ETA of Flight Delay Large Data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flight ETA Challenge: Arrival time data for Airlines\n",
    "    Author: Rishabh Shrivas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task: \n",
    "Build a binary classification model for predicting arrival delays > 15minutes without using departure delay as an input feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset: \n",
    "US Dept. of Transportation on-time performance data for non-stop domestic flights\n",
    "    - Link: https://transtats.bts.gov/DL_SelectFields.asp?Table_ID=236&DB_Short_Name=On-Time\n",
    "    - Data range: [Geography = All of America], [Period = Jan-Apr 2017, May-Jul 2016 and Nov-Dec 2016]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach: \n",
    "    1) Load data\n",
    "    2) Wrangle data: Check for class imbalances and handle it by sampling from the dataset\n",
    "    3) Wrangle data: Check for sparse columns to remove them\n",
    "    4) Wrangle data: Check for columns with a few missing values to impute with zero, mean or median\n",
    "    5) Wrangle data: Encode categorical values to numerical values\n",
    "    6) Exploratory analyss: Infer distribution of data using histograms\n",
    "    7) Exploratory analyss: Use measures of central tendency and IQR to understand data at various positions\n",
    "    8) Variable interdependence: Infer multicollinearity of data through correlation matrix\n",
    "    9) Feature selection: Remove redundant variables (i.e. columns that refer to the same thing e.g. ID)\n",
    "    10) Feature engineering: Remove highly collinear variables (i.e. correlation > 0.8)\n",
    "    11) Feature engineering: Reduce data dimension to the variables that most explain variation in target variable\n",
    "    12) Modeling building: Random forest is chosen for machine learning modeling\n",
    "    13) Model comparison: Random forest modeling with original raw data (PART 2) and PCA transformed data (PART 3)\n",
    "    14) Machine learning process:\n",
    "        (a) Train/test data: Split data for training and testing\n",
    "        (b) Model creation: Create models in a grid search for a combination of parameters\n",
    "        (c) Model selection: Use 10-fold cross validation to evaluate model performance and select the best one\n",
    "        (c) Final Model training: Use parameters of the best model from above to train on entire train set\n",
    "        (d) Final Model evaluation: Use 10-fold cross validation for average error on 10 folds of training data\n",
    "        (e) Final Model performance evaluation: Use confusion matrix, Precision, Recall, ROC to evaluate performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PART 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Environment set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\homeuser\\Anaconda3\\lib\\site-packages\\sklearn\\cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import csv\n",
    "import os\n",
    "import tabulate\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n",
    "from sklearn.preprocessing import Imputer\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn import linear_model, decomposition, datasets\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.model_selection import train_test_split, cross_val_score, GridSearchCV\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn import cross_validation\n",
    "from sklearn.metrics import confusion_matrix, roc_curve\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "%matplotlib inline\n",
    "get_ipython().magic('matplotlib inline')\n",
    "matplotlib.rcParams.update({'font.size': 12})\n",
    "matplotlib.rc('xtick', labelsize=8) \n",
    "matplotlib.rc('ytick', labelsize=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Set Up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "startTime = datetime.now()\n",
    "folderPath = \"C:/Users/homeuser/Documents/MEJ/DS Challenge/StartUpML/Flight Delay/dataFiles\"\n",
    "os.chdir(folderPath)\n",
    "fdata = pd.DataFrame()\n",
    "for filename in os.listdir(os.getcwd()):#Reads all data files from above location\n",
    "    temp = pd.read_csv(filename)\n",
    "    fdata = fdata.append(temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "folderPath = \"C:/Users/homeuser/Documents/MEJ/DS Challenge/StartUpML/Flight Delay\"\n",
    "os.chdir(folderPath)#Setting working directory\n",
    "#fileName = \"On_Time_On_Time_Performance_2017_1.csv\"\n",
    "#fdata = pd.read_csv(fileName)\n",
    "#fdata.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Wrangling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Target variable is 'ArrDel15' and there was substantial class imbalances as seen below. In order to avoid the classifier learning one class better than the other, sampling was done to even out the class imbalance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class imbalance:\n",
      "0.0    3336085\n",
      "1.0     794668\n",
      "Name: ArrDel15, dtype: int64\n",
      "Class imbalance evened out:\n",
      "1.0    794668\n",
      "0.0    794668\n",
      "Name: ArrDel15, dtype: int64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "110"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Handles class imbalance through sampling\n",
    "classDistribution = fdata['ArrDel15'].value_counts()\n",
    "print('Class imbalance:')\n",
    "print(classDistribution)\n",
    "zero = fdata[fdata['ArrDel15']==0].tail(classDistribution.min())\n",
    "one = fdata[fdata['ArrDel15']==1]\n",
    "data = zero.append(one)\n",
    "del zero, one\n",
    "data.sort(['Year','Month','DayofMonth','DayOfWeek'], ascending=[False,False,False,False])\n",
    "#del fdata\n",
    "print('Class imbalance evened out:')\n",
    "print(data['ArrDel15'].value_counts())\n",
    "len(data.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>FlightDate</th>\n",
       "      <th>UniqueCarrier</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>Carrier</th>\n",
       "      <th>TailNum</th>\n",
       "      <th>...</th>\n",
       "      <th>Div4TailNum</th>\n",
       "      <th>Div5Airport</th>\n",
       "      <th>Div5AirportID</th>\n",
       "      <th>Div5AirportSeqID</th>\n",
       "      <th>Div5WheelsOn</th>\n",
       "      <th>Div5TotalGTime</th>\n",
       "      <th>Div5LongestGTime</th>\n",
       "      <th>Div5WheelsOff</th>\n",
       "      <th>Div5TailNum</th>\n",
       "      <th>Unnamed: 109</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>366268</th>\n",
       "      <td>2017</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>17</td>\n",
       "      <td>5</td>\n",
       "      <td>2017-02-17</td>\n",
       "      <td>WN</td>\n",
       "      <td>19393</td>\n",
       "      <td>WN</td>\n",
       "      <td>N760SW</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>366269</th>\n",
       "      <td>2017</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>17</td>\n",
       "      <td>5</td>\n",
       "      <td>2017-02-17</td>\n",
       "      <td>WN</td>\n",
       "      <td>19393</td>\n",
       "      <td>WN</td>\n",
       "      <td>N944WN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 110 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Year  Quarter  Month  DayofMonth  DayOfWeek  FlightDate UniqueCarrier  \\\n",
       "366268  2017        1      2          17          5  2017-02-17            WN   \n",
       "366269  2017        1      2          17          5  2017-02-17            WN   \n",
       "\n",
       "        AirlineID Carrier TailNum      ...       Div4TailNum  Div5Airport  \\\n",
       "366268      19393      WN  N760SW      ...               NaN          NaN   \n",
       "366269      19393      WN  N944WN      ...               NaN          NaN   \n",
       "\n",
       "        Div5AirportID  Div5AirportSeqID Div5WheelsOn Div5TotalGTime  \\\n",
       "366268            NaN               NaN          NaN            NaN   \n",
       "366269            NaN               NaN          NaN            NaN   \n",
       "\n",
       "       Div5LongestGTime  Div5WheelsOff Div5TailNum  Unnamed: 109  \n",
       "366268              NaN            NaN         NaN           NaN  \n",
       "366269              NaN            NaN         NaN           NaN  \n",
       "\n",
       "[2 rows x 110 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(2)#Showing top 2 rows as sampled data is ordered by time with older data at the top"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>FlightDate</th>\n",
       "      <th>UniqueCarrier</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>Carrier</th>\n",
       "      <th>TailNum</th>\n",
       "      <th>...</th>\n",
       "      <th>Div4TailNum</th>\n",
       "      <th>Div5Airport</th>\n",
       "      <th>Div5AirportID</th>\n",
       "      <th>Div5AirportSeqID</th>\n",
       "      <th>Div5WheelsOn</th>\n",
       "      <th>Div5TotalGTime</th>\n",
       "      <th>Div5LongestGTime</th>\n",
       "      <th>Div5WheelsOff</th>\n",
       "      <th>Div5TailNum</th>\n",
       "      <th>Unnamed: 109</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>468304</th>\n",
       "      <td>2017</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>25</td>\n",
       "      <td>2</td>\n",
       "      <td>2017-04-25</td>\n",
       "      <td>WN</td>\n",
       "      <td>19393</td>\n",
       "      <td>WN</td>\n",
       "      <td>N7738A</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>468309</th>\n",
       "      <td>2017</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>25</td>\n",
       "      <td>2</td>\n",
       "      <td>2017-04-25</td>\n",
       "      <td>WN</td>\n",
       "      <td>19393</td>\n",
       "      <td>WN</td>\n",
       "      <td>N8696E</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 110 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Year  Quarter  Month  DayofMonth  DayOfWeek  FlightDate UniqueCarrier  \\\n",
       "468304  2017        2      4          25          2  2017-04-25            WN   \n",
       "468309  2017        2      4          25          2  2017-04-25            WN   \n",
       "\n",
       "        AirlineID Carrier TailNum      ...       Div4TailNum  Div5Airport  \\\n",
       "468304      19393      WN  N7738A      ...               NaN          NaN   \n",
       "468309      19393      WN  N8696E      ...               NaN          NaN   \n",
       "\n",
       "        Div5AirportID  Div5AirportSeqID Div5WheelsOn Div5TotalGTime  \\\n",
       "468304            NaN               NaN          NaN            NaN   \n",
       "468309            NaN               NaN          NaN            NaN   \n",
       "\n",
       "       Div5LongestGTime  Div5WheelsOff Div5TailNum  Unnamed: 109  \n",
       "468304              NaN            NaN         NaN           NaN  \n",
       "468309              NaN            NaN         NaN           NaN  \n",
       "\n",
       "[2 rows x 110 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail(2)#Showing bottom 2 rows as sampled data is ordered by time with latest data at the bottom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Sparsity: \n",
    "Columns with >80% missing values are worth not pursuing for analysis and cannot be imputed sensibly as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = data.iloc[:,0:56]#Removing sparse columns based on the information given in DOT website\n",
    "print('Dimension reduced to:')\n",
    "len(data.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "56\n",
      "Sparsity per variable:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Year                    0.0\n",
       "Quarter                 0.0\n",
       "Month                   0.0\n",
       "DayofMonth              0.0\n",
       "DayOfWeek               0.0\n",
       "FlightDate              0.0\n",
       "UniqueCarrier           0.0\n",
       "AirlineID               0.0\n",
       "Carrier                 0.0\n",
       "TailNum                 0.0\n",
       "FlightNum               0.0\n",
       "OriginAirportID         0.0\n",
       "OriginAirportSeqID      0.0\n",
       "OriginCityMarketID      0.0\n",
       "Origin                  0.0\n",
       "OriginCityName          0.0\n",
       "OriginState             0.0\n",
       "OriginStateFips         0.0\n",
       "OriginStateName         0.0\n",
       "OriginWac               0.0\n",
       "DestAirportID           0.0\n",
       "DestAirportSeqID        0.0\n",
       "DestCityMarketID        0.0\n",
       "Dest                    0.0\n",
       "DestCityName            0.0\n",
       "DestState               0.0\n",
