PCA_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set(style=\"white\", color_codes=True)\n",
    "sns.set_context(rc={\"font.family\":'sans',\"font.size\":24,\"axes.titlesize\":24,\"axes.labelsize\":24})  \n",
    "\n",
    "import warnings \n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>StoreID</th>\n",
       "      <th>Date</th>\n",
       "      <th>IsHoliday</th>\n",
       "      <th>IsOpen</th>\n",
       "      <th>HasPromotions</th>\n",
       "      <th>StoreType</th>\n",
       "      <th>AssortmentType</th>\n",
       "      <th>NearestCompetitor</th>\n",
       "      <th>Region</th>\n",
       "      <th>NumberOfCustomers</th>\n",
       "      <th>...</th>\n",
       "      <th>Mean_TemperatureC</th>\n",
       "      <th>Mean_VisibilityKm</th>\n",
       "      <th>Mean_Wind_SpeedKm_h</th>\n",
       "      <th>Min_Dew_PointC</th>\n",
       "      <th>Min_Humidity</th>\n",
       "      <th>Min_Sea_Level_PressurehPa</th>\n",
       "      <th>Min_TemperatureC</th>\n",
       "      <th>Min_VisibilitykM</th>\n",
       "      <th>Precipitationmm</th>\n",
       "      <th>WindDirDegrees</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1000</td>\n",
       "      <td>01/03/2016</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Hyper Market</td>\n",
       "      <td>General</td>\n",
       "      <td>326</td>\n",
       "      <td>7</td>\n",
       "      <td>495</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>11.0</td>\n",
       "      <td>16</td>\n",
       "      <td>-2</td>\n",
       "      <td>70</td>\n",
       "      <td>1029</td>\n",
       "      <td>1</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1000</td>\n",
       "      <td>02/03/2016</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Hyper Market</td>\n",
       "      <td>General</td>\n",
       "      <td>326</td>\n",
       "      <td>7</td>\n",
       "      <td>608</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>13.0</td>\n",
       "      <td>10</td>\n",
       "      <td>-2</td>\n",
       "      <td>58</td>\n",
       "      <td>1025</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1000</td>\n",
       "      <td>04/03/2016</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Hyper Market</td>\n",
       "      <td>General</td>\n",
       "      <td>326</td>\n",
       "      <td>7</td>\n",
       "      <td>665</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>11.0</td>\n",
       "      <td>10</td>\n",
       "      <td>-3</td>\n",
       "      <td>55</td>\n",
       "      <td>1023</td>\n",
       "      <td>2</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1000</td>\n",
       "      <td>05/03/2016</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Hyper Market</td>\n",
       "      <td>General</td>\n",
       "      <td>326</td>\n",
       "      <td>7</td>\n",
       "      <td>630</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>15.0</td>\n",
       "      <td>10</td>\n",
       "      <td>-6</td>\n",
       "      <td>25</td>\n",
       "      <td>1022</td>\n",
       "      <td>-1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1000</td>\n",
       "      <td>06/03/2016</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Hyper Market</td>\n",
       "      <td>General</td>\n",
       "      <td>326</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>12.0</td>\n",
       "      <td>5</td>\n",
       "      <td>-6</td>\n",
       "      <td>48</td>\n",
       "      <td>1022</td>\n",
       "      <td>-5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 36 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   StoreID        Date  IsHoliday  IsOpen  HasPromotions     StoreType  \\\n",
       "0     1000  01/03/2016          0       1              0  Hyper Market   \n",
       "1     1000  02/03/2016          0       1              0  Hyper Market   \n",
       "2     1000  04/03/2016          0       1              0  Hyper Market   \n",
       "3     1000  05/03/2016          0       1              0  Hyper Market   \n",
       "4     1000  06/03/2016          0       0              0  Hyper Market   \n",
       "\n",
       "  AssortmentType  NearestCompetitor  Region  NumberOfCustomers  \\\n",
       "0        General                326       7                495   \n",
       "1        General                326       7                608   \n",
       "2        General                326       7                665   \n",
       "3        General                326       7                630   \n",
       "4        General                326       7                  0   \n",
       "\n",
       "        ...        Mean_TemperatureC  Mean_VisibilityKm  Mean_Wind_SpeedKm_h  \\\n",
       "0       ...                        1               11.0                   16   \n",
       "1       ...                        3               13.0                   10   \n",
       "2       ...                        3               11.0                   10   \n",
       "3       ...                        3               15.0                   10   \n",
       "4       ...                        1               12.0                    5   \n",
       "\n",
       "   Min_Dew_PointC  Min_Humidity Min_Sea_Level_PressurehPa  Min_TemperatureC  \\\n",
       "0              -2            70                      1029                 1   \n",
       "1              -2            58                      1025                 1   \n",
       "2              -3            55                      1023                 2   \n",
       "3              -6            25                      1022                -1   \n",
       "4              -6            48                      1022                -5   \n",
       "\n",
       "   Min_VisibilitykM  Precipitationmm  WindDirDegrees  \n",
       "0               6.0              0.0              23  \n",
       "1              10.0              0.0              56  \n",
       "2               8.0              0.0              22  \n",
       "3              10.0              0.0             108  \n",
