Module 6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PROBLEM STATEMENT\n",
    "# 6.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plot,show\n",
    "from numpy import vstack, array\n",
    "from numpy.random import rand\n",
    "from scipy.cluster.vq import kmeans, vq\n",
    "import pandas as pd\n",
    "import pandas_datareader as dr\n",
    "from math import sqrt\n",
    "from sklearn.cluster import KMeans\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Asian_paint</th>\n",
       "      <th>Titan</th>\n",
       "      <th>Bajfinance</th>\n",
       "      <th>Gail</th>\n",
       "      <th>Hdfc</th>\n",
       "      <th>Hindalco</th>\n",
       "      <th>Hindunilvr</th>\n",
       "      <th>Ioc</th>\n",
       "      <th>Tcs</th>\n",
       "      <th>Infratel</th>\n",
       "      <th>...</th>\n",
       "      <th>Ashoka</th>\n",
       "      <th>BajajElec</th>\n",
       "      <th>Fortis</th>\n",
       "      <th>Idfc</th>\n",
       "      <th>Ircon</th>\n",
       "      <th>Itdc</th>\n",
       "      <th>Pvr</th>\n",
       "      <th>Rcom</th>\n",
       "      <th>Suzlon</th>\n",
       "      <th>Luxind</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-05-15</th>\n",
       "      <td>1148.05</td>\n",
       "      <td>483.65</td>\n",
       "      <td>1332.95</td>\n",
       "      <td>414.00</td>\n",
       "      <td>1559.50</td>\n",
       "      <td>198.45</td>\n",
       "      <td>983.25</td>\n",
       "      <td>442.10</td>\n",
       "      <td>2365.10</td>\n",
       "      <td>371.05</td>\n",
       "      <td>...</td>\n",
       "      <td>216.05</td>\n",
       "      <td>341.15</td>\n",
       "      <td>205.25</td>\n",
       "      <td>63.70</td>\n",
       "      <td>415.3</td>\n",
       "      <td>650.15</td>\n",
       "      <td>1524.95</td>\n",
       "      <td>32.00</td>\n",
       "      <td>19.60</td>\n",
       "      <td>819.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-16</th>\n",
       "      <td>1142.85</td>\n",
       "      <td>488.30</td>\n",
       "      <td>1347.75</td>\n",
       "      <td>411.40</td>\n",
       "      <td>205.00</td>\n",
       "      <td>196.50</td>\n",
       "      <td>1000.40</td>\n",
       "      <td>446.60</td>\n",
       "      <td>2429.15</td>\n",
       "      <td>376.55</td>\n",
       "      <td>...</td>\n",
       "      <td>214.90</td>\n",
       "      <td>347.00</td>\n",
       "      <td>207.90</td>\n",
       "      <td>64.25</td>\n",
       "      <td>427.0</td>\n",
       "      <td>636.70</td>\n",
       "      <td>1539.00</td>\n",
       "      <td>32.10</td>\n",
       "      <td>19.70</td>\n",
       "      <td>817.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-17</th>\n",
       "      <td>1154.95</td>\n",
       "      <td>481.75</td>\n",
       "      <td>1324.80</td>\n",
       "      <td>408.30</td>\n",
       "      <td>1566.55</td>\n",
       "      <td>198.85</td>\n",
       "      <td>1009.40</td>\n",
       "      <td>444.25</td>\n",
       "      <td>2455.35</td>\n",
       "      <td>389.90</td>\n",
       "      <td>...</td>\n",
       "      <td>217.00</td>\n",
       "      <td>349.85</td>\n",
       "      <td>205.90</td>\n",
       "      <td>63.35</td>\n",
       "      <td>421.4</td>\n",
       "      <td>626.75</td>\n",
       "      <td>1530.30</td>\n",
       "      <td>31.95</td>\n",
       "      <td>19.90</td>\n",
       "      <td>819.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-18</th>\n",
       "      <td>1151.35</td>\n",
       "      <td>471.65</td>\n",
       "      <td>1314.55</td>\n",
       "      <td>404.75</td>\n",
       "      <td>1552.50</td>\n",
       "      <td>194.00</td>\n",
       "      <td>990.25</td>\n",
       "      <td>439.90</td>\n",
       "      <td>2536.20</td>\n",
       "      <td>378.90</td>\n",
       "      <td>...</td>\n",
       "      <td>209.65</td>\n",
       "      <td>334.10</td>\n",
       "      <td>196.85</td>\n",
       "      <td>61.50</td>\n",
       "      <td>407.1</td>\n",
       "      <td>604.65</td>\n",
       "      <td>1515.05</td>\n",
       "      <td>31.05</td>\n",
       "      <td>20.00</td>\n",
       "      <td>820.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-19</th>\n",
       "      <td>1123.15</td>\n",
       "      <td>471.15</td>\n",
       "      <td>1289.15</td>\n",
       "      <td>401.05</td>\n",