       "DestStateFips           0.0\n",
       "DestStateName           0.0\n",
       "DestWac                 0.0\n",
       "CRSDepTime              0.0\n",
       "DepTime                 0.0\n",
       "DepDelay                0.0\n",
       "DepDelayMinutes         0.0\n",
       "DepDel15                0.0\n",
       "DepartureDelayGroups    0.0\n",
       "DepTimeBlk              0.0\n",
       "TaxiOut                 0.0\n",
       "WheelsOff               0.0\n",
       "WheelsOn                0.0\n",
       "TaxiIn                  0.0\n",
       "CRSArrTime              0.0\n",
       "ArrTime                 0.0\n",
       "ArrDelay                0.0\n",
       "ArrDelayMinutes         0.0\n",
       "ArrDel15                0.0\n",
       "ArrivalDelayGroups      0.0\n",
       "ArrTimeBlk              0.0\n",
       "Cancelled               0.0\n",
       "CancellationCode        1.0\n",
       "Diverted                0.0\n",
       "CRSElapsedTime          0.0\n",
       "ActualElapsedTime       0.0\n",
       "AirTime                 0.0\n",
       "Flights                 0.0\n",
       "Distance                0.0\n",
       "DistanceGroup           0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Dimension reduced to:')\n",
    "print(len(data.columns))\n",
    "print('Sparsity per variable:')\n",
    "((len(data.index) - data.count())/len(data.index))#Sparsity per variable retained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.drop(['DepDelay','DepDel15','ArrDelay','DepDelayMinutes','ArrDelayMinutes'],\n",
    "          axis=1, inplace=True)#To be excluded as per the task\n",
    "data.drop(['CancellationCode'], axis=1, inplace=True)#Removed due to 100% sparsity as seen in above cell\n",
    "data[\"FlightDate\"] = data[\"FlightDate\"].apply(lambda x: int(''.join(x.split(\"-\"))))#Formatting date for convinience"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Datatype of variables:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Year                      int64\n",
       "Quarter                   int64\n",
       "Month                     int64\n",
       "DayofMonth                int64\n",
       "DayOfWeek                 int64\n",
       "FlightDate                int64\n",
       "UniqueCarrier            object\n",
       "AirlineID                 int64\n",
       "Carrier                  object\n",
       "TailNum                  object\n",
       "FlightNum                 int64\n",
       "OriginAirportID           int64\n",
       "OriginAirportSeqID        int64\n",
       "OriginCityMarketID        int64\n",
       "Origin                   object\n",
       "OriginCityName           object\n",
       "OriginState              object\n",
       "OriginStateFips           int64\n",
       "OriginStateName          object\n",
       "OriginWac                 int64\n",
       "DestAirportID             int64\n",
       "DestAirportSeqID          int64\n",
       "DestCityMarketID          int64\n",
       "Dest                     object\n",
       "DestCityName             object\n",
       "DestState                object\n",
       "DestStateFips             int64\n",
       "DestStateName            object\n",
       "DestWac                   int64\n",
       "CRSDepTime                int64\n",
       "DepTime                 float64\n",
       "DepartureDelayGroups    float64\n",
       "DepTimeBlk               object\n",
       "TaxiOut                 float64\n",
       "WheelsOff               float64\n",
       "WheelsOn                float64\n",
       "TaxiIn                  float64\n",
       "CRSArrTime                int64\n",
       "ArrTime                 float64\n",
       "ArrDel15                float64\n",
       "ArrivalDelayGroups      float64\n",
       "ArrTimeBlk               object\n",
       "Cancelled               float64\n",
       "Diverted                float64\n",
       "CRSElapsedTime          float64\n",
       "ActualElapsedTime       float64\n",
       "AirTime                 float64\n",
       "Flights                 float64\n",
       "Distance                float64\n",
       "DistanceGroup             int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Datatype of variables:')\n",
    "data.dtypes#Checking variable data type as numeric type is most easy to deal with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploratory Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24700d8f080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qEUJVvX8b9T8OnA2cmGRfmlkYTwKeCqyeNPNjVOe1cbwxyZnA/wAf\nq6obO7QlqWcmFZJGNcqjh9pSr6oqyVOBNwDPAY6kWefij6tq9XSfm6m8qr6Z5LU0vSRPoult3RfY\nMGobkuZOqvy3JkmSxueYCkmS1AuTCkmS1AuTCkmS1AuTCkmS1AuTCkmS1AuTCkmS1AuTCkmS1AuT\nCkmS1AuTCkmS1AuTCkmS1AuTCkmS1AuTCkmS1Iv/DydWhWzjKXupAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x247080868d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rQYOVVJiZmdkI46TCzMzMSuGkwszMzErRkkmFpAmSbpQ0W9Itkl42jFrSJpJelNQu6fbs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\nMzMzK4WTCjMzMyuFkwozMzMrxf8H7XP+vsSpFXQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470b985e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AysCHgbUjYrkqy5DOhWlmZmbdrujlj22AkyLi150MxszMzMqraEvF32g8qqaZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470b9e2e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wUWFmZmaFaHqgpqQNgHWBByLimeabZGZmZkVo95wnuYsKSbsD3wPekC16D3CtpDHAVcDR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\nH6PPYpk+5Q4pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470bad4978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FxZHAO4F/AgeRbnO+naQfAPeSBm4eW0gLzczMrBRyFRURMRnYlHSK4zhSEfFN4AhSUbFZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470b9b4cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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E/Kb1EM2WPB5iMLMlUa6kQtIewBXA7cDFwEn9+yKiT9ITwOGAkwqzGjzEYGZLorw9FV8D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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d55b5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QQkWFpC2Bq0nX+Gh0emkALirMzMy6RNFTSs8gXSd1D2CliFiszm1QeWmamZnZ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\nAAupAAAWAQv1z5UCGSpcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d65bf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vgFV7qHMcEPfee28Utc8++xTet16OPXhi33vvvdko+3sDosqyTw/r0v5FPsuO7diO7dhF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\n4OQwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d6b8400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Proportion of late flights per category based on all other flights\n",
    "\n",
    "avgLate = np.sum(data['ArrDel15'])/len(data['ArrDel15'])\n",
    "attributes = ['Month','DayOfWeek', 'DayofMonth', 'DepTimeBlk','ArrTimeBlk','UniqueCarrier',\n",
    "             'ArrivalDelayGroups','DepartureDelayGroups']\n",
    "for i,pred in enumerate(attributes):\n",
    "    plt.figure(i, figsize=(15, 5))\n",
    "    group = data.groupby([pred], as_index=False).aggregate(np.mean)[[pred, 'ArrDel15']]\n",
    "    group.sort_values(by=pred, inplace=True)    \n",
    "    group.plot.bar(x=pred, y='ArrDel15')\n",
    "    plt.axhline(y=avgLate, label='Average')\n",
    "    plt.ylabel('Percent of Flights that Arrive Late')\n",
    "    plt.title(pred)\n",
    "    plt.legend().remove()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Exploratory analysis reveals:\n",
    "\n",
    "    (1) Delay changes substantially with Month e.g. lower delays in Autumn months   \n",
    "    (2) Not much variation within week and day of month    \n",
    "    (3) Higher delays for flights with departure and arrival time blocks from 3pm until midnight   \n",
    "        (a) There seems to be a lag in the pattern for arrival time block   \n",
    "        (b) Pattern starts with departure time block around 2pm and lasts until midnight    \n",
    "        (c) Pattern starts with arrival time block around 4pm and lasts until 1am (with a lag of 1-2hrs)   \n",
    "    (5)Similar pattern is observed for arrival and departure delay groups    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Label encoding:\n",
    "Conversion of categorical values to numericals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "le = LabelEncoder()\n",
    "\n",
    "data[\"Unique_Carrier\"] = le.fit_transform(data[\"UniqueCarrier\"])\n",
    "UniqueCarrier = list(le.classes_)\n",
    "data[\"Carrier_Name\"] = le.fit_transform(data[\"Carrier\"])\n",
    "Carrier = list(le.classes_)\n",
    "data[\"Tail_Number\"] = le.fit_transform(data[\"TailNum\"])\n",
    "TailNum = list(le.classes_)\n",
    "\n",
    "data[\"Origin_Point\"] = le.fit_transform(data[\"Origin\"])\n",
    "Origin = list(le.classes_)\n",
    "data[\"Origin_CityName\"] = le.fit_transform(data[\"OriginCityName\"])\n",
    "OriginCityName = list(le.classes_)\n",
    "data[\"Origin_State\"] = le.fit_transform(data[\"OriginState\"])\n",
    "OriginState = list(le.classes_)\n",
    "data[\"OriginState_Name\"] = le.fit_transform(data[\"OriginStateName\"])\n",
    "OriginStateName = list(le.classes_)\n",
    "\n",
    "data[\"Destination\"] = le.fit_transform(data[\"Dest\"])\n",
    "Dest = list(le.classes_)\n",
    "data[\"Dest_CityName\"] = le.fit_transform(data[\"DestCityName\"])\n",
    "DestCityName = list(le.classes_)\n",
    "data[\"Dest_State\"] = le.fit_transform(data[\"DestState\"])\n",
    "DestState = list(le.classes_)\n",
    "data[\"Dest_StateName\"] = le.fit_transform(data[\"DestStateName\"])\n",
    "DestStateName = list(le.classes_)\n",
    "\n",
    "data[\"DepTime_Blk\"] = le.fit_transform(data[\"DepTimeBlk\"])\n",
    "DepTimeBlk = list(le.classes_)\n",
    "data[\"ArrTime_Blk\"] = le.fit_transform(data[\"ArrTimeBlk\"])\n",
    "ArrTimeBlk = list(le.classes_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.drop(['UniqueCarrier','Carrier','TailNum',\n",
    "           'Origin','OriginCityName','OriginState','OriginStateName',\n",
    "          'Dest','DestCityName','DestState','DestStateName',\n",
    "          'DepTimeBlk','ArrTimeBlk'], axis=1, inplace=True)#Removing original encoded columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.drop(['DepartureDelayGroups','ArrivalDelayGroups'], axis=1, inplace=True)#Removing delay details as per the task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "48\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>FlightDate</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>FlightNum</th>\n",
       "      <th>OriginAirportID</th>\n",
       "      <th>OriginAirportSeqID</th>\n",
       "      <th>...</th>\n",
       "      <th>Origin_Point</th>\n",
       "      <th>Origin_CityName</th>\n",
       "      <th>Origin_State</th>\n",
       "      <th>OriginState_Name</th>\n",
       "      <th>Destination</th>\n",
       "      <th>Dest_CityName</th>\n",
       "      <th>Dest_State</th>\n",
       "      <th>Dest_StateName</th>\n",
       "      <th>DepTime_Blk</th>\n",
       "      <th>ArrTime_Blk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.016716e+03</td>\n",
       "      <td>1.849681e+00</td>\n",
       "      <td>4.556488e+00</td>\n",
       "      <td>1.585441e+01</td>\n",
       "      <td>3.983558e+00</td>\n",
       "      <td>2.016763e+07</td>\n",
       "      <td>1.988975e+04</td>\n",
       "      <td>2.125698e+03</td>\n",
       "      <td>1.270613e+04</td>\n",
       "      <td>1.270616e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.577828e+02</td>\n",
       "      <td>1.512563e+02</td>\n",
       "      <td>2.052470e+01</td>\n",
       "      <td>2.035186e+01</td>\n",
       "      <td>1.591979e+02</td>\n",
       "      <td>1.535284e+02</td>\n",
       "      <td>2.049524e+01</td>\n",
       "      <td>2.031854e+01</td>\n",
       "      <td>8.609646e+00</td>\n",
       "      <td>1.022948e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.511033e-01</td>\n",
       "      <td>9.402156e-01</td>\n",
       "      <td>2.779950e+00</td>\n",
       "      <td>8.767598e+00</td>\n",
       "      <td>1.979431e+00</td>\n",
       "      <td>4.289726e+03</td>\n",
       "      <td>3.929491e+02</td>\n",
       "      <td>1.730777e+03</td>\n",
       "      <td>1.523025e+03</td>\n",
       "      <td>1.523022e+05</td>\n",
       "      <td>...</td>\n",
       "      <td>8.572949e+01</td>\n",
       "      <td>8.880323e+01</td>\n",
       "      <td>1.534332e+01</td>\n",
       "      <td>1.531394e+01</td>\n",
       "      <td>8.573690e+01</td>\n",
       "      <td>8.861223e+01</td>\n",
       "      <td>1.537263e+01</td>\n",
       "      <td>1.534030e+01</td>\n",
       "      <td>4.784717e+00</td>\n",