       "4               5.0              0.0              46  \n",
       "\n",
       "[5 rows x 36 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.read_csv('./dataset/train.csv')\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 523021 entries, 0 to 523020\n",
      "Data columns (total 36 columns):\n",
      "StoreID                       523021 non-null int64\n",
      "Date                          523021 non-null object\n",
      "IsHoliday                     523021 non-null int64\n",
      "IsOpen                        523021 non-null int64\n",
      "HasPromotions                 523021 non-null int64\n",
      "StoreType                     523021 non-null object\n",
      "AssortmentType                523021 non-null object\n",
      "NearestCompetitor             523021 non-null int64\n",
      "Region                        523021 non-null int64\n",
      "NumberOfCustomers             523021 non-null int64\n",
      "NumberOfSales                 523021 non-null int64\n",
      "Region_AreaKM2                523021 non-null int64\n",
      "Region_GDP                    523021 non-null int64\n",
      "Region_PopulationK            523021 non-null int64\n",
      "CloudCover                    481840 non-null float64\n",
      "Events                        398923 non-null object\n",
      "Max_Dew_PointC                523021 non-null int64\n",
      "Max_Gust_SpeedKm_h            113074 non-null float64\n",
      "Max_Humidity                  523021 non-null int64\n",
      "Max_Sea_Level_PressurehPa     523021 non-null int64\n",
      "Max_TemperatureC              523021 non-null int64\n",
      "Max_VisibilityKm              511683 non-null float64\n",
      "Max_Wind_SpeedKm_h            523021 non-null int64\n",
      "Mean_Dew_PointC               523021 non-null int64\n",
      "Mean_Humidity                 523021 non-null int64\n",
      "Mean_Sea_Level_PressurehPa    523021 non-null int64\n",
      "Mean_TemperatureC             523021 non-null int64\n",
      "Mean_VisibilityKm             511683 non-null float64\n",
      "Mean_Wind_SpeedKm_h           523021 non-null int64\n",
      "Min_Dew_PointC                523021 non-null int64\n",
      "Min_Humidity                  523021 non-null int64\n",
      "Min_Sea_Level_PressurehPa     523021 non-null int64\n",
      "Min_TemperatureC              523021 non-null int64\n",
      "Min_VisibilitykM              511683 non-null float64\n",
      "Precipitationmm               523021 non-null float64\n",
      "WindDirDegrees                523021 non-null int64\n",
      "dtypes: float64(6), int64(26), object(4)\n",
      "memory usage: 143.7+ MB\n"
     ]
    }
   ],
   "source": [
    "dataset.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This is PCA considering only Attributes 'IsHoliday','HasPromotions','NearestCompetitor','Region','Region_PopulationK',\n",
    "'Region_GDP','Region_AreaKM2' to analyze their impact by reducing the number of dimensions from 6 to 2 principal components. \n",
    " The attributes are firstly normalized then PCA is performed and plotted into a two-dimensional graph were the two \n",
    " principal components represent a combination of the 6 input attributes to produce the two main relevant directions. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th>0</th>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
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       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
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       "      <td>1.117597</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.665359</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522991</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522992</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522993</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522994</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522995</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522996</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522997</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522998</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>522999</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523000</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523001</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523002</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523003</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523004</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523005</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523006</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523007</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523008</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523009</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523010</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523011</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523012</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523013</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523014</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523015</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>1.268453</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523016</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523017</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523018</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523019</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>523020</th>\n",
       "      <td>-0.175008</td>\n",
       "      <td>-0.788362</td>\n",
       "      <td>-0.294314</td>\n",
       "      <td>0.383312</td>\n",
       "      <td>-0.387515</td>\n",
       "      <td>1.117597</td>\n",
       "      <td>-0.299569</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>523021 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               0         1         2         3         4         5         6\n",