       "      <td>207.00</td>\n",
       "      <td>191.00</td>\n",
       "      <td>1008.00</td>\n",
       "      <td>435.40</td>\n",
       "      <td>2507.15</td>\n",
       "      <td>378.95</td>\n",
       "      <td>...</td>\n",
       "      <td>206.25</td>\n",
       "      <td>336.20</td>\n",
       "      <td>203.55</td>\n",
       "      <td>61.15</td>\n",
       "      <td>399.8</td>\n",
       "      <td>594.30</td>\n",
       "      <td>1513.55</td>\n",
       "      <td>30.55</td>\n",
       "      <td>20.60</td>\n",
       "      <td>817.80</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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\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>2019-05-06</th>\n",
       "      <td>1387.80</td>\n",
       "      <td>1082.85</td>\n",
       "      <td>3017.05</td>\n",
       "      <td>337.50</td>\n",
       "      <td>1875.10</td>\n",
       "      <td>200.45</td>\n",
       "      <td>1697.50</td>\n",
       "      <td>153.45</td>\n",
       "      <td>2215.40</td>\n",
       "      <td>266.70</td>\n",
       "      <td>...</td>\n",
       "      <td>115.45</td>\n",
       "      <td>534.45</td>\n",
       "      <td>135.20</td>\n",
       "      <td>37.10</td>\n",
       "      <td>NaN</td>\n",
       "      <td>251.95</td>\n",
       "      <td>1780.10</td>\n",
       "      <td>2.20</td>\n",
       "      <td>5.95</td>\n",
       "      <td>1268.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-05-07</th>\n",
       "      <td>1385.70</td>\n",
       "      <td>1086.50</td>\n",
       "      <td>2921.30</td>\n",
       "      <td>340.40</td>\n",
       "      <td>399.05</td>\n",
       "      <td>200.00</td>\n",
       "      <td>1688.70</td>\n",
       "      <td>152.20</td>\n",
       "      <td>2132.00</td>\n",
       "      <td>267.10</td>\n",
       "      <td>...</td>\n",
       "      <td>115.30</td>\n",
       "      <td>531.85</td>\n",
       "      <td>133.60</td>\n",
       "      <td>37.60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>246.25</td>\n",
       "      <td>1748.50</td>\n",
       "      <td>2.30</td>\n",
       "      <td>5.65</td>\n",
       "      <td>1248.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-05-08</th>\n",
       "      <td>1354.20</td>\n",
       "      <td>1088.70</td>\n",
       "      <td>2971.35</td>\n",
       "      <td>341.55</td>\n",
       "      <td>1853.00</td>\n",
       "      <td>198.15</td>\n",
       "      <td>1703.75</td>\n",
       "      <td>150.60</td>\n",
       "      <td>2157.85</td>\n",
       "      <td>262.25</td>\n",
       "      <td>...</td>\n",
       "      <td>117.45</td>\n",
       "      <td>540.90</td>\n",
       "      <td>133.00</td>\n",
       "      <td>37.60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>251.15</td>\n",
       "      <td>1758.45</td>\n",
       "      <td>2.40</td>\n",
       "      <td>6.40</td>\n",
       "      <td>1239.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-05-09</th>\n",
       "      <td>1341.05</td>\n",
       "      <td>1104.45</td>\n",
       "      <td>2922.85</td>\n",
       "      <td>332.05</td>\n",
       "      <td>380.15</td>\n",
       "      <td>195.80</td>\n",
       "      <td>1687.45</td>\n",
       "      <td>147.60</td>\n",
       "      <td>2151.95</td>\n",
       "      <td>265.45</td>\n",
       "      <td>...</td>\n",
       "      <td>117.15</td>\n",
       "      <td>541.55</td>\n",
       "      <td>131.90</td>\n",
       "      <td>38.10</td>\n",
       "      <td>NaN</td>\n",
       "      <td>242.75</td>\n",
       "      <td>1715.40</td>\n",
       "      <td>2.30</td>\n",
       "      <td>5.60</td>\n",
       "      <td>1211.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-05-10</th>\n",
       "      <td>1332.50</td>\n",
       "      <td>1132.10</td>\n",
       "      <td>2931.85</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1819.20</td>\n",
       "      <td>192.20</td>\n",
       "      <td>1702.00</td>\n",
       "      <td>142.60</td>\n",
       "      <td>2152.85</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>129.70</td>\n",
       "      <td>34.75</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1724.00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>495 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Asian_paint    Titan  Bajfinance    Gail     Hdfc  Hindalco  \\\n",