       "      <td>4.969031e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>2.016050e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>1.013503e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>8.000000e+00</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>2.016122e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>7.280000e+02</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>1.129202e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>7.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>7.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>6.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.600000e+01</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>2.017031e+07</td>\n",
       "      <td>1.980500e+04</td>\n",
       "      <td>1.648000e+03</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>1.289204e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.700000e+02</td>\n",
       "      <td>1.650000e+02</td>\n",
       "      <td>1.700000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>1.700000e+02</td>\n",
       "      <td>1.740000e+02</td>\n",
       "      <td>1.700000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>9.000000e+00</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>2.300000e+01</td>\n",
       "      <td>6.000000e+00</td>\n",
       "      <td>2.017040e+07</td>\n",
       "      <td>2.030400e+04</td>\n",
       "      <td>3.035000e+03</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>1.405702e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>2.300000e+02</td>\n",
       "      <td>2.310000e+02</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>2.300000e+02</td>\n",
       "      <td>2.310000e+02</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>1.300000e+01</td>\n",
       "      <td>1.400000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.200000e+01</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.017043e+07</td>\n",
       "      <td>2.117100e+04</td>\n",
       "      <td>7.439000e+03</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>1.621801e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>3.130000e+02</td>\n",
       "      <td>3.090000e+02</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>3.130000e+02</td>\n",
       "      <td>3.090000e+02</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 48 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Year       Quarter         Month    DayofMonth     DayOfWeek  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06   \n",
       "mean   2.016716e+03  1.849681e+00  4.556488e+00  1.585441e+01  3.983558e+00   \n",
       "std    4.511033e-01  9.402156e-01  2.779950e+00  8.767598e+00  1.979431e+00   \n",
       "min    2.016000e+03  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "25%    2.016000e+03  1.000000e+00  3.000000e+00  8.000000e+00  2.000000e+00   \n",
       "50%    2.017000e+03  2.000000e+00  4.000000e+00  1.600000e+01  4.000000e+00   \n",
       "75%    2.017000e+03  2.000000e+00  5.000000e+00  2.300000e+01  6.000000e+00   \n",
       "max    2.017000e+03  4.000000e+00  1.200000e+01  3.100000e+01  7.000000e+00   \n",
       "\n",
       "         FlightDate     AirlineID     FlightNum  OriginAirportID  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06     1.589336e+06   \n",
       "mean   2.016763e+07  1.988975e+04  2.125698e+03     1.270613e+04   \n",
       "std    4.289726e+03  3.929491e+02  1.730777e+03     1.523025e+03   \n",
       "min    2.016050e+07  1.939300e+04  1.000000e+00     1.013500e+04   \n",
       "25%    2.016122e+07  1.939300e+04  7.280000e+02     1.129200e+04   \n",
       "50%    2.017031e+07  1.980500e+04  1.648000e+03     1.289200e+04   \n",
       "75%    2.017040e+07  2.030400e+04  3.035000e+03     1.405700e+04   \n",
       "max    2.017043e+07  2.117100e+04  7.439000e+03     1.621800e+04   \n",
       "\n",
       "       OriginAirportSeqID      ...       Origin_Point  Origin_CityName  \\\n",
       "count        1.589336e+06      ...       1.589336e+06     1.589336e+06   \n",
       "mean         1.270616e+06      ...       1.577828e+02     1.512563e+02   \n",
       "std          1.523022e+05      ...       8.572949e+01     8.880323e+01   \n",
       "min          1.013503e+06      ...       0.000000e+00     0.000000e+00   \n",
       "25%          1.129202e+06      ...       8.000000e+01     7.100000e+01   \n",
       "50%          1.289204e+06      ...       1.700000e+02     1.650000e+02   \n",
       "75%          1.405702e+06      ...       2.300000e+02     2.310000e+02   \n",
       "max          1.621801e+06      ...       3.130000e+02     3.090000e+02   \n",
       "\n",
       "       Origin_State  OriginState_Name   Destination  Dest_CityName  \\\n",
       "count  1.589336e+06      1.589336e+06  1.589336e+06   1.589336e+06   \n",
       "mean   2.052470e+01      2.035186e+01  1.591979e+02   1.535284e+02   \n",
       "std    1.534332e+01      1.531394e+01  8.573690e+01   8.861223e+01   \n",
       "min    0.000000e+00      0.000000e+00  0.000000e+00   0.000000e+00   \n",
       "25%    7.000000e+00      7.000000e+00  8.000000e+01   7.100000e+01   \n",
       "50%    1.700000e+01      1.800000e+01  1.700000e+02   1.740000e+02   \n",
       "75%    3.300000e+01      3.300000e+01  2.300000e+02   2.310000e+02   \n",
       "max    5.100000e+01      5.100000e+01  3.130000e+02   3.090000e+02   \n",
       "\n",
       "         Dest_State  Dest_StateName   DepTime_Blk   ArrTime_Blk  \n",
       "count  1.589336e+06    1.589336e+06  1.589336e+06  1.589336e+06  \n",
       "mean   2.049524e+01    2.031854e+01  8.609646e+00  1.022948e+01  \n",
       "std    1.537263e+01    1.534030e+01  4.784717e+00  4.969031e+00  \n",
       "min    0.000000e+00    0.000000e+00  0.000000e+00  0.000000e+00  \n",
       "25%    7.000000e+00    7.000000e+00  5.000000e+00  6.000000e+00  \n",
       "50%    1.700000e+01    1.800000e+01  9.000000e+00  1.100000e+01  \n",
       "75%    3.300000e+01    3.300000e+01  1.300000e+01  1.400000e+01  \n",
       "max    5.100000e+01    5.100000e+01  1.800000e+01  1.800000e+01  \n",
       "\n",
       "[8 rows x 48 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Dimension reduced to:')\n",
    "print(len(data.columns))\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All variables are now numeric. But above statistics makes sense only for originally numeric variables. For e.g. central tendency measures for Year, Airline ID etc. do not make much sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Forest is chosen for Machine Learning due to following reasons:\n",
    "(1) Large data size   \n",
    "(2) Categorical nature of many variables   \n",
    "(3) Non-linearity of dataset (LinearRegression was attempted but had high MSE; Linear relation doesn't exist for many variables)  \n",
    "(4) Underlying complex dependencies between variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PART 2: Model creation with original raw data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Selection to remove redundant variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Creation of data subset:\n",
    "Predictor and target variable columns along with some basic statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "47\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>FlightDate</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>FlightNum</th>\n",
       "      <th>OriginAirportID</th>\n",
       "      <th>OriginAirportSeqID</th>\n",
       "      <th>...</th>\n",
       "      <th>Origin_Point</th>\n",
       "      <th>Origin_CityName</th>\n",
       "      <th>Origin_State</th>\n",
       "      <th>OriginState_Name</th>\n",
       "      <th>Destination</th>\n",
       "      <th>Dest_CityName</th>\n",
       "      <th>Dest_State</th>\n",
       "      <th>Dest_StateName</th>\n",
       "      <th>DepTime_Blk</th>\n",
       "      <th>ArrTime_Blk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.016716e+03</td>\n",
       "      <td>1.849681e+00</td>\n",
       "      <td>4.556488e+00</td>\n",
       "      <td>1.585441e+01</td>\n",
       "      <td>3.983558e+00</td>\n",
       "      <td>2.016763e+07</td>\n",
       "      <td>1.988975e+04</td>\n",
       "      <td>2.125698e+03</td>\n",
       "      <td>1.270613e+04</td>\n",
       "      <td>1.270616e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.577828e+02</td>\n",
       "      <td>1.512563e+02</td>\n",
       "      <td>2.052470e+01</td>\n",
       "      <td>2.035186e+01</td>\n",
       "      <td>1.591979e+02</td>\n",
       "      <td>1.535284e+02</td>\n",
       "      <td>2.049524e+01</td>\n",
       "      <td>2.031854e+01</td>\n",
       "      <td>8.609646e+00</td>\n",
       "      <td>1.022948e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.511033e-01</td>\n",
       "      <td>9.402156e-01</td>\n",
       "      <td>2.779950e+00</td>\n",
       "      <td>8.767598e+00</td>\n",
       "      <td>1.979431e+00</td>\n",
       "      <td>4.289726e+03</td>\n",
       "      <td>3.929491e+02</td>\n",
       "      <td>1.730777e+03</td>\n",
       "      <td>1.523025e+03</td>\n",
       "      <td>1.523022e+05</td>\n",
       "      <td>...</td>\n",
       "      <td>8.572949e+01</td>\n",
       "      <td>8.880323e+01</td>\n",
       "      <td>1.534332e+01</td>\n",
       "      <td>1.531394e+01</td>\n",
       "      <td>8.573690e+01</td>\n",
       "      <td>8.861223e+01</td>\n",
       "      <td>1.537263e+01</td>\n",
       "      <td>1.534030e+01</td>\n",
       "      <td>4.784717e+00</td>\n",
       "      <td>4.969031e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>2.016050e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>1.013503e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>8.000000e+00</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>2.016122e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>7.280000e+02</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>1.129202e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>7.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>7.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>6.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.600000e+01</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>2.017031e+07</td>\n",
       "      <td>1.980500e+04</td>\n",
       "      <td>1.648000e+03</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>1.289204e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.700000e+02</td>\n",
       "      <td>1.650000e+02</td>\n",
       "      <td>1.700000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>1.700000e+02</td>\n",
       "      <td>1.740000e+02</td>\n",
       "      <td>1.700000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>9.000000e+00</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>2.300000e+01</td>\n",
       "      <td>6.000000e+00</td>\n",
       "      <td>2.017040e+07</td>\n",
       "      <td>2.030400e+04</td>\n",
       "      <td>3.035000e+03</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>1.405702e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>2.300000e+02</td>\n",
       "      <td>2.310000e+02</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>2.300000e+02</td>\n",
       "      <td>2.310000e+02</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>3.300000e+01</td>\n",
       "      <td>1.300000e+01</td>\n",
       "      <td>1.400000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.200000e+01</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.017043e+07</td>\n",
       "      <td>2.117100e+04</td>\n",
       "      <td>7.439000e+03</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>1.621801e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>3.130000e+02</td>\n",
       "      <td>3.090000e+02</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>3.130000e+02</td>\n",
       "      <td>3.090000e+02</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 48 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Year       Quarter         Month    DayofMonth     DayOfWeek  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06   \n",
       "mean   2.016716e+03  1.849681e+00  4.556488e+00  1.585441e+01  3.983558e+00   \n",
       "std    4.511033e-01  9.402156e-01  2.779950e+00  8.767598e+00  1.979431e+00   \n",
       "min    2.016000e+03  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "25%    2.016000e+03  1.000000e+00  3.000000e+00  8.000000e+00  2.000000e+00   \n",
       "50%    2.017000e+03  2.000000e+00  4.000000e+00  1.600000e+01  4.000000e+00   \n",
       "75%    2.017000e+03  2.000000e+00  5.000000e+00  2.300000e+01  6.000000e+00   \n",
       "max    2.017000e+03  4.000000e+00  1.200000e+01  3.100000e+01  7.000000e+00   \n",
