)\n",
    "#c=plt.plot(y_median,'--b',Linewidth=2, label='median')\n",
    "#d=plt.plot(y_mean,'--g',Linewidth=2, label='mean')\n",
    "font = {'family' : 'Arial',\n",
    "        'weight' : 'light',\n",
    "        'size'   : 16}\n",
    "\n",
    "ax.set_xlim(0-100, len(data.loc[:,('price')].values)+100)\n",
    "ax.set_ylim(0, max(data.loc[:,('price')].values))\n",
    "\n",
    "ax.set_xlabel('Increasing index of sorted prices',fontsize=16)\n",
    "ax.set_ylabel('Price in euros', fontsize=16)\n",
    "\n",
    "#ax.legend(frameon=False,loc=2,fontsize=14)\n",
    "\n",
    "plt.tick_params(\n",
    "    axis='x',          # changes apply to the x-axis\n",
    "    which='both',      # both major and minor ticks are affected\n",
    "    bottom='off',      # ticks along the bottom edge are off\n",
    "    top='off',         # ticks along the top edge are off\n",
    "    labelbottom='off') # labels along the bottom edge are off\n",
    "\n",
    "plt.title('Price- raw data',weight='bold')\n",
    "fig1.set_alpha(0) #transparent background\n",
    "ax.yaxis.grid(True)\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig1.savefig('raw_data_price.png',dpi=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Separating the three property types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to remove the outliers in the price feature, we should conisder the fact that the apartments are divided into three different property types: entire apartment, private room or shared room. This means that we should separate the thress populations in order to apply any statistical analysis to find the outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#ler's get our boolean masks for the price:\n",
    "#here we retrieve the three columns of interest as boolean vectors\n",
    "entire_home=data.loc[:,('entire_home_apt')].values.astype(bool)\n",
    "private=data.loc[:,('private_room')].values.astype(bool)\n",
    "shared=data.loc[:,('shared_room')].values.astype(bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#here we use the boolean vectors to \"filter\" the price column and get three separate price vectors for the three categories\n",
    "population_entire=data.loc[:,('price')].values[entire_home]\n",
    "population_private=data.loc[:,('price')].values[private]\n",
    "population_shared=data.loc[:,('price')].values[shared]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#let's get the indexes\n",
    "index_entire=data.loc[:,('price')].index[entire_home]\n",
    "index_private=data.loc[:,('price')].index[private]\n",
    "index_shared=data.loc[:,('price')].index[shared]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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dCLySVDfz7SriYGZm1SibkZwGfFHSeuACOsw/EhE39xiXHUmTZLXcRspciIjLgMumOkFx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\nRmJmZj1xRmJmZj1xRmJmZj35/5hpekwlqfRHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e79b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's look at the price\n",
    "binwidth=20\n",
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True)\n",
    "\n",
    "ax1.hist(population_entire, bins=np.arange(min(population_entire),max(population_entire) + binwidth, binwidth), facecolor='blue')\n",
    "ax2.hist(population_private, bins=np.arange(min(population_private),max(population_private) + binwidth, binwidth),facecolor='purple')\n",
    "ax3.hist(population_shared, bins=np.arange(min(population_shared),max(population_shared)+ binwidth, binwidth), facecolor='cyan')\n",
    "\n",
    "ax1.set_title('entire apt')\n",
    "ax2.set_title('private room')\n",
    "ax3.set_title('shared room')\n",
    "ax1.set_xlim(0,1200)\n",
    "ax1.set_xticks([0, 300, 600, 900,1200])\n",
    "ax2.set_xlim(0,600)\n",
    "ax2.set_xticks([0, 300, 600])\n",
    "ax3.set_xlim(0,200)\n",
    "ax3.set_xticks([0, 50, 150, 200])\n",
    "\n",
    "ax1.set_ylabel('Num of apartments',fontsize=16)\n",
    "\n",
    "ax2.set_xlabel('Price in euros',fontsize=16)\n",
    "\n",
    "plt.yscale('log', nonposy='clip')\n",
    "plt.show()\n",
    "\n",
    "#data = data.drop(data[data.price >= 400].index)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "125.0 39.0 22.0\n",
      "(30.0, 45.0) (10.0, 13.0) (3.0, 13.0)\n"