       "Date                                                                      \n",
       "2017-05-15      1148.05   483.65     1332.95  414.00  1559.50    198.45   \n",
       "2017-05-16      1142.85   488.30     1347.75  411.40   205.00    196.50   \n",
       "2017-05-17      1154.95   481.75     1324.80  408.30  1566.55    198.85   \n",
       "2017-05-18      1151.35   471.65     1314.55  404.75  1552.50    194.00   \n",
       "2017-05-19      1123.15   471.15     1289.15  401.05   207.00    191.00   \n",
       "...                 ...      ...         ...     ...      ...       ...   \n",
       "2019-05-06      1387.80  1082.85     3017.05  337.50  1875.10    200.45   \n",
       "2019-05-07      1385.70  1086.50     2921.30  340.40   399.05    200.00   \n",
       "2019-05-08      1354.20  1088.70     2971.35  341.55  1853.00    198.15   \n",
       "2019-05-09      1341.05  1104.45     2922.85  332.05   380.15    195.80   \n",
       "2019-05-10      1332.50  1132.10     2931.85     NaN  1819.20    192.20   \n",
       "\n",
       "            Hindunilvr     Ioc      Tcs  Infratel  ...  Ashoka  BajajElec  \\\n",
       "Date                                               ...                      \n",
       "2017-05-15      983.25  442.10  2365.10    371.05  ...  216.05     341.15   \n",
       "2017-05-16     1000.40  446.60  2429.15    376.55  ...  214.90     347.00   \n",
       "2017-05-17     1009.40  444.25  2455.35    389.90  ...  217.00     349.85   \n",
       "2017-05-18      990.25  439.90  2536.20    378.90  ...  209.65     334.10   \n",
       "2017-05-19     1008.00  435.40  2507.15    378.95  ...  206.25     336.20   \n",
       "...                ...     ...      ...       ...  ...     ...        ...   \n",
       "2019-05-06     1697.50  153.45  2215.40    266.70  ...  115.45     534.45   \n",
       "2019-05-07     1688.70  152.20  2132.00    267.10  ...  115.30     531.85   \n",
       "2019-05-08     1703.75  150.60  2157.85    262.25  ...  117.45     540.90   \n",
       "2019-05-09     1687.45  147.60  2151.95    265.45  ...  117.15     541.55   \n",
       "2019-05-10     1702.00  142.60  2152.85       NaN  ...     NaN        NaN   \n",
       "\n",
       "            Fortis   Idfc  Ircon    Itdc      Pvr   Rcom  Suzlon   Luxind  \n",
       "Date                                                                       \n",
       "2017-05-15  205.25  63.70  415.3  650.15  1524.95  32.00   19.60   819.60  \n",
       "2017-05-16  207.90  64.25  427.0  636.70  1539.00  32.10   19.70   817.50  \n",
       "2017-05-17  205.90  63.35  421.4  626.75  1530.30  31.95   19.90   819.80  \n",
       "2017-05-18  196.85  61.50  407.1  604.65  1515.05  31.05   20.00   820.05  \n",
       "2017-05-19  203.55  61.15  399.8  594.30  1513.55  30.55   20.60   817.80  \n",
       "...            ...    ...    ...     ...      ...    ...     ...      ...  \n",
       "2019-05-06  135.20  37.10    NaN  251.95  1780.10   2.20    5.95  1268.50  \n",
       "2019-05-07  133.60  37.60    NaN  246.25  1748.50   2.30    5.65  1248.20  \n",
       "2019-05-08  133.00  37.60    NaN  251.15  1758.45   2.40    6.40  1239.95  \n",
       "2019-05-09  131.90  38.10    NaN  242.75  1715.40   2.30    5.60  1211.55  \n",
       "2019-05-10  129.70  34.75    NaN     NaN  1724.00    NaN     NaN      NaN  \n",
       "\n",
       "[495 rows x 30 columns]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame()\n",
    "# Large Caps\n",
    "Asian_paint = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\ASIANPAINT.csv')\n",
    "df['Asian_paint'] = Asian_paint['Close Price']\n",
    "Titan = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\TITAN.csv')\n",
    "df['Titan'] = Titan['Close Price']\n",
    "Bajfinance = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\BAJFINANCE.csv')\n",
    "df['Bajfinance'] = Bajfinance['Close Price']\n",
    "Gail = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\GAIL.csv')\n",
    "df['Gail'] = Gail['Close Price']\n",
    "Hdfc = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\HDFC.csv')\n",
    "df['Hdfc'] = Hdfc['Close Price']\n",
    "Hindalco = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\HINDALCO.csv')\n",
    "df['Hindalco'] = Hindalco['Close Price']\n",
    "Hindunilvr = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\HINDUNILVR.csv')\n",
    "df['Hindunilvr'] = Hindunilvr['Close Price']\n",