       "\n",
       "         FlightDate     AirlineID     FlightNum  OriginAirportID  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06     1.589336e+06   \n",
       "mean   2.016763e+07  1.988975e+04  2.125698e+03     1.270613e+04   \n",
       "std    4.289726e+03  3.929491e+02  1.730777e+03     1.523025e+03   \n",
       "min    2.016050e+07  1.939300e+04  1.000000e+00     1.013500e+04   \n",
       "25%    2.016122e+07  1.939300e+04  7.280000e+02     1.129200e+04   \n",
       "50%    2.017031e+07  1.980500e+04  1.648000e+03     1.289200e+04   \n",
       "75%    2.017040e+07  2.030400e+04  3.035000e+03     1.405700e+04   \n",
       "max    2.017043e+07  2.117100e+04  7.439000e+03     1.621800e+04   \n",
       "\n",
       "       OriginAirportSeqID      ...       Origin_Point  Origin_CityName  \\\n",
       "count        1.589336e+06      ...       1.589336e+06     1.589336e+06   \n",
       "mean         1.270616e+06      ...       1.577828e+02     1.512563e+02   \n",
       "std          1.523022e+05      ...       8.572949e+01     8.880323e+01   \n",
       "min          1.013503e+06      ...       0.000000e+00     0.000000e+00   \n",
       "25%          1.129202e+06      ...       8.000000e+01     7.100000e+01   \n",
       "50%          1.289204e+06      ...       1.700000e+02     1.650000e+02   \n",
       "75%          1.405702e+06      ...       2.300000e+02     2.310000e+02   \n",
       "max          1.621801e+06      ...       3.130000e+02     3.090000e+02   \n",
       "\n",
       "       Origin_State  OriginState_Name   Destination  Dest_CityName  \\\n",
       "count  1.589336e+06      1.589336e+06  1.589336e+06   1.589336e+06   \n",
       "mean   2.052470e+01      2.035186e+01  1.591979e+02   1.535284e+02   \n",
       "std    1.534332e+01      1.531394e+01  8.573690e+01   8.861223e+01   \n",
       "min    0.000000e+00      0.000000e+00  0.000000e+00   0.000000e+00   \n",
       "25%    7.000000e+00      7.000000e+00  8.000000e+01   7.100000e+01   \n",
       "50%    1.700000e+01      1.800000e+01  1.700000e+02   1.740000e+02   \n",
       "75%    3.300000e+01      3.300000e+01  2.300000e+02   2.310000e+02   \n",
       "max    5.100000e+01      5.100000e+01  3.130000e+02   3.090000e+02   \n",
       "\n",
       "         Dest_State  Dest_StateName   DepTime_Blk   ArrTime_Blk  \n",
       "count  1.589336e+06    1.589336e+06  1.589336e+06  1.589336e+06  \n",
       "mean   2.049524e+01    2.031854e+01  8.609646e+00  1.022948e+01  \n",
       "std    1.537263e+01    1.534030e+01  4.784717e+00  4.969031e+00  \n",
       "min    0.000000e+00    0.000000e+00  0.000000e+00  0.000000e+00  \n",
       "25%    7.000000e+00    7.000000e+00  5.000000e+00  6.000000e+00  \n",
       "50%    1.700000e+01    1.800000e+01  9.000000e+00  1.100000e+01  \n",
       "75%    3.300000e+01    3.300000e+01  1.300000e+01  1.400000e+01  \n",
       "max    5.100000e+01    5.100000e+01  1.800000e+01  1.800000e+01  \n",
       "\n",
       "[8 rows x 48 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Data set up as predictors and target\n",
    "rfDataOriginal = pd.DataFrame(data)\n",
    "Delay_YesNo = rfDataOriginal['ArrDel15']\n",
    "rfDataOriginal.drop(['ArrDel15'], axis=1, inplace=True)#Removing target variable\n",
    "print('Dimension reduced to:')\n",
    "print(len(rfDataOriginal.columns))\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Check for multi-collinearity of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EXYZ6wQPzv8SSKRO6pJ/OCqeE3wVjldP9wZstCPxuQQBH2InJ9N3Du9wyc5nu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\naqKgKyIiUhMFXRERkZoo6IqIiNTk/wMY1bMH7HvvgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d775278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(rfDataOriginal.corr())\n",
    "plt.title('Correlation matrix for MULTI-COLLINEAR data')\n",
    "corr = rfDataOriginal.corr()\n",
    "#corr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Darker cells indicate high collinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Year', 'FlightDate'),\n",
       " ('Quarter', 'Month'),\n",
       " ('OriginAirportID', 'OriginAirportSeqID'),\n",
       " ('OriginAirportID', 'Origin_Point'),\n",
       " ('OriginAirportSeqID', 'Origin_Point'),\n",
       " ('OriginStateFips', 'Origin_State'),\n",
       " ('OriginStateFips', 'OriginState_Name'),\n",
       " ('DestAirportID', 'DestAirportSeqID'),\n",
       " ('DestAirportID', 'Destination'),\n",
       " ('DestAirportSeqID', 'Destination'),\n",
       " ('DestStateFips', 'Dest_State'),\n",
       " ('DestStateFips', 'Dest_StateName'),\n",
       " ('CRSDepTime', 'DepTime'),\n",
       " ('CRSDepTime', 'WheelsOff'),\n",
       " ('CRSDepTime', 'DepTime_Blk'),\n",
       " ('DepTime', 'WheelsOff'),\n",
       " ('DepTime', 'DepTime_Blk'),\n",
       " ('WheelsOff', 'DepTime_Blk'),\n",
       " ('WheelsOn', 'ArrTime'),\n",
       " ('CRSArrTime', 'ArrTime_Blk'),\n",
       " ('CRSElapsedTime', 'ActualElapsedTime'),\n",
       " ('CRSElapsedTime', 'AirTime'),\n",
       " ('CRSElapsedTime', 'Distance'),\n",
       " ('CRSElapsedTime', 'DistanceGroup'),\n",
       " ('ActualElapsedTime', 'AirTime'),\n",
       " ('ActualElapsedTime', 'Distance'),\n",
       " ('ActualElapsedTime', 'DistanceGroup'),\n",
       " ('AirTime', 'Distance'),\n",
       " ('AirTime', 'DistanceGroup'),\n",
       " ('Distance', 'DistanceGroup'),\n",
       " ('Unique_Carrier', 'Carrier_Name'),\n",
       " ('Origin_State', 'OriginState_Name'),\n",
       " ('Dest_State', 'Dest_StateName')]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr = rfDataOriginal.corr()#Lists all pairs of highly collinear variables\n",
    "indices = np.where(corr > 0.8)\n",
    "indices = [(corr.columns[x], corr.columns[y]) for x, y in zip(*indices)\n",
    "                                        if x != y and x < y]\n",
    "indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Removal of only redundant columns\n",
    "Note: Collinearity is not the main consideration here(Part 3 deals with it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Subsetting to remove redundant variables using results from above cell for quick filtering\n",
    "rfDataOriginal.drop(['OriginAirportSeqID','OriginCityMarketID', 'OriginStateFips', 'OriginWac', \n",
    "                     'DestAirportSeqID', 'DestCityMarketID', 'DestStateFips', 'DestWac',\n",
    "                     'CRSDepTime', 'CRSElapsedTime', 'CRSArrTime','Carrier_Name', \n",
    "                     'Origin_Point', 'Origin_CityName', 'Origin_State', 'OriginState_Name', \n",
    "                     'Destination', 'Dest_CityName', 'Dest_State', 'Dest_StateName'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension finally reduced to:\n",
      "27\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['Year',\n",
       " 'Quarter',\n",
       " 'Month',\n",
       " 'DayofMonth',\n",
       " 'DayOfWeek',\n",
       " 'FlightDate',\n",
       " 'AirlineID',\n",
       " 'FlightNum',\n",
       " 'OriginAirportID',\n",
       " 'DestAirportID',\n",
       " 'DepTime',\n",
       " 'TaxiOut',\n",
       " 'WheelsOff',\n",
       " 'WheelsOn',\n",
       " 'TaxiIn',\n",
       " 'ArrTime',\n",
       " 'Cancelled',\n",
       " 'Diverted',\n",
       " 'ActualElapsedTime',\n",
       " 'AirTime',\n",
       " 'Flights',\n",
       " 'Distance',\n",
       " 'DistanceGroup',\n",
       " 'Unique_Carrier',\n",
       " 'Tail_Number',\n",
       " 'DepTime_Blk',\n",
       " 'ArrTime_Blk']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Dimension finally reduced to:')\n",
    "print(len(rfDataOriginal.columns))\n",
    "list(rfDataOriginal.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model building with non-redundant variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Train/test split\n",
    "- Train:Test split = 80:20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(rfDataOriginal, Delay_YesNo, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Grid search\n",
    "Grid search is not performed for all the desired parameter combinations and values due to computational time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random forest Grid Search with non-redundant variables took [ 1:20:38.521561 ] seconds.\n"
     ]
    }
   ],
   "source": [
    "startTimeGS = datetime.now()\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "rf = RandomForestClassifier()\n",
    "param_grid = {\n",
    "                 'n_estimators': [10, 25],\n",
    "#                 'min_samples_split': [2, 4],\n",
    "#                 'min_samples_leaf': [2, 4],\n",
    "#                 'max_features': ['sqrt', 'log2'],\n",
    "                 \"criterion\" : [\"gini\", \"entropy\"]\n",
    "             }\n",
    "grid_rf = GridSearchCV(rf, param_grid, cv=10)\n",
    "grid_rf.fit(X_train, Y_train)\n",
    "bestModel = grid_rf.best_estimator_\n",
    "bestParameters = grid_rf.best_params_\n",
    "gridScores = grid_rf.grid_scores_\n",
    "print('Random forest Grid Search with non-redundant variables took [', datetime.now() - startTimeGS, '] seconds.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Best model, corresponding parameters and CV results\n",
    "Used for model selection in next step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='entropy',\n",
      "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
      "            min_impurity_split=1e-07, min_samples_leaf=1,\n",
      "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
      "            n_estimators=25, n_jobs=1, oob_score=False, random_state=None,\n",
      "            verbose=0, warm_start=False)\n",
      "{'n_estimators': 25, 'criterion': 'entropy'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[mean: 0.95709, std: 0.00073, params: {'n_estimators': 10, 'criterion': 'gini'},\n",
       " mean: 0.96161, std: 0.00075, params: {'n_estimators': 25, 'criterion': 'gini'},\n",
       " mean: 0.95691, std: 0.00101, params: {'n_estimators': 10, 'criterion': 'entropy'},\n",
       " mean: 0.96202, std: 0.00054, params: {'n_estimators': 25, 'criterion': 'entropy'}]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(bestModel)\n",
    "print(bestParameters)\n",
    "gridScores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Model selection\n",
    "- Best model and parameters from above are used to train the final model on entire training set\n",
    "- 10-fold Cross validation is performed to find the overall error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean cross validation score is: 0.962069041124\n",
      "Random forest training and testing with with non-redundant variables took [ 0:31:59.416214 ] seconds.\n"
     ]
    }
   ],
   "source": [
    "startTimeRF = datetime.now()\n",
    "rf = RandomForestClassifier(n_estimators = bestParameters.get('n_estimators'), \n",
    "#                            min_samples_split=bestParameters.get('min_samples_split'),\n",
    "#                           min_samples_leaf = bestParameters.get('min_samples_leaf'),\n",
    "#                           max_features = bestParameters.get('max_features'),\n",
    "                           criterion = bestParameters.get('criterion'))\n",
    "cv = cross_validation.KFold(len(X_train), n_folds=10, shuffle=True, random_state=2)\n",
    "cvScores = cross_val_score(rf, X_train, Y_train, cv=cv)\n",
    "print ('Mean cross validation score is: ' + str(np.mean(cvScores)))\n",
    "rf.fit(X_train, Y_train)\n",
    "print('Random forest training and testing with with non-redundant variables took [', \n",
    "      datetime.now() - startTimeRF, '] seconds.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Performance evaluation\n",
    "- Prediction is done on the hold out test set to evaluate performance\n",
    "- Confusion matrix, Accuracy and Recall are computed\n",
    "- ROC curve is also plotted to pictorically depict 'Area under curve (AUC)' as 'Accuracy' "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 96.27%\n",
      "Recall: 94.0%\n",
      "Confusion matrix:\n",
      "[[156043   2277]\n",
      " [  9573 149975]]\n",
      "Area under the ROC curve: 0.0371915079472\n"
     ]
    },
    {
     "data": {