       "0      -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "1      -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "2      -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "3      -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "4      -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "5      -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "6      -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "7      -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "8      -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "9      -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "10     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "11     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "12     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "13     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "14     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "15     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "16     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "17     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "18     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "19     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "20     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "21     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "22     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "23     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "24     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "25     -0.175008 -0.788362 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "26     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "27     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "28     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "29     -0.175008  1.268453 -0.665359  0.383312 -0.387515  1.117597 -0.299569\n",
       "...          ...       ...       ...       ...       ...       ...       ...\n",
       "522991 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522992 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522993 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522994 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522995 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522996 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522997 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522998 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "522999 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523000 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523001 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523002 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523003 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523004 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523005 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523006 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523007 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523008 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523009 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523010 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523011 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523012 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523013 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523014 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523015 -0.175008  1.268453 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523016 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523017 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523018 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523019 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "523020 -0.175008 -0.788362 -0.294314  0.383312 -0.387515  1.117597 -0.299569\n",
       "\n",
       "[523021 rows x 7 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "features = ['IsHoliday','HasPromotions','NearestCompetitor','Region','Region_PopulationK',\n",
    "            'Region_GDP','Region_AreaKM2']\n",
    "# Separating out the features\n",
    "x = dataset.loc[:, features].values\n",
    "# Separating out the target\n",
    "y = dataset.loc[:,['NumberOfSales']].values\n",
    "# Standardizing the features\n",
    "x = StandardScaler().fit_transform(x)\n",
    "df=pd.DataFrame(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "principalComponents = pca.fit_transform(x)\n",
    "principalDf = pd.DataFrame(data = principalComponents\n",
    "             , columns = ['principal component 1', 'principal component 2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "finalDf = pd.concat([principalDf, dataset[['NumberOfSales']]], axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph below represents the PCA with NumberOfSales as target variable, the 3-range domain allows to see how the number of sales are distributed along the two main directions considering their amount. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ea2e860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(principalComponents[:, 0], principalComponents[:, 1],\n",
    "            c=dataset.NumberOfSales, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('spectral', 3))\n",
    "plt.xlabel('component 1')\n",
    "plt.ylabel('component 2')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.29097148, 0.15710125])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This shows the variance of the two principal components, considering that the sum of them is arounf 0.44 \n",
    " we can conclude that the two principal components together contain the 44% of the information \n",
    " contained by the original 6 attributes, this suggests us that they cannot be merged in 2 components. \n",
    " This result was expectd because I used attributes that should be very relevant for the analysis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.29097148, 0.15710125, 0.14642615])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=3)\n",
    "principalComponents = pca.fit_transform(x)\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.29097148, 0.15710125, 0.14642615, 0.14339871])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=4)\n",
    "principalComponents = pca.fit_transform(x)\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}