    "Ioc = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\IOC.csv')\n",
    "df['Ioc'] = Ioc['Close Price']\n",
    "Tcs = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\TCS.csv')\n",
    "df['Tcs'] = Tcs['Close Price']\n",
    "Infratel = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Large_Cap\\INFRATEL.csv')\n",
    "df['Infratel'] = Infratel['Close Price']\n",
    "\n",
    "# Mid Caps\n",
    "Adani_power = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\ADANIPOWER.csv')\n",
    "df['Adani_power'] = Adani_power['Close Price']\n",
    "Dhfl = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\DHFL.csv')\n",
    "df['Dhfl'] = Dhfl['Close Price']\n",
    "Idbi = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\IDBI.csv')\n",
    "df['Idbi'] = Idbi['Close Price']\n",
    "Igl = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\IGL.csv')\n",
    "df['Igl'] = Igl['Close Price']\n",
    "Mrpl = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\MRPL.csv')\n",
    "df['Mrpl'] = Mrpl['Close Price']\n",
    "TataPower = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\TATAPOWER.csv')\n",
    "df['TataPower'] = TataPower['Close Price']\n",
    "Pnb = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\PNB.csv')\n",
    "df['Pnb'] = Pnb['Close Price']\n",
    "suntv = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\SUNTV.csv')\n",
    "df['suntv'] = suntv['Close Price']\n",
    "Voltas = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\VOLTAS.csv')\n",
    "df['Voltas'] = Voltas['Close Price']\n",
    "Rblbank = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Mid_Cap\\RBLBANK.csv')\n",
    "df['Rblbank'] = Rblbank['Close Price']\n",
    "\n",
    "#Small Caps\n",
    "Ashoka = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\ASHOKA.csv')\n",
    "df['Ashoka'] = Ashoka['Close Price']\n",
    "BajajElec = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\BAJAJELEC.csv')\n",
    "df['BajajElec'] = BajajElec['Close Price']\n",
    "Fortis = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\FORTIS.csv')\n",
    "df['Fortis'] = Fortis['Close Price']\n",
    "Idfc = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\IDFC.csv')\n",
    "df['Idfc'] = Idfc['Close Price']\n",
    "Ircon = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\IRCON.csv')\n",
    "df['Ircon'] = Ircon['Close Price']\n",
    "Itdc = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\ITDC.csv')\n",
    "df['Itdc'] = Itdc['Close Price']\n",
    "Pvr = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\PVR.csv')\n",
    "df['Pvr'] = Pvr['Close Price']\n",
    "Rcom = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\RCOM.csv')\n",
    "df['Rcom'] = Rcom['Close Price']\n",
    "Suzlon = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\SUZLON.csv')\n",
    "df['Suzlon'] = Suzlon['Close Price']\n",
    "Luxind = pd.read_csv('D:\\codes\\Machine-learning\\internship\\Stocks\\Small_Cap\\LUXIND.csv')\n",
    "df['Luxind'] = Luxind['Close Price']\n",
    "\n",
    "df['Date'] = Titan['Date']\n",
    "df['Date'] = pd.to_datetime(df['Date'])\n",
    "df.set_index('Date',inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PROBLEM STATEMENT\n",
    "# 6.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Returns</th>\n",
       "      <th>Volatility</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Asian_paint</th>\n",
       "      <td>0.001428</td>\n",
       "      <td>0.188060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Titan</th>\n",
       "      <td>1.014747</td>\n",
       "      <td>0.429079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bajfinance</th>\n",
       "      <td>0.509863</td>\n",
       "      <td>0.303276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gail</th>\n",
       "      <td>0.343332</td>\n",
       "      <td>0.284225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hdfc</th>\n",
       "      <td>545.109735</td>\n",
       "      <td>48.925656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hindalco</th>\n",
       "      <td>0.428701</td>\n",
       "      <td>0.293251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hindunilvr</th>\n",
       "      <td>0.527013</td>\n",
       "      <td>0.184322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ioc</th>\n",
       "      <td>-0.090250</td>\n",
       "      <td>0.277190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tcs</th>\n",