      "image/png": 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OJx6S9gA+AbwaaOu2rxFxF6mfSPX0Y6uefxr4dDvbgJR4rDxl5XYXNzMzsxa1\ndDmtpN0k/SQbsOsaSf9TMe8NkuYAvwC2Bb7c4Vg7zjUeZmZm+Wq6xkPS64DLSbUYzwArAq+WtA4w\nFTiK1DH0Y6SOqAs6H25nOfEwMzPLVytNLZ8AHgPeGBG3SFoDOI+UcPQBRwLfioihzofZHYOlQSb3\nOfEwMzPLSytNLTOBUyPiFoCIeBz4FKm240sR8bXlKekAj+NhZmaWt1YSj5WB+6um3Zf9vakj0eRs\nqDTkphYzM7MctXqvlpE6zwc7EEvu3MfDzMwsX61eTrufpG0rnk8j3aztg5LeUFU2IuLoMUXXZU48\nzMzM8tVq4rFn9qj2zhrTgnSflnHLiYeZmVm+Wkk8pnUtioI48TAzM8tX04lHRDzXzUCK4MTDzMws\nXy01tUh6EXAIsAnwBPDjiLiiG4HlwYmHmZlZvloZufTFwO+B6RWTD5L0kYg4ueORdVlEMDQyxECf\nx/EwMzPLSyuX0x5H6jD6TmANYCfgb8DnJHXtLrfdMjwyDOAaDzMzsxy1knjsCJwSET+JiHkR8Qfg\nI8AM4MVdia6LBktp6BEnHmZmZvlpJfHYgFTDUek2QMCqHYsoJ048zMzM8tdK4tEHDFdNK7WxnnHB\niYeZmVn+Wu2b8TpJq1Q8X4HU7+Ot2RUvS4mIU8cSXDc58TAzM8tfq4nHgdmj2odrTAvAiYeZmZk9\nr5XEY6uuRVEAJx5mZmb5ayXxmAHcExHzuhVMnsqJx0C/x/EwMzPLSyudQm8Equ9Au9waGhkCXONh\nZmaWp1YSD3UtigK4qcXMzCx/y91lsJ3ixMPMzCx/rSYe0ZUoCuDEw8zMLH+tXk77fUnfbbJsRMQK\nrQaUFyceZmZm+Ws18bgB+Hs3AsmbEw8zM7P8tZp4fCcizu1KJDlz4mFmZpa/nu9cOtDncTzMzMzy\n0rOJx1ApjePhAcTMzMzy07OJx2BpkEl9k+hTz+4CMzOz3LXSx2MaMNitQPI2WBp0/w4zM7OcNXW6\nL2kW0BcRLY3jIWl6tuy448TDzMwsf822MxwKPCDpa5J2alRQySslfRN4ADhkrEF2gxMPMzOz/DXb\n1LI1cBDwMeAISc8CtwD3AU+S7uOyKrAJsC2pWeZu4BPA9zsbcmc48TAzM8tfU4lHRJSA7wLflbQz\n8DZgZ9LdalfNij0J3AGcAlwSETd0PtzOceJhZmaWv1YHECMibgRu7EIsuRosDXoMDzMzs5z17LWk\nQyNDrvHYqnTWAAAgAElEQVQwMzPLWc8mHm5qMTMzy58TDzMzM8uNEw8zMzPLjRMPMzMzy40TDzMz\nM8tNy5fTVpK0JvBKYC3gZxHxL0kiDSC2qNUh1vM0WBpk6qSpRYdhZmbWU9qu8ZD0BeBB4ELgVOBF\n2axVgH8DHxpzdF00WBpkoN/jeJiZmeWprcRD0kdJw6GfCryZNGQ6ABHxJHARsG8nAuwWj+NhZmaW\nv3abWg4FzomIj0pavcb8W4E92g+r+wZLg0zuc+JhZmaWp3abWl4AXNdg/jPAjDbXnQt3LjUzM8tf\nu4nHv4H1G8zfFvhnm+vOhRMPMzOz/LWbeFwCHCppw+oZknYD3kfqdDpuOfEwMzPLX7uJxzHAPFJf\njjOAAI6Q9CvgGuAO4ISORNglTjzMzMzy11biERHzgJcDpwAvJiUebwI2Bk4Edo2IZzsUY1c48TAz\nM8tf2wOIZYnFZ7IHkjSeBwyr5nE8zMzM8tfuOB6XS9q9clpl0iFpN0mXjzG2rhoqeRwPMzOzvLXb\nx+MNwHoN5q8LvL7NdSNpM0nXS7pT0u8lbVWn3IaSLpV0h6TbJB3e7Dbc1GJmZpa/sdwkrlGzyibA\ngjGs+3TgtIjYktRn5Ow65S4GzoqIF0XES4ALmt2AEw8zM7P8Nd3HQ9L+wP4Vkz4u6T01iq4C7AD8\nsp2AshvPzQReBxARF0o6WdKmEXFvRbn/BBZHxEXlaRHxWDPbKI2UKEXJiYeZmVnOWulcuhqwefZ/\nAOsAK1aVCVJNxw9Il9y2Y0Pg4YgYqZj2ALARcG/FtK2BxyXNBrYE7gOOjIj7RtvA0MgQgBMPMzOz\nnDWdeETEt4BvAUh6GDgsIi7uVmBNmAS8BnhFRNwh6RBSU8uO9RaYNWsWM2bMYHhkGO6Gk649if4P\n9rPffvvlFbOZmdm4NXv2bGbPnr3UtPnz53d0GxpvV8BmTS13A6uVaz2yRGfXqqaWfYAPR8Tu2fPp\nwNPAlIgoVa1ze2DOnDlz2H777Xl84eOs+ZU1ufhdF/O2F70tnxdmZma2HJo7dy4zZ84EmBkRc8e6\nvrF0LgVA0mRJa0haq/rRzvqyfhpzgfdk698XeLAy6cj8AthAUvnqmj2B26uTjloGS4MADPR5HA8z\nM7M8tT2AmKT/Bj4KbAWoTrH+Nld/KHCWpE8B84GDsm0eDzwUEWdExEJJhwI/l0RW7r+aWflQyX08\nzMzMitBW4iHpfcB3gGtJN4M7BjgZGAIOAB4iXRLbloi4C9ilxvRjq57/Ctiu1fWXazyceJiZmeWr\n3aaWWcDVEfEfpIQD4KcR8THS1SarAlM6EF9XOPEwMzMrRruJx2bAT7P/h7K/kwEi4gnSHWs/PLbQ\nuseJh5mZWTHaTTyeLi8bEfOBRcAGFfOfAtYfW2jd48TDzMysGO0mHn8FXlrx/A/AB8tXtwAHA/eM\nNbhuceJhZmZWjHavapkNHCZpSkQ8BxwHXAU8ms0vAe8Ye3jd4cTDzMysGG0lHhFxJnBmxfPfSHoZ\n8FZS0nFFRNzWmRA77/lxPPo9joeZmVmeWk48JE0F3gvcFhE3lKdHxB3AHR2MrWt8rxYzM7NitNzH\nIyIWA98EXtz5cPLhphYzM7NijKVz6YadDCRPTjzMzMyK0W7icQypc+krOxlMXpx4mJmZFaPdq1oO\nBB4HfiPpduA+0lgelSIi3jWW4LplsDSIEP1q91YyZmZm1o52E4/dgAD+DayePapFu0F122BpkMn9\nk8luLmdmZmY5afdy2nU6HUieyomHmZmZ5avdPh7LtcHSoMfwMDMzK0BPJh5DpSHXeJiZmRWgJxMP\nN7WYmZkVw4mHmZmZ5caJh5mZmeXGiYeZmZnlpt1xPACQtCbwSmAt4GcR8S+lwTGmAYsiYlyO5eHE\nw8zMrBht13hI+gLwIHAhcCrwomzWKqSBxT405ui6ZHDEiYeZmVkR2ko8JH0U+AQp4Xgz8PwQoBHx\nJHARsG8nAuyGwdIgA30ex8PMzCxv7Ta1HAqcExEflVRruPRbgT3aD6u7PI6HmZlZMdptankBcF2D\n+c8AM9pcd9e5j4eZmVkx2k08/g2s32D+tsA/21x31znxMDMzK0a7icclwKGSNqyeIWk34H2kTqfj\nkhMPMzOzYrSbeBwDzCP15TgDCOAISb8CrgHuAE7oSIRd4MTDzMysGG0lHhExD3g5cArwYlLi8SZg\nY+BEYNeIeLZDMXacEw8zM7NitD2AWJZYfCZ7IEnjdcCwak48zMzMitHuOB7vk7RK5bTlJekAGBoZ\n8jgeZmZmBWi3j8d3gEck/UzS/pJW6mRQ3eYaDzMzs2K0m3hsB3yNNEz6D4FHJV0o6R2SpnUsui5x\n4mFmZlaMdjuX3hIRn4qIzVnSyXR74Hzg35LOk/T2DsbZUU48zMzMitH2TeLKIuJPEXFURGwC7Ayc\nCbwR+PFY190tTjzMzMyKMebEo0zSFqT7s+wBrASUOrXuTnPiYWZmVoy2L6cFkLQp8K7s8VJghDSA\n2NdId6gdl5x4mJmZFaOtxEPSUcA7Sf06AvgtcBhwYUQ83rnwOi8inHiYmZkVpN0ajy8BNwJHAD+O\niEc6F1J3lSK1AA30exwPMzOzvLWbeLwgIsbt3WcbGSwNArjGw8zMrADtXk67XCYd4MTDzMysSE3V\neEi6nNSXY6+IKGXPRxMRseeYousCJx5mZmbFabapZTVS4qGq58sdJx5mZmbFaSrxiIidGj1fnjjx\nMDMzK067d6d9uaTVGsxfVdLL2w+re5x4mJmZFafdkUtvBN7QYP4eWZlxx4mHmZlZcdpNPDTK/CmM\n0yHTh0pDAAz0eRwPMzOzvDU9joek9YANKiZtWqc5ZRXgYODBMcbWFa7xMDMzK04rA4h9ADiWdDVL\nAMdnj2rK5h8+5ui6wImHmZlZcVpJPC4C7iElFj8Avg3cUFUmgAXAzRHxQEci7DAnHmZmZsVpOvGI\niL8AfwGQtAJwdUTc063AusWJh5mZWXHauldLRJze6UDy4sTDzMysOM0OmX4qqRnlwxExkj0fTUTE\nuOvn4cTDzMysOM3WeOwNjABHZH/3ZvQh08dlB1MnHmZmZsVpdsj0dRo97zRJmwFnA2sATwEHRcTt\nDcqfBbwXWCUinm607qGRbByPfo/jYWZmlrd2BxDrttOB0yJiS+BEUhJSk6S3A4M0edO6wdIg/eqn\nT+P1pZuZmU1c7d6rZZqkNaumrSXpU5KOl/SydgPK1jsTOAcgIi4ENpS0aY2yawOfBGYx+miqQEo8\n3MxiZmZWjLauagHOBF4E7AAgaUXgJmDjbP5RkvaIiN+1se4NgYcjYqRi2gPARsC9VWXPAI6KiAVS\nU3mHEw8zM7MCtdvesBtwacXzA4AXAP8BrAncDnx2bKE1Jun9wD8i4jetLOfEw8zMrDjt1nisydL3\nYtkLuD4irgWQdDbwmTbX/SCwrqS+ilqPjUi1HpVeA7xK0ptZ0sxyq6S3RsQttVY8a9YsHhl+hGee\neoa9frsXAPvttx/77bdfm6GamZlNHLNnz2b27NlLTZs/f35Ht6GIpvpkLr2Q9Ajw9Yj4sqQpwBPA\nlyLihGz+IcDXImKFtoKSrgHOjoizJe0LfDwiat2QrnKZEWBGRDxTY972wJw5c+bwkyd/wnm3nce9\nH6lutTEzM7Nqc+fOZebMmQAzI2LuWNfXbo3HTcBhkm4F3ghMY+mml82Bh8cQ16HAWZI+BcwHDgKQ\ndDzwUEScUWOZoIkOpm5qMTMzK067iccngF8CP8+enxIRtwJI6gPeAfyq3aAi4i5glxrTj22wTH8z\n6x4qDXkMDzMzs4K0e6+WOyRtDrwMeCoi7qyYvSLwcWBOB+LrONd4mJmZFafdGg8iYjHw+xrTnwbO\nH0tQ3eTEw8zMrDhtJx5KA2e8E9iTdCktwD+Ay4AfRzu9VnMwOOLEw8zMrChtJR7ZgGGXA7sCi0kJ\nB6QRR/cHDpe0Z0Q825EoO8g1HmZmZsVpdwCxE0idP48CVo+IrSNia2B14EhSQvL5zoTYWU48zMzM\nitNu4rEv6SZuX8v6egAQEc9FxNdJN3l7RycC7DQnHmZmZsVpN/FYA/hbg/l/zcqMO048zMzMitNu\n4nEf8KYG89+UlRl3hkpDDPR5HA8zM7MitJt4nAa8SdLFknaTtE72eLWki0ijmX67c2F2jms8zMzM\nitPuAGLfkLQu8DHSDeIqjQAnRsQ3xxpcNzjxMDMzK85YBhD7hKRvAq8n3T0W0mW1V0XEvzoRXDc4\n8TAzMytO24kHQJZgfL9DseTCiYeZmVlxxpR4SHotqSPpxtmk+4HLI6LtG8R1mxMPMzOz4rQ7culK\nwI+B15FuRf9YNuttwEck/QrYNyKe6UiUHeTEw8zMrDjtXtVyEinpOBZYLSLWjoi1gdWA44DXZmXG\nHSceZmZmxWk38diHNHLpCRHxVHliRDwVEZ8HzsjKjDtDIx7Hw8zMrCjtJh4jpNFJ67kNKLW57q5y\njYeZmVlx2k08Lgb2lrTM8tm0vbMy444TDzMzs+K0e1XLGdnjN5JOA+7Jpm8OHAqsCHxK0taVC0VE\no/u7dN1IjDA8MuzEw8zMrCDtJh43Vvy/S9U8ZX9vqLFcf5vb64jh0jCAEw8zM7OCtJt4HAZEJwPJ\nw9DIEODEw8zMrCjt3qvltE4HkoehkhMPMzOzIrXbuXS55BoPMzOzYvVU4jE8kvp4DPR7HA8zM7Mi\n9GTi4RoPMzOzYvRU4uGmFjMzs2L1VuLhzqVmZmaF6q3EwzUeZmZmhWo78ZC0rqSTJN0i6WFJr8ym\nry7pREnbdC7MznCNh5mZWbHaGsdD0hbA74CpwBzgJcBkgIh4QtLrgVWAD3Yozo5wjYeZmVmx2h25\n9ERgEbAtMAj8u2r+ZcC+Y4irK3xVi5mZWbHabWrZHTglIv5F7aHT7wfWb3PdXVO+V8tAn8fxMDMz\nK0K7icck4NkG81cHhtpcd9e4qcXMzKxY7SYetwB71JohqR94F/CHdoPqFncuNTMzK1a7iceXgL0k\nfR3YLJu2anZly8+BlwJf7kB8HeUaDzMzs2K1e3fan0n6IPA14P9lky/I/i4EPhAR13Qgvo4qJx6T\n+trtU2tmZmZj0fYROCK+I+nHwJtItR59wN+ByyNiXofi66jh0jCT+ycjqehQzMzMetKYTv0jYj4w\nu0OxdN3QyJCbWczMzArU7gBiazVTLiKqx/co1FDJiYeZmVmR2q3xeITa43dU629z/V0xHMMew8PM\nzKxA7SYeh7Fs4tEPbAzsDzwEfLf9sLrDNR5mZmbFaveqltPqzZN0AvB7xuGdb93Hw8zMrFgdTw4i\n4mlSbceRnV73WLnGw8zMrFjdqpUIYL0urbttwyPDTjzMzMwK1NGRtCRNBnYj1Xbc2sl1d4KbWszM\nzIrV7uW0i6h9VcsUQKSrXj40hri6wk0tZmZmxWq3xuMbLJt4BPAkafTSyyJicCyBdYNrPMzMzIrV\nbuJxDFCKiFIng+m24ZFhBvo9joeZmVlRWu5cKmkq6UZwR3U+nO5yjYeZmVmxWk48ImIx8Cgp+Viu\nuI+HmZlZsdq9nPZHwP6Slqv7y/tyWjMzs2K1mzjcBOwJ3CLpe8D9wKLqQhFxefuhdZ6bWszMzIrV\nbuJxYcX/X6maF6RLaoNxdpO4odIQk/uceJiZmRWl3cTjjR2NooqkzYCzgTWAp4CDIuL2qjIvAU4B\n1gSGgT8Ah0fEc/XW6xoPMzOzYjWdeEjaDbg9Ih6LiCu7GBPA6cBpEfFDSfuQkpCXV5VZTEo0bpMk\nYDZwNPC5eit151IzM7NitdK59NfA67oVSJmkNYGZwDkAEXEhsKGkTSvLRcQ9EXFb9n8AfwQ2brRu\nj+NhZmZWrFYSD3UtiqVtCDwcESMV0x4ANqq3gKQVgIOBnzZasWs8zMzMitWtu9PmRtIAcB5wRURc\n2qisL6c1MzMrVqudS2vdGK7THgTWldRXUeuxEanWYynZOCLnAw9FxKzRVvzUJU9x3h/P40+r/en5\nafvttx/77bdfZyI3MzNbjs2ePZvZs2cvNW3+/Pkd3YZS94gmCkojtJZ4RES0e/fba4CzI+JsSfsC\nH4+Il1eV6QcuAOZFxAdGWd/2wJzph0/n8/t/no/u/NF2wjIzM+s5c+fOZebMmQAzI2LuWNfXamLw\nK+CusW60CYcCZ0n6FDAfOAhA0vGk2o0zgHcBbwNulXQzKSm6PiI+XG+lvpzWzMysWK0mHmdHxLld\niaRCRNwF7FJj+rEV/58LtBSLO5eamZkVa7nvXNoqJx5mZmbF6bnEY6DP43iYmZkVpecSD9d4mJmZ\nFafpPh4RMSGSFCceZmZmxZkQyUQrnHiYmZkVx4mHmZmZ5caJh5mZmeXGiYeZmZnlxomHmZmZ5abn\nEo+Bfo/jYWZmVpSeSzxc42FmZlYcJx5mZmaWGyceZmZmlhsnHmZmZpYbJx5mZmaWGyceZmZmlpue\nSzwG+nw5rZmZWVF6KvGQRH9ff9FhmJmZ9ayeSjw8eJiZmVmxeivxcDOLmZlZoZx4mJmZWW56KvGY\n1D+p6BDMzMx6Wk8lHq7xMDMzK1ZvJR7uXGpmZlao3ko8XONhZmZWqJ5KPCb1uY+HmZlZkXoq8XCN\nh5mZWbF6K/FwHw8zM7NC9VTi4aYWMzOzYvVU4uGmFjMzs2L1VuLhphYzM7NC9Vbi4RoPMzOzQvVW\n4uEaDzMzs0L1VOLhzqVmZmbF6qnEw00tZmZmxeqpxMM1HmZmZsXqqcTDNR5mZmbF6q3Ew51LzczM\nCtVbiYdrPMzMzArVW4mHazzMzMwK1VOJhzuXmpmZFau3Eo9+Jx5mZmZF6qnEw308zMzMiuXEw8zM\nzHLTW4mHO5eamZkVqrcSD9d4mJmZFaq3Eg/XeJiZmRWqpxIPX05rZmZWrJ5KPNzUYmZmVqyeSjxc\n42FmZlasnko8XONhZmZWrN5KPNy51MzMrFC9lXi4xiNXs2fPLjqEnuN9nj/v8/x5ny/fxmXiIWkz\nSddLulPS7yVtVafcmyXdnpX7iaQVG63XNR758o9D/rzP8+d9nj/v8+XbuEw8gNOB0yJiS+BE4Ozq\nApJWAL4D7JWVexg4ptFK3bnUzMysWOMu8ZC0JjATOAcgIi4ENpS0aVXRNwJzI+Lu7PmpwH6N1u2m\nFjMzs2KNu8QD2BB4OCJGKqY9AGxUVW4j4B8Vz+8H1pFU9zW5qcXMzKxYvdL2MBXg3rvvZe70uUXH\n0jPmz5/P3Lne33nyPs+f93n+vM/zdfvtt5f/ndqJ9SkiOrGejsmaWu4GVivXekh6GNg1Iu6tKLcv\n8P6IeGP2fGvgioiorhlB0rvJmm7MzMysLftHxLljXcm4q/GIiMckzQXeA5ydJRgPViYdmSuAkyVt\nERF3Af8DnFdntVcC+5OaYxZ3J3IzM7MJaSqwMelYOmbjrsYDQNIWwFnA6sB84KCI+Juk44GHIuKM\nrNybga8A/cBtwIER8UwxUZuZmdloxmXiYWZmZhPTeLyqxczMzCYoJx5mZmaWmwmVeHRrqHWrr5l9\nLuklkn4j6W+SbpX0HUlTioh3Imj2c15R/ixJI5JWzivGiaaF35YNJV0q6Q5Jt0k6PO9YJ4oW9vnR\nkv4q6WZJN0jaMe9YJwpJ35B0X/Z7sU2DcmM6hk6oxIMuDbVuDY26z0lXEh0eEVsDLwNWBI7OL8QJ\np5l9DoCktwODgDtzjU2z+/xi4KyIeFFEvAS4IK8AJ6Bmfs9fRrqicYeI2A44BTg51ygnlh8Du5Ku\nAK2pE8fQCZN4dHOodaut2X0eEfdExG3Z/wH8kXRplrWohc85ktYGPgnMApRnnBNJs/tc0n8CiyPi\novK0iHgsz1gnihY+50EaFmKl7PkqwIN5xTnRRMTvIuJfNP69GPMxdMIkHnRxqHWrq9l9/rwsWz4Y\n+GmXY5uoWtnnZwBHRcSCXCKbuJrd51sDj0uaLWmupAslbZJblBNLU/s8Im4FTgLuk/QAcATw4dyi\n7E1jPob6YGu5kTRAGuTtioi4tOh4JjJJ7wf+ERG/KTqWHjIJeA1wfERsD1yFm1q6StLGwN7Aptmo\n1SfhfT7uTaTE40Fg3aqsayNSllzpAZau5t+EZTNra06z+xxJk4DzSQPAzcopvomo2X3+GuCtku6V\ndF827dasTdxa08pvy80RcUf2/IfAdpL6c4hxoml2n+8D3BoRj2bPvw/smv3eWHeM+Rg6YRKPrC21\nPNR6+V4u9YZa3y4bHRUaD7VuDTS7z7Mf3vOBJyLi0NwDnUCa3ecRcUBEvCAiNo2IcnX/SyPilnwj\nXv618NvyC2ADSetlz/cEbo+IUm7BThAt7PN7SYnGCtnztwB3RsRwbsH2njEfQyfUyKUeaj1/zezz\n7CZ9PwRuzRYL4PqIcFtsG5r9nFctUwJWjYincw12gmjht+W1pN8WsnKHR8RfCwh5udfCPv9fUnPL\nYmAB8OGIuLmYqJdvkk4jJcxrA08Az0TEFp0+hk6oxMPMzMzGtwnT1GJmZmbjnxMPMzMzy40TDzMz\nM8uNEw8zMzPLjRMPMzMzy40TDzMzM8uNEw8zMzPLjRMPsw6R9DtJVxUdR7dJOkHSUJNlD5Y0UjGa\np2UkfUrSX4qOo0zSHyWdUHQcNvE58bCeJenA7KBY6/GFNlbZK6PxBbDUfRkkfVrSW+qUXS73i6Rd\nJR0racUurHsGcCTwxYpp/Q0+jw9UlPt81bxnJd0m6fjKWCW9v6rckKQHJX1X0ro1wvoy8BFJq3f6\n9ZpV8o10rNcF8FnSrZ0r3ZZ/KMuNY4HPVU37DGlY/J9VTf8e8MOIGMwjsA57JXAMcCbwbIfX/QHS\nZ6/WnVSvAH5UNW1B1fMAPggsAlYE3kD6HO8OvLqq3KdIN12bCuwM/Dfp/iYvjYjKmquLgFNI995w\nzYd1jRMPM7giIuYWHcTyIrsLZVN3oox0T4ZxkXRImh4RC1tZpGvBwEHAT+vczOyOiDi3iXX8uOLe\nO2dI+inwFkkzI2JORblfRET5Pknfk/QU8FHSPTl+Wi4UESOSLgTeixMP6yI3tZiNIquyvlrSo5IW\nZdXaH2hy2Y9I+qukBZLmSfqDpHdUlVlf0lmSHpG0WNJfJB3YxLrLVfNfk/QeSXdm8f1B0i41ys+U\ndKWkpyU9I+mXknasKjMpq7K/O1vXY5Kuk/SaijLP9/EoxwBMBsr9OUYklW8mtVQfD0m/kHRnndfz\nR0k3VE07UNKfJC2U9ISkc5rpL5LFOCJpC0nnS3oS+HU272WSzpZ0b7a/H5Z0pqRVK5b/PFBubvtn\ntq5S5bbHENtmwNbAr0Yr26Jrsr+bNCwFvyUlVS+sMe+XwAslvbiTgZlVco2HGcyobteOiCcqnv4P\ncDNwCTAMvBU4XRIRcWa9lUr6H+DrwOzs7zRgG+AVwI+zMusAfyDVCnyTdEfINwHfl7RCRJzaRPz/\nCbw7W34IOBy4UtIOEXFntp1tgN8A80gH1BHgUOA3kl5ZUePzv6S+B6cBc4AZwI7AdmQHbir6bURE\nSdIBwPeB3wHfzcrcU102cz7wXUkvi4hbKvbVJsBM4CMV044lNXWcS2ruWCub/3JJ20VEo+aP8jYv\nAu4Ajq6Y93pgwyzWR4CXAIcAW5GaVyA1gWwGvBP4EPBUNn1eB2LbJYuvXi3b1Br9LJ5porlqs+zv\nEw1LLUlMnqwxbw4pKdkV8F11rTsiwg8/evIBHEg6AFc/SlXlptRY9pfA7VXTfgtcVfH8Z8DcUWI4\nC3gAmFE1/QLgcWCgwbL9WbzDwEsqpr+AdIvw86piWQBsWDFtPeAZ4JcV0/4CXDRKzJ8HBqumLQLO\nqFH2/UAJWC97PiOL7QtV5T6ZvY51s+ebZs8/VlXupaTk6sgmYhwBzqoxr9b7uX8W5ysqph1dGXvF\n9LHG9oVsvZPrvJ+l6s8j8O6q11YiJRCrZ+/3odl+faC83op9v1tWbn3gHcC/s/d97TrxDQEnFfGd\n9KM3Hq7xsF4XwGHA3XULRDxX/l/SysAAqfbgeEnTImJRnUWfAnbOzoBvrp4pScDbgR8Ak6rOcq8C\n9gG2Bf44ymv4bUQ83xk2Iv4h6WekDodImgS8ltQn4MGKcv+SdB5wYMXreAp4qaQXRsTfR9luyyJi\nvtIlx+8kdXoseyfwu4h4OHu+D+m9ubBqvzwM3Au8BvjqaJsj1dxUx1D5fk4hdc78PelMf/vs/0bG\nGtvqwOKoX4NxEfDtqmnVnZ0FVL4/AdwKHFi1XgHXVi37d+BdEfFone0/BaxRZ57ZmDnxMIM/RoPO\npZJeBRwPvByYXjErSGfw9RKPL5KuMpgj6W5SMnFORNyUzV8HWImU+BxeY/kgVeGP5p4a0+4C9pa0\nGqmJZ0o2rdrtpDPtDUjJ12dJB767lcaY+AXpqpROVrufD/wgawr6k6QtgZeR9kPZZllc99ZYPoCn\na0yv5b7qCVmycBwp2Vmzar0zmlhnJ2Jr1HH1wYi4psH88nbeCiwkNdP9MyLur1PuEFKsq5BqQXah\ncYdfsZxeAm3LByceZg1I2pzUrHIbMIt0WeIgsBfwYRp00I6Iv2UH1TeTah/2AQ6X9NmI+N+KZc9m\n2csny26pM70rIuJaSS8kHdT2IF32+TFJ74+IH3RoM5cAz5EO/H/K/g4DF1aU6cumvaHOOp5pclu1\nksILSf1JvkyqJVhAqsW6nOY63I81tieAKZKmVNa+tOG6WHJVSyN/iOyqFkmXADcA50raMiIW1yg/\ng9TMZ9YVTjzMGtuLdFDas7JqWtLrm1k40uWbFwAXSBogHXQ/K+lLpI6NC4C+Js5wG9m8xrQtSR0S\n52VNLc9l06ptReoH8M+KmJ8k9T05S9IKwPWkGoJGiUfTZ8gR8ayky0kJx8ezv9dGxGMVxf5OVqtQ\n50y+LVltx27AJyPiyxXTX1Qr1DqrGWtsd2R/N6n4PxeROgN/ipRMHwZ8rXK+pI1Ir+32POOy3uLL\naSgL6OgAAAMTSURBVM0aK2V/n/+uZJddvne0BbNmjudFGqzpjmxdAxFRAi4G3ilpqxrLN9vO/srs\nqpXychuTalmuyLY7TDrQ7C1pg4py6wLvIh30F9WJeQHpQDtllBgWkKrym3U+sKHSZckvBs6rmn8h\n6cB/bK2Fq+NswTLvZ2YWyyYa5UG7ql/XWGO7kdScscMo5boiIq4mXVEzK0tKK80kvbYbllnQrENc\n42G9brRBoq4kVclfLulMYGVS88PDjN7/4hqloa5vBB4lHWAPAy6pqOL+OOkM/A/Z+m8HViMdlF5F\n6gcymr8CV0n6FqkJ4LDs7/EVZT5N6vR4g6RTWdL238/Sl5reJemXpMsqnyRd+vtW0uXAjcwB9pB0\nBGnf/D0i/tSg/GWk/glfJV1FcXHlzIi4O7tk9XNZ08+lpNFDNyV1yP0W6fLhlkTEU9lYIZ+UNA34\nF6nJZCOW/SyULy39oqQfZ3H+dKyxZcvfQerwW6+JrVPqfb6/QrrM+72k0WXL9iDV5HjkXuueoi+r\n8cOPoh6ky2lLwPajlHsLqa/FQlJHziOAg6m61JJ0Oe2VFc8PIV1R8O9s2btI42SsULX+NYGTScO2\nLwYeIiU8B44SV/nyy68BB2TrX0i6KmOXGuW3I9WCPJ09rgJ2qCrzaeAmUj+EZ0l9W44iNQeVy3we\neK5quRdlr/XZbL+ckU1f6nLaqmVmZ/Mua/Aa9wauq4j5r8BJwKaj7JvyJacr15i3PqnWYl72Os8B\n1s3Kf7Kq7GdJ/XqGarzfbcWWLXtktv2Bimn92Tb+r93XVlWuvO+3qTGvj9Th9PaqaY8Anyn6u+nH\nxH4owp2XzZZHkvpZMubCR4uO5/+3d8c2CMVAEAX3OqAHWqIQIrogoAYapIMj+BFEBHB8SzMVOHxa\nWzKfq6pDtiusc3ff/32eJKmqU7b149iv723gq7zxABjW3Y8k12xXbXtxSXITHfyaxQMWZfEAVmTx\ngLW9/4UCsGsWDwBgjMUDABgjPACAMcIDABgjPACAMcIDABgjPACAMcIDABgjPACAMcIDABjzBP7o\n1WBmfcuFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d93cb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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n4L8Hkt4ErMrMnYDnAh+OiC1q2suBnTNzR+DJwJsj4lF1fnsA+wG7AI8G9oqI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470dd66b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y_rf_pred = rf.predict(X_test)\n",