     ]
    }
   ],
   "source": [
    "print np.median(population_entire), np.median(population_private), np.median(population_shared)\n",
    "print mad.doubleMAD(population_entire), mad.doubleMAD(population_private), mad.doubleMAD(population_shared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying the filter based on median and MAD to find the outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we calculate the MAD and use its value to define the the price limits to find and remove the outliers.\n",
    "In particular, since the distributions are strongly asymmetrical, we will take the asymmetry into account computing the MAD separately for the data above and below the median, thus obtaining a MADlow and a MADhigh value, so our criteria of selection of good data becomes:\n",
    "\n",
    "m-t x MADlow<x<m+t x MADhigh\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "thresh=8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#boolean maks for the good data we want to keep\n",
    "good_entire=mad.doubleMAD_mask(data.loc[:,('price')].values[entire_home],thresh)\n",
    "good_private=mad.doubleMAD_mask(data.loc[:,('price')].values[private],thresh)\n",
    "good_shared=mad.doubleMAD_mask(data.loc[:,('price')].values[shared],thresh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7661 6627 150\n",
      "7763 6706 154\n",
      "102 79 4\n"
     ]
    }
   ],
   "source": [
    "print np.sum(good_entire), np.sum(good_private), np.sum(good_shared)\n",
    "print population_entire.size, population_private.size, population_shared.size\n",
    "print population_entire.size-np.sum(good_entire), population_private.size-np.sum(good_private), population_shared.size-np.sum(good_shared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3PjQzMzNrp6wtAR8FvhQRxwILqo4tJ20VaBdJe0k6S9L3Jf1DO69l1i5TmYqkjdvsgdlF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\nw2IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcf0bf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#let's look at what we will cut\n",
    "\n",
    "binwidth=20\n",
    "#f = plt.figure(figsize=(8,6))\n",
    "f,((ax1, ax2, ax3),(ax4,ax5,ax6))= plt.subplots(2, 3, sharey=True,figsize=(8,7))\n",
    "ax1.hist(population_entire, bins=np.arange(min(population_entire),max(population_entire) + binwidth, binwidth),facecolor='blue')\n",
    "ax2.hist(population_private, bins=np.arange(min(population_private),max(population_private) + binwidth, binwidth),facecolor='purple')\n",
    "ax3.hist(population_shared, bins=np.arange(min(population_shared),max(population_shared)+ binwidth, binwidth),facecolor='cyan')\n",
    "\n",
    "ax4.hist(population_entire[good_entire], bins=np.arange(min(population_entire),max(population_entire) + binwidth, binwidth),facecolor='blue')\n",
    "ax5.hist(population_private[good_private], bins=np.arange(min(population_private),max(population_private) + binwidth, binwidth),facecolor='purple')\n",
    "ax6.hist(population_shared[good_shared], bins=np.arange(min(population_shared),max(population_shared)+ binwidth, binwidth),facecolor='cyan')\n",
    "\n",
    "ax1.set_title('entire apt')\n",
    "ax2.set_title('private room')\n",
    "ax3.set_title('shared room')\n",
    "ax1.set_xlim(0,1200)\n",
    "ax1.set_xticks([0, 300, 600, 900,1200])\n",
    "ax2.set_xlim(0,600)\n",
    "ax2.set_xticks([0, 300, 600])\n",
    "ax3.set_xlim(0,200)\n",
    "ax3.set_xticks([0, 50, 150, 200])\n",
    "ax4.set_xlim(0,1200)\n",
    "ax4.set_xticks([0, 300, 600, 900,1200])\n",
    "ax5.set_xlim(0,600)\n",
    "ax5.set_xticks([0, 300, 600])\n",
    "ax6.set_xlim(0,200)\n",
    "ax6.set_xticks([0, 50, 150, 200])\n",
    "\n",
    "ax1.set_ylabel('Num of apartments',fontsize=16)\n",
    "ax4.set_ylabel('Num of apartments', fontsize=16)\n",
    "\n",
    "ax2.set_xlabel('Price in euros',fontsize=16)\n",
    "ax5.set_xlabel('Price in euros',fontsize=16)\n",
    "\n",
    "plt.yscale('log', nonposy='clip')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f.savefig('outliers_price.png',dpi=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Joining the three categories and outliers dropping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#from the individual bolean masks let's get an array with all the indeces of the rows we want to drop\n",