    "\n",
    "labels = [0, 1]\n",
    "cm = confusion_matrix(Y_test, Y_rf_pred,labels)\n",
    "\n",
    "print('Accuracy: ' + str(np.round(100*float(cm[0][0]+cm[1][1])/float((cm[0][0]+cm[1][1] + cm[1][0] + cm[0][1])),2))+'%')\n",
    "print('Recall: ' + str(np.round(100*float((cm[1][1]))/float((cm[1][0]+cm[1][1])),2))+'%')\n",
    "print('Confusion matrix:')\n",
    "print(cm)\n",
    "\n",
    "fpr, tpr, _ = roc_curve(Y_test, Y_rf_pred)\n",
    "auc = np.trapz(fpr,tpr)\n",
    "print('Area under the ROC curve: ' + str(auc))\n",
    "\n",
    "fig = plt.figure(1)\n",
    "plt.plot(fpr,tpr,color='green')\n",
    "plt.xlabel('False positive rate (FPR)')\n",
    "plt.ylabel('True positive rate (TPR)')\n",
    "plt.title('Receiver operating characteristic (ROC)')\n",
    "\n",
    "fig = plt.figure(2)\n",
    "ax = fig.add_subplot(111)\n",
    "cax = ax.matshow(cm)\n",
    "plt.title('Confusion matrix for Random Forest classifier with original data')\n",
    "fig.colorbar(cax)\n",
    "ax.set_xticklabels([''] + labels)\n",
    "ax.set_yticklabels([''] + labels)\n",
    "plt.xlabel('Predicted')\n",
    "plt.ylabel('True')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inferences:\n",
    "- High accuracy was obtained when model was first created.\n",
    "- This prompted cross validation with 10-fold in order to be convinced that it wasnt a chance performance\n",
    "- Accuracy improved when more data was added. More data is always better than any sophisticated model!\n",
    "- Inferences from exploratory analysis was critical in doing feature selection and obtaining good performance\n",
    "- E.g. Certain features (DepTimeBlk, Month etc.) with substantial variation were added to improve performance\n",
    "- Handling of class imbalance improved Accuracy and Recall respectively by more than 10% and 15%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PART 3: Model creation with PCA components"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Engineering by removing multi-collinear variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Removal of redundant and highly collinear variables from dataset\n",
    "Highly collinear variables are removed before PCA as they amplify their correlation through the common underlying factor and distort PCA results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "28\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>FlightDate</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>FlightNum</th>\n",
       "      <th>OriginAirportID</th>\n",
       "      <th>DestAirportID</th>\n",
       "      <th>...</th>\n",
       "      <th>Diverted</th>\n",
       "      <th>ActualElapsedTime</th>\n",
       "      <th>AirTime</th>\n",
       "      <th>Flights</th>\n",
       "      <th>Distance</th>\n",
       "      <th>DistanceGroup</th>\n",
       "      <th>Unique_Carrier</th>\n",
       "      <th>Tail_Number</th>\n",
       "      <th>DepTime_Blk</th>\n",
       "      <th>ArrTime_Blk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.016716e+03</td>\n",
       "      <td>1.849681e+00</td>\n",
       "      <td>4.556488e+00</td>\n",
       "      <td>1.585441e+01</td>\n",
       "      <td>3.983558e+00</td>\n",
       "      <td>2.016763e+07</td>\n",
       "      <td>1.988975e+04</td>\n",
       "      <td>2.125698e+03</td>\n",
       "      <td>1.270613e+04</td>\n",
       "      <td>1.273135e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.465977e+02</td>\n",
       "      <td>1.203909e+02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.652024e+02</td>\n",
       "      <td>3.930325e+00</td>\n",
       "      <td>5.976681e+00</td>\n",
       "      <td>2.633907e+03</td>\n",
       "      <td>8.609646e+00</td>\n",
       "      <td>1.022948e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.511033e-01</td>\n",
       "      <td>9.402156e-01</td>\n",
       "      <td>2.779950e+00</td>\n",
       "      <td>8.767598e+00</td>\n",
       "      <td>1.979431e+00</td>\n",
       "      <td>4.289726e+03</td>\n",
       "      <td>3.929491e+02</td>\n",
       "      <td>1.730777e+03</td>\n",
       "      <td>1.523025e+03</td>\n",
       "      <td>1.523896e+03</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.901650e+01</td>\n",
       "      <td>7.595698e+01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.224418e+02</td>\n",
       "      <td>2.447818e+00</td>\n",
       "      <td>4.135267e+00</td>\n",
       "      <td>1.449892e+03</td>\n",
       "      <td>4.784717e+00</td>\n",
       "      <td>4.969031e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>2.016050e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.500000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>8.000000e+00</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>2.016122e+07</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>7.280000e+02</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.700000e+01</td>\n",
       "      <td>6.300000e+01</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.970000e+02</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>1.444000e+03</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>6.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.600000e+01</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>2.017031e+07</td>\n",
       "      <td>1.980500e+04</td>\n",
       "      <td>1.648000e+03</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.280000e+02</td>\n",
       "      <td>1.020000e+02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.960000e+02</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.621000e+03</td>\n",
       "      <td>9.000000e+00</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>2.300000e+01</td>\n",
       "      <td>6.000000e+00</td>\n",
       "      <td>2.017040e+07</td>\n",
       "      <td>2.030400e+04</td>\n",
       "      <td>3.035000e+03</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.810000e+02</td>\n",
       "      <td>1.520000e+02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.107000e+03</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>3.932000e+03</td>\n",
       "      <td>1.300000e+01</td>\n",
       "      <td>1.400000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.200000e+01</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.017043e+07</td>\n",
       "      <td>2.117100e+04</td>\n",
       "      <td>7.439000e+03</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.840000e+02</td>\n",
       "      <td>7.230000e+02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.983000e+03</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>5.057000e+03</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>1.800000e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Year       Quarter         Month    DayofMonth     DayOfWeek  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06   \n",
       "mean   2.016716e+03  1.849681e+00  4.556488e+00  1.585441e+01  3.983558e+00   \n",
       "std    4.511033e-01  9.402156e-01  2.779950e+00  8.767598e+00  1.979431e+00   \n",
       "min    2.016000e+03  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "25%    2.016000e+03  1.000000e+00  3.000000e+00  8.000000e+00  2.000000e+00   \n",
       "50%    2.017000e+03  2.000000e+00  4.000000e+00  1.600000e+01  4.000000e+00   \n",
       "75%    2.017000e+03  2.000000e+00  5.000000e+00  2.300000e+01  6.000000e+00   \n",
       "max    2.017000e+03  4.000000e+00  1.200000e+01  3.100000e+01  7.000000e+00   \n",
       "\n",
       "         FlightDate     AirlineID     FlightNum  OriginAirportID  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06     1.589336e+06   \n",
       "mean   2.016763e+07  1.988975e+04  2.125698e+03     1.270613e+04   \n",
       "std    4.289726e+03  3.929491e+02  1.730777e+03     1.523025e+03   \n",
       "min    2.016050e+07  1.939300e+04  1.000000e+00     1.013500e+04   \n",
       "25%    2.016122e+07  1.939300e+04  7.280000e+02     1.129200e+04   \n",
       "50%    2.017031e+07  1.980500e+04  1.648000e+03     1.289200e+04   \n",
       "75%    2.017040e+07  2.030400e+04  3.035000e+03     1.405700e+04   \n",
       "max    2.017043e+07  2.117100e+04  7.439000e+03     1.621800e+04   \n",
       "\n",
       "       DestAirportID      ...        Diverted  ActualElapsedTime  \\\n",
       "count   1.589336e+06      ...       1589336.0       1.589336e+06   \n",
       "mean    1.273135e+04      ...             0.0       1.465977e+02   \n",
       "std     1.523896e+03      ...             0.0       7.901650e+01   \n",
       "min     1.013500e+04      ...             0.0       1.500000e+01   \n",
       "25%     1.129200e+04      ...             0.0       8.700000e+01   \n",
       "50%     1.289200e+04      ...             0.0       1.280000e+02   \n",
       "75%     1.405700e+04      ...             0.0       1.810000e+02   \n",
       "max     1.621800e+04      ...             0.0       7.840000e+02   \n",
       "\n",
       "            AirTime    Flights      Distance  DistanceGroup  Unique_Carrier  \\\n",
       "count  1.589336e+06  1589336.0  1.589336e+06   1.589336e+06    1.589336e+06   \n",
       "mean   1.203909e+02        1.0  8.652024e+02   3.930325e+00    5.976681e+00   \n",
       "std    7.595698e+01        0.0  6.224418e+02   2.447818e+00    4.135267e+00   \n",
       "min    7.000000e+00        1.0  3.100000e+01   1.000000e+00    0.000000e+00   \n",
       "25%    6.300000e+01        1.0  3.970000e+02   2.000000e+00    3.000000e+00   \n",
       "50%    1.020000e+02        1.0  6.960000e+02   3.000000e+00    7.000000e+00   \n",
       "75%    1.520000e+02        1.0  1.107000e+03   5.000000e+00    1.100000e+01   \n",
       "max    7.230000e+02        1.0  4.983000e+03   1.100000e+01    1.100000e+01   \n",
       "\n",
       "        Tail_Number   DepTime_Blk   ArrTime_Blk  \n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06  \n",
       "mean   2.633907e+03  8.609646e+00  1.022948e+01  \n",
       "std    1.449892e+03  4.784717e+00  4.969031e+00  \n",
       "min    0.000000e+00  0.000000e+00  0.000000e+00  \n",
       "25%    1.444000e+03  5.000000e+00  6.000000e+00  \n",
       "50%    2.621000e+03  9.000000e+00  1.100000e+01  \n",
       "75%    3.932000e+03  1.300000e+01  1.400000e+01  \n",
       "max    5.057000e+03  1.800000e+01  1.800000e+01  \n",
       "\n",
       "[8 rows x 28 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfDataPCA = pd.DataFrame(data)\n",
    "#Subsetting based on earlier feature selection of variables (derived from correlation)\n",
    "rfDataPCA.drop(['OriginAirportSeqID','OriginCityMarketID', 'OriginStateFips', 'OriginWac', \n",
    "                     'DestAirportSeqID', 'DestCityMarketID', 'DestStateFips', 'DestWac',\n",
    "                     'CRSDepTime', 'CRSElapsedTime', 'CRSArrTime','Carrier_Name', \n",
    "                     'Origin_Point', 'Origin_CityName', 'Origin_State', 'OriginState_Name', \n",
    "                     'Destination', 'Dest_CityName', 'Dest_State', 'Dest_StateName'], axis=1, inplace=True)\n",
    "print('Dimension reduced to:')\n",
    "print(len(rfDataPCA.columns))\n",
    "list(rfDataPCA.columns)\n",
    "rfDataPCA.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Year', 'FlightDate'),\n",
       " ('Quarter', 'Month'),\n",
       " ('OriginAirportID', 'OriginAirportSeqID'),\n",
       " ('OriginAirportID', 'Origin_Point'),\n",
       " ('OriginAirportID', 'Origin_CityName'),\n",
       " ('OriginAirportSeqID', 'Origin_Point'),\n",
       " ('OriginAirportSeqID', 'Origin_CityName'),\n",
       " ('OriginStateFips', 'Origin_State'),\n",
       " ('OriginStateFips', 'OriginState_Name'),\n",
       " ('DestAirportID', 'DestAirportSeqID'),\n",
       " ('DestAirportID', 'Destination'),\n",
       " ('DestAirportID', 'Dest_CityName'),\n",
       " ('DestAirportSeqID', 'Destination'),\n",
       " ('DestAirportSeqID', 'Dest_CityName'),\n",
       " ('DestStateFips', 'Dest_State'),\n",
       " ('DestStateFips', 'Dest_StateName'),\n",
       " ('CRSDepTime', 'DepTime'),\n",
       " ('CRSDepTime', 'WheelsOff'),\n",
       " ('CRSDepTime', 'DepTime_Blk'),\n",
       " ('CRSDepTime', 'ArrTime_Blk'),\n",
       " ('DepTime', 'WheelsOff'),\n",
       " ('DepTime', 'DepTime_Blk'),\n",
       " ('DepTime', 'ArrTime_Blk'),\n",
       " ('WheelsOff', 'DepTime_Blk'),\n",
       " ('WheelsOff', 'ArrTime_Blk'),\n",
       " ('WheelsOn', 'CRSArrTime'),\n",
       " ('WheelsOn', 'ArrTime'),\n",
       " ('WheelsOn', 'ArrTime_Blk'),\n",
       " ('CRSArrTime', 'ArrTime'),\n",
       " ('CRSArrTime', 'ArrTime_Blk'),\n",
       " ('CRSElapsedTime', 'ActualElapsedTime'),\n",
       " ('CRSElapsedTime', 'AirTime'),\n",
       " ('CRSElapsedTime', 'Distance'),\n",
       " ('CRSElapsedTime', 'DistanceGroup'),\n",
       " ('ActualElapsedTime', 'AirTime'),\n",
       " ('ActualElapsedTime', 'Distance'),\n",
       " ('ActualElapsedTime', 'DistanceGroup'),\n",
       " ('AirTime', 'Distance'),\n",
       " ('AirTime', 'DistanceGroup'),\n",
       " ('Distance', 'DistanceGroup'),\n",
       " ('Unique_Carrier', 'Carrier_Name'),\n",
       " ('Origin_Point', 'Origin_CityName'),\n",
       " ('Origin_State', 'OriginState_Name'),\n",
       " ('Destination', 'Dest_CityName'),\n",
       " ('Dest_State', 'Dest_StateName'),\n",
       " ('DepTime_Blk', 'ArrTime_Blk')]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = np.where(corr > 0.7)\n",
    "indices = [(corr.columns[x], corr.columns[y]) for x, y in zip(*indices)\n",
    "                                        if x != y and x < y]\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rfDataPCA.drop(['FlightDate','DepTime','DepTime_Blk','ActualElapsedTime','AirTime','DistanceGroup','DepTime_Blk'], \n",
    "          axis=1, inplace=True)#Further reduction of multicollinearity for PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AiEDiBAAgAokTAIAIJE4AACKQOAEAiEDiBAAgAokTAIAIJE4AACKQOAEAiEDi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\nJE4AACKQOAEAiEDiBAAgwv8BhUasM0u10X8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d8d69e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Check for collinearity\n",
    "plt.matshow(rfDataPCA.corr())\n",
    "plt.title('Correlation matrix for NON-COLLINEAR data')\n",
    "corr = rfDataPCA.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Darker cells indicate high collinearity. It is seen here only between the variable and itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Quarter', 'Month'),\n",
       " ('WheelsOff', 'ArrTime_Blk'),\n",
       " ('WheelsOn', 'ArrTime'),\n",
       " ('WheelsOn', 'ArrTime_Blk')]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = np.where(corr > 0.7)\n",
    "indices = [(corr.columns[x], corr.columns[y]) for x, y in zip(*indices)\n",
    "                                        if x != y and x < y]\n",
    "indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Data ready for PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "22\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Quarter</th>\n",
       "      <th>Month</th>\n",
       "      <th>DayofMonth</th>\n",
       "      <th>DayOfWeek</th>\n",
       "      <th>AirlineID</th>\n",
       "      <th>FlightNum</th>\n",
       "      <th>OriginAirportID</th>\n",
       "      <th>DestAirportID</th>\n",
       "      <th>TaxiOut</th>\n",
       "      <th>...</th>\n",
       "      <th>TaxiIn</th>\n",
       "      <th>ArrTime</th>\n",
       "      <th>ArrDel15</th>\n",
       "      <th>Cancelled</th>\n",
       "      <th>Diverted</th>\n",
       "      <th>Flights</th>\n",
       "      <th>Distance</th>\n",
       "      <th>Unique_Carrier</th>\n",
       "      <th>Tail_Number</th>\n",
       "      <th>ArrTime_Blk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1589336.0</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "      <td>1.589336e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.016716e+03</td>\n",
       "      <td>1.849681e+00</td>\n",
       "      <td>4.556488e+00</td>\n",
       "      <td>1.585441e+01</td>\n",
       "      <td>3.983558e+00</td>\n",
       "      <td>1.988975e+04</td>\n",
       "      <td>2.125698e+03</td>\n",
       "      <td>1.270613e+04</td>\n",
       "      <td>1.273135e+04</td>\n",
       "      <td>1.813505e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>8.071743e+00</td>\n",
       "      <td>1.506145e+03</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.652024e+02</td>\n",
       "      <td>5.976681e+00</td>\n",
       "      <td>2.633907e+03</td>\n",
       "      <td>1.022948e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.511033e-01</td>\n",
       "      <td>9.402156e-01</td>\n",
       "      <td>2.779950e+00</td>\n",
       "      <td>8.767598e+00</td>\n",
       "      <td>1.979431e+00</td>\n",
       "      <td>3.929491e+02</td>\n",
       "      <td>1.730777e+03</td>\n",
       "      <td>1.523025e+03</td>\n",
       "      <td>1.523896e+03</td>\n",
       "      <td>1.191527e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>7.438466e+00</td>\n",
       "      <td>5.786371e+02</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.224418e+02</td>\n",
       "      <td>4.135267e+00</td>\n",
       "      <td>1.449892e+03</td>\n",
       "      <td>4.969031e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>1.013500e+04</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.016000e+03</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>8.000000e+00</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>1.939300e+04</td>\n",
       "      <td>7.280000e+02</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>1.129200e+04</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.120000e+03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.970000e+02</td>\n",
       "      <td>3.000000e+00</td>\n",
       "      <td>1.444000e+03</td>\n",
       "      <td>6.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.600000e+01</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.980500e+04</td>\n",
       "      <td>1.648000e+03</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>1.289200e+04</td>\n",
       "      <td>1.500000e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>6.000000e+00</td>\n",
       "      <td>1.603000e+03</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.960000e+02</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.621000e+03</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>2.000000e+00</td>\n",
       "      <td>5.000000e+00</td>\n",
       "      <td>2.300000e+01</td>\n",
       "      <td>6.000000e+00</td>\n",
       "      <td>2.030400e+04</td>\n",
       "      <td>3.035000e+03</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>1.405700e+04</td>\n",
       "      <td>2.100000e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>9.000000e+00</td>\n",
       "      <td>1.959000e+03</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.107000e+03</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>3.932000e+03</td>\n",
       "      <td>1.400000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.017000e+03</td>\n",
       "      <td>4.000000e+00</td>\n",
       "      <td>1.200000e+01</td>\n",
       "      <td>3.100000e+01</td>\n",
       "      <td>7.000000e+00</td>\n",
       "      <td>2.117100e+04</td>\n",
       "      <td>7.439000e+03</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>1.621800e+04</td>\n",
       "      <td>1.830000e+02</td>\n",
       "      <td>...</td>\n",
       "      <td>4.130000e+02</td>\n",
       "      <td>2.400000e+03</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.983000e+03</td>\n",
       "      <td>1.100000e+01</td>\n",
       "      <td>5.057000e+03</td>\n",
       "      <td>1.800000e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Year       Quarter         Month    DayofMonth     DayOfWeek  \\\n",
       "count  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06  1.589336e+06   \n",
       "mean   2.016716e+03  1.849681e+00  4.556488e+00  1.585441e+01  3.983558e+00   \n",
       "std    4.511033e-01  9.402156e-01  2.779950e+00  8.767598e+00  1.979431e+00   \n",
       "min    2.016000e+03  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "25%    2.016000e+03  1.000000e+00  3.000000e+00  8.000000e+00  2.000000e+00   \n",
       "50%    2.017000e+03  2.000000e+00  4.000000e+00  1.600000e+01  4.000000e+00   \n",
       "75%    2.017000e+03  2.000000e+00  5.000000e+00  2.300000e+01  6.000000e+00   \n",
       "max    2.017000e+03  4.000000e+00  1.200000e+01  3.100000e+01  7.000000e+00   \n",
       "\n",
       "          AirlineID     FlightNum  OriginAirportID  DestAirportID  \\\n",
       "count  1.589336e+06  1.589336e+06     1.589336e+06   1.589336e+06   \n",
       "mean   1.988975e+04  2.125698e+03     1.270613e+04   1.273135e+04   \n",
       "std    3.929491e+02  1.730777e+03     1.523025e+03   1.523896e+03   \n",
       "min    1.939300e+04  1.000000e+00     1.013500e+04   1.013500e+04   \n",
       "25%    1.939300e+04  7.280000e+02     1.129200e+04   1.129200e+04   \n",
       "50%    1.980500e+04  1.648000e+03     1.289200e+04   1.289200e+04   \n",
       "75%    2.030400e+04  3.035000e+03     1.405700e+04   1.405700e+04   \n",
       "max    2.117100e+04  7.439000e+03     1.621800e+04   1.621800e+04   \n",
       "\n",
       "            TaxiOut      ...             TaxiIn       ArrTime   ArrDel15  \\\n",
       "count  1.589336e+06      ...       1.589336e+06  1.589336e+06  1589336.0   \n",
       "mean   1.813505e+01      ...       8.071743e+00  1.506145e+03        0.5   \n",
       "std    1.191527e+01      ...       7.438466e+00  5.786371e+02        0.5   \n",
       "min    1.000000e+00      ...       1.000000e+00  1.000000e+00        0.0   \n",
       "25%    1.100000e+01      ...       4.000000e+00  1.120000e+03        0.0   \n",
       "50%    1.500000e+01      ...       6.000000e+00  1.603000e+03        0.5   \n",
       "75%    2.100000e+01      ...       9.000000e+00  1.959000e+03        1.0   \n",
       "max    1.830000e+02      ...       4.130000e+02  2.400000e+03        1.0   \n",
       "\n",
       "       Cancelled   Diverted    Flights      Distance  Unique_Carrier  \\\n",
       "count  1589336.0  1589336.0  1589336.0  1.589336e+06    1.589336e+06   \n",
       "mean         0.0        0.0        1.0  8.652024e+02    5.976681e+00   \n",
       "std          0.0        0.0        0.0  6.224418e+02    4.135267e+00   \n",
       "min          0.0        0.0        1.0  3.100000e+01    0.000000e+00   \n",
       "25%          0.0        0.0        1.0  3.970000e+02    3.000000e+00   \n",
       "50%          0.0        0.0        1.0  6.960000e+02    7.000000e+00   \n",
       "75%          0.0        0.0        1.0  1.107000e+03    1.100000e+01   \n",
       "max          0.0        0.0        1.0  4.983000e+03    1.100000e+01   \n",
       "\n",
       "        Tail_Number   ArrTime_Blk  \n",
       "count  1.589336e+06  1.589336e+06  \n",
       "mean   2.633907e+03  1.022948e+01  \n",
       "std    1.449892e+03  4.969031e+00  \n",
       "min    0.000000e+00  0.000000e+00  \n",
       "25%    1.444000e+03  6.000000e+00  \n",
       "50%    2.621000e+03  1.100000e+01  \n",
       "75%    3.932000e+03  1.400000e+01  \n",
       "max    5.057000e+03  1.800000e+01  \n",
       "\n",
       "[8 rows x 22 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Dimension reduced to:')\n",
    "print(len(rfDataPCA.columns))\n",
    "rfDataPCA.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimension reduction with PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA is done on three variants of the dataset to identify which one needs to be used for modeling:\n",
    "- PCA 1: Dataset with Multi-Collinear variables: Highly collinear variables have amplified contribution in PCA\n",
    "- PCA 2: Dataset with Redundant variables removed (i.e. repeated ID, dep time, arr time etc.)\n",
    "- PCA 3: Dataset without any Non-Collinear variables\n",
    "\n",
    "This was a last minute approach to demonstrate that my initial hypothesis was wrong. My initial thought was that PCA would be better with non-collinear variables and this would give better model performance.\n",
    "\n",
    "However, I saw better model performance (> 10% for accuracy and recall) with PCs derived from multi-collinear dataset. This was because the first two components could almost fully explain the variance in target variable. But in the second and third cases,around 8PCs were needed to fully explain the variance while the scree plot was giving an intuition of choosing 3 or 4 components.\n",
    "\n",