    "\n",
    "outliers_entire= np.ones(len(good_entire),dtype=int)\n",
    "outliers_entire= (outliers_entire-good_entire.astype(int)).astype(bool)\n",
    "mask_entire=index_entire[outliers_entire]\n",
    "\n",
    "outliers_private= np.ones(len(good_private),dtype=int)\n",
    "outliers_private= (outliers_private-good_private.astype(int)).astype(bool)\n",
    "mask_private=index_private[outliers_private]\n",
    "\n",
    "outliers_shared= np.ones(len(good_shared),dtype=int)\n",
    "outliers_shared= (outliers_shared-good_shared.astype(int)).astype(bool)\n",
    "mask_shared=index_shared[outliers_shared]\n",
    "\n",
    "full_mask=np.append(mask_entire,mask_private)\n",
    "full_mask=np.append(full_mask,mask_shared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "full_mask=np.unique(full_mask)\n",
    "#print full_mask, full_mask.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14438, 160)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#now apply the boolean mask using the indices\n",
    "for ind in full_mask:\n",
    "    data=data.drop(labels=ind, axis=0)\n",
    "    \n",
    "#data.drop(data.index[[ind, for ind in mask_entire]]) #this doesnt work but something similar, more pythonic than \n",
    "#the previous for should work...\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train-test splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Get 5 dataset to do cross validation\\n#prepare train and test groups and create two new dataframes\\nyfull = data.loc[:,\\'price\\'].copy()\\nxfull = data.copy()\\nxfull.drop(\\'price\\', axis=1, inplace=True,errors=\\'ignore\\')\\nrandom_seed=[1,42,3,121,17]\\ncounter=1\\nfor i in random_seed:\\n    x_train, x_test, y_train, y_test = train_test_split(xfull.values, yfull.values, test_size = .3, random_state = i)\\n    train=pd.DataFrame(x_train, columns=xfull.columns)\\n    train=train.join(pd.DataFrame(y_train,columns=[\\'price\\']))\\n    test=pd.DataFrame(x_test, columns=xfull.columns)\\n    test=test.join(pd.DataFrame(y_test,columns=[\\'price\\']))\\n    train.to_csv(\"raw/step3_output_train_\"+str(counter)+\".csv\", sep=\";\", index=False, header=True)\\n    test.to_csv(\"raw/step3_output_test_\"+str(counter)+\".csv\", sep=\";\", index=False, header=True)\\n    counter=counter+1'"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''Get 5 dataset to do cross validation\n",
    "#prepare train and test groups and create two new dataframes\n",
    "yfull = data.loc[:,'price'].copy()\n",
    "xfull = data.copy()\n",
    "xfull.drop('price', axis=1, inplace=True,errors='ignore')\n",
    "random_seed=[1,42,3,121,17]\n",
    "counter=1\n",
    "for i in random_seed:\n",
    "    x_train, x_test, y_train, y_test = train_test_split(xfull.values, yfull.values, test_size = .3, random_state = i)\n",
    "    train=pd.DataFrame(x_train, columns=xfull.columns)\n",
    "    train=train.join(pd.DataFrame(y_train,columns=['price']))\n",
    "    test=pd.DataFrame(x_test, columns=xfull.columns)\n",
    "    test=test.join(pd.DataFrame(y_test,columns=['price']))\n",
    "    train.to_csv(\"raw/step3_output_train_\"+str(counter)+\".csv\", sep=\";\", index=False, header=True)\n",
    "    test.to_csv(\"raw/step3_output_test_\"+str(counter)+\".csv\", sep=\";\", index=False, header=True)\n",
    "    counter=counter+1'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yfull = data.loc[:,'price'].copy()\n",
    "xfull = data.copy()\n",
    "xfull.drop('price', axis=1, inplace=True,errors='ignore')\n",
    "x_train, x_test, y_train, y_test = train_test_split(xfull.values, yfull.values, test_size = .3, random_state = 1)\n",
    "train=pd.DataFrame(x_train, columns=xfull.columns)\n",
    "train=train.join(pd.DataFrame(y_train,columns=['price']))\n",
    "test=pd.DataFrame(x_test, columns=xfull.columns)\n",
    "test=test.join(pd.DataFrame(y_test,columns=['price']))\n",
    "\n",
    "train.to_csv(\"raw/step3_output_train.csv\", sep=\";\", index=False, header=True)\n",
    "test.to_csv(\"raw/step3_output_test.csv\", sep=\";\", index=False, header=True)\n",
    "\n",
    "#data.to_csv(\"raw/step3_output.csv\", sep=\";\", index=False, header=True)"
   ]
  }
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