    "Due to limitation in training time, results are demonstrated only for model creation with PCs derived from multi-collinear data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### PCA 1: On HIGHLY MULTI-COLLINEAR data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  5.10437477e-01   4.88965331e-01   3.96674386e-04   6.56055689e-05\n",
      "   4.50305685e-05   2.62220344e-05   2.24592784e-05   2.01350522e-05]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 51.04,  99.94,  99.98,  99.99,  99.99,  99.99,  99.99,  99.99])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=8)\n",
    "data_reduced = pca.fit_transform(data)\n",
    "print(pca.explained_variance_ratio_)\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2470da36438>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bcUU47bTm2gMPlPVVJEmSJEmSJGmoMlSRVIuPfxze8pbm2vTpMHNmPf1IkiRJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470d92c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(20, 5))\n",
    "plt.plot(pca.explained_variance_, linewidth=3)\n",
    "plt.axis('tight')\n",
    "plt.title('Scree plot for PCA with COLLINEAR data')\n",
    "plt.xlabel('No. of principal components')\n",
    "plt.ylabel('Explained variance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Elbow is used to choose the number of principal components (Here, #PCs chosen = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### PCA 2: On PARTIALLY MULTI-COLLINEAR data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.61641751  0.10176803  0.0821394   0.07602882  0.06768832  0.02958812\n",
      "  0.01189005  0.00863503]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 61.64,  71.82,  80.03,  87.63,  94.4 ,  97.36,  98.55,  99.41])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=8)\n",
    "rfDataOriginal_reduced = pca.fit_transform(rfDataOriginal)\n",
    "print(pca.explained_variance_ratio_)\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2470d963a58>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SJEmSJEmSpJHBoko/OeQQGD++OfbNb8JvflNPPpIkSZIkSZIkqX9ZVOknY8aU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470dcabbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(20, 5))\n",
    "plt.plot(pca.explained_variance_, linewidth=3)\n",
    "plt.axis('tight')\n",
    "plt.title('Scree plot for PCA with FEATURE SELECTED data')\n",
    "plt.xlabel('No. of principal components')\n",
    "plt.ylabel('Explained variance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Elbow is used to choose the number of principal components (Here, #PCs chosen = 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### PCA 3: On LOW MULTI-COLLINEAR data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.27129582  0.21898846  0.20263852  0.18061511  0.06696999  0.03077711\n",
      "  0.01416097  0.01316053]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 27.13,  49.03,  69.29,  87.35,  94.05,  97.13,  98.55,  99.87])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=8)\n",
    "rfDataPCA_reduced = pca.fit_transform(rfDataPCA)\n",
    "print(pca.explained_variance_ratio_)\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2470d9f3278>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gEuDAlNLcou5MYIWIeAn4J/CNlNJbRd0VwAvAaPJonV+mlJ4DSCndA1wLPAs8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\n/w9NEM28uWYaZQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470dd8d1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(20, 5))\n",
    "plt.plot(pca.explained_variance_, linewidth=3)\n",
    "plt.axis('tight')\n",
    "plt.title('Scree plot for PCA with FEATURE RE-ENGINEERED data')\n",
    "plt.xlabel('No. of principal components')\n",
    "plt.ylabel('Explained variance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Elbow is used to choose the number of principal components (Here, #PCs chosen = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension reduced to:\n",
      "47\n",
      "[ 0.51043748  0.48896533]\n",
      "Cumulative explained variance:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 51.04,  99.94])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Delay_YesNo = data['ArrDel15']\n",
    "data.drop(['ArrDel15'], axis=1, inplace=True)#Removing target variable\n",
    "print('Dimension reduced to:')\n",
    "print(len(data.columns))\n",
    "data.describe()\n",
    "pca = PCA(n_components=2)\n",
    "data_reduced = pca.fit_transform(data)\n",
    "print(pca.explained_variance_ratio_)\n",
    "print('Cumulative explained variance:')\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model building with dimension reduced data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Train/test split\n",
    "Train:Test split = 80:20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(data, Delay_YesNo, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Grid search\n",
    "Grid search is not performed for all the desired parameter combinations and values due to computational time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random forest Grid Search with dimension reduced data took [ 1:42:32.520642 ] seconds.\n"
     ]
    }
   ],
   "source": [
    "startTimeGS = datetime.now()\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "rf = RandomForestClassifier()\n",
    "param_grid = {\n",
    "                 'n_estimators': [10, 25],\n",
    "#                 'min_samples_split': [2, 4],\n",
    "#                 'min_samples_leaf': [2, 4],\n",
    "#                 'max_features': [sqrt', 'log2'],\n",
    "                 \"criterion\" : [\"gini\", \"entropy\"]\n",
    "             }\n",
    "grid_rf = GridSearchCV(rf, param_grid, cv=10)\n",
    "grid_rf.fit(x_train, y_train)\n",
    "bestModel = grid_rf.best_estimator_\n",
    "bestParameters = grid_rf.best_params_\n",
    "gridScores = grid_rf.grid_scores_\n",
    "print('Random forest Grid Search with dimension reduced data took [', datetime.now() - startTimeGS, '] seconds.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
      "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
      "            min_impurity_split=1e-07, min_samples_leaf=1,\n",
      "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
      "            n_estimators=25, n_jobs=1, oob_score=False, random_state=None,\n",
      "            verbose=0, warm_start=False)\n",
      "{'n_estimators': 25, 'criterion': 'gini'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[mean: 0.96794, std: 0.00106, params: {'n_estimators': 10, 'criterion': 'gini'},\n",
       " mean: 0.97418, std: 0.00112, params: {'n_estimators': 25, 'criterion': 'gini'},\n",
       " mean: 0.96757, std: 0.00062, params: {'n_estimators': 10, 'criterion': 'entropy'},\n",
       " mean: 0.97369, std: 0.00087, params: {'n_estimators': 25, 'criterion': 'entropy'}]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(bestModel)\n",
    "print(bestParameters)\n",
    "gridScores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Model selection\n",
    "- Best model and parameters from above are used to train the final model on entire training set\n",
    "- 10- fold Cross validation is performed to find the overall error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean cross validation score is: 0.974501126167\n",
      "Random forest training and testing with PCs took [ 0:37:48.068291 ] seconds.\n"
     ]
    }
   ],
   "source": [
    "startTimeRF = datetime.now()\n",
    "rf = RandomForestClassifier(n_estimators = bestParameters.get('n_estimators'), \n",
    "#                            min_samples_split=bestParameters.get('min_samples_split'),\n",
    "#                           min_samples_leaf = bestParameters.get('min_samples_leaf'),\n",
    "#                           max_features = bestParameters.get('max_features'),\n",
    "                           criterion = bestParameters.get('criterion'))\n",
    "cv = cross_validation.KFold(len(x_train), n_folds=10, shuffle=True, random_state=2)\n",
    "cvScores = cross_val_score(rf, x_train, y_train, cv=cv)\n",
    "print ('Mean cross validation score is: ' + str(np.mean(cvScores)))\n",
    "rf.fit(x_train, y_train)\n",
    "print('Random forest training and testing with PCs took [', datetime.now() - startTimeRF, '] seconds.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Performance evaluation\n",
    "- Prediction is done on the hold out test set to evaluate performance\n",
    "- Confusion matrix, Accuracy and Recall are computed\n",
    "- ROC curve is also plotted to pictorically depict 'Area under curve (AUC)' as 'Accuracy' "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 97.5%\n",
      "Recall: 95.95%\n",
      "Confusion matrix:\n",
      "[[156839   1481]\n",
      " [  6455 153093]]\n",
      "Area under the ROC curve: 0.0249062579649\n"
     ]
    },
    {
     "data": {
      "image/png": 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diLhP2aPqM8D2Zbt95HX1F+BIMsgD+V3zQLJNZyvy+/Cj5Phb+zXsf6h7rV2d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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2470dd3ebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_rf_pred = rf.predict(x_test)\n",
    "\n",
    "labels = [0, 1]\n",
    "cm = confusion_matrix(y_test, y_rf_pred,labels)\n",
    "\n",
    "print('Accuracy: ' + str(np.round(100*float(cm[0][0]+cm[1][1])/float((cm[0][0]+cm[1][1] + cm[1][0] + cm[0][1])),2))+'%')\n",
    "print('Recall: ' + str(np.round(100*float((cm[1][1]))/float((cm[1][0]+cm[1][1])),2))+'%')\n",
    "print('Confusion matrix:')\n",
    "print(cm)\n",
    "\n",
    "fpr, tpr, _ = roc_curve(y_test, y_rf_pred)\n",
    "auc = np.trapz(fpr,tpr)\n",
    "print('Area under the ROC curve: ' + str(auc))\n",
    "\n",
    "fig = plt.figure(figsize=(20, 5))\n",
    "\n",
    "plt.subplot2grid((2, 2), (1, 0), colspan=1)\n",
    "#plt.subplot(1,2,1)\n",
    "plt.plot(fpr,tpr,color='green')\n",
    "plt.xlabel('False positive rate (FPR)')\n",
    "plt.ylabel('True positive rate (TPR)')\n",
    "plt.title('Receiver operating characteristic (ROC)')\n",
    "\n",
    "ax1 = plt.subplot2grid((2, 2), (1, 1))\n",
    "#ax = fig.add_subplot(122)\n",
    "cax = ax1.matshow(cm)\n",
    "plt.title('Confusion matrix for Random Forest classifier with PCs')\n",
    "fig.colorbar(cax)\n",
    "ax1.set_xticklabels([''] + labels)\n",
    "ax1.set_yticklabels([''] + labels)\n",
    "plt.xlabel('Predicted')\n",
    "plt.ylabel('True')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inferences:\n",
    "- Random forest on PCs always demonstrated slightly better performance, but this was marginal (1-2%).\n",
    "- It is inferred that dimension reduction with PCA is not really required for Random forest as it is already a modeling method that inherently handles variance in data through bagging, random splitting and voting.\n",
    "- It may however be a delightful approach if one wants to reduce dimension by avoiding the hassle of removing collinear variables. A PCA can capture all the variation easily and be fed straight to random forest thus enabling quicker modeling. \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Future Work:\n",
    "- As performance was observed to be improving with more data, it is strongly suggested to train on more data which is easily available from DOT website.\n",
    "- This will improve Recall and give better prediction for 'Delayed' flights which is the problem in hand.\n",
    "- It is also recommended that an initial coarser search followed by finer grid search can help in identifying optimal model parameters that can enable prediction with higher performance.\n",
    "- Sampling of data to avoid class imbalance resulted in discarding a lot of data. I am not much concerned about this due to availability of huge amounts of data in DOT website. But, this may need to be addressed elsewhere by exploring imputation. In this problem, regression imputation is suggested as mean and zero imputation did not provide good results.\n",
    "- Feature transformation could have been explored by deriving new features from existing data. Examples can be Airport delay, Airline delay etc from taxi duration, wheels on, wheels off etc. This would have provided much more intuitive analysis results.\n",
    "- Lastly and more importantly, grid search with more trees in Random Forest is essential and is highly likely to give improved results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "- Kaggle.com\n",
    "- stats.stackexchange.com\n",
    "- fivethirtyeight.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall execution took [ 4:17:09.190782 ] seconds.\n"
     ]
    }
   ],
   "source": [
    "print('Overall execution took [', datetime.now() - startTime, '] seconds.')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}