       "      <td>0.165402</td>\n",
       "      <td>0.195432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Infratel</th>\n",
       "      <td>-0.008249</td>\n",
       "      <td>0.326391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Adani_power</th>\n",
       "      <td>0.379545</td>\n",
       "      <td>0.462123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dhfl</th>\n",
       "      <td>30.245076</td>\n",
       "      <td>8.769715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idbi</th>\n",
       "      <td>-0.323429</td>\n",
       "      <td>0.424137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Igl</th>\n",
       "      <td>-0.479287</td>\n",
       "      <td>1.090425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mrpl</th>\n",
       "      <td>-0.084480</td>\n",
       "      <td>0.359268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TataPower</th>\n",
       "      <td>0.175810</td>\n",
       "      <td>0.248390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pnb</th>\n",
       "      <td>0.324857</td>\n",
       "      <td>0.708476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>suntv</th>\n",
       "      <td>0.129259</td>\n",
       "      <td>0.346028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Voltas</th>\n",
       "      <td>0.688500</td>\n",
       "      <td>0.334858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rblbank</th>\n",
       "      <td>-0.152965</td>\n",
       "      <td>0.227492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ashoka</th>\n",
       "      <td>0.247757</td>\n",
       "      <td>0.361509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BajajElec</th>\n",
       "      <td>0.646189</td>\n",
       "      <td>0.409396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fortis</th>\n",
       "      <td>-0.587881</td>\n",
       "      <td>0.461533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idfc</th>\n",
       "      <td>-0.105036</td>\n",
       "      <td>0.332030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ircon</th>\n",
       "      <td>-0.079240</td>\n",
       "      <td>0.301518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Itdc</th>\n",
       "      <td>-0.255867</td>\n",
       "      <td>0.524879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pvr</th>\n",
       "      <td>-0.183927</td>\n",
       "      <td>0.285611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rcom</th>\n",
       "      <td>-1.426379</td>\n",
       "      <td>0.696354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Suzlon</th>\n",
       "      <td>-0.559556</td>\n",
       "      <td>0.384850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Luxind</th>\n",
       "      <td>1.051938</td>\n",
       "      <td>0.347181</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Returns  Volatility\n",
       "Asian_paint    0.001428    0.188060\n",
       "Titan          1.014747    0.429079\n",
       "Bajfinance     0.509863    0.303276\n",
       "Gail           0.343332    0.284225\n",
       "Hdfc         545.109735   48.925656\n",
       "Hindalco       0.428701    0.293251\n",
       "Hindunilvr     0.527013    0.184322\n",
       "Ioc           -0.090250    0.277190\n",
       "Tcs            0.165402    0.195432\n",
       "Infratel      -0.008249    0.326391\n",
       "Adani_power    0.379545    0.462123\n",
       "Dhfl          30.245076    8.769715\n",
       "Idbi          -0.323429    0.424137\n",
       "Igl           -0.479287    1.090425\n",
       "Mrpl          -0.084480    0.359268\n",
       "TataPower      0.175810    0.248390\n",
       "Pnb            0.324857    0.708476\n",
       "suntv          0.129259    0.346028\n",
       "Voltas         0.688500    0.334858\n",
       "Rblbank       -0.152965    0.227492\n",
       "Ashoka         0.247757    0.361509\n",
       "BajajElec      0.646189    0.409396\n",
       "Fortis        -0.587881    0.461533\n",
       "Idfc          -0.105036    0.332030\n",
       "Ircon         -0.079240    0.301518\n",
       "Itdc          -0.255867    0.524879\n",
       "Pvr           -0.183927    0.285611\n",
       "Rcom          -1.426379    0.696354\n",
       "Suzlon        -0.559556    0.384850\n",
       "Luxind         1.051938    0.347181"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "returns = df.pct_change().mean() * 252\n",
    "returns = pd.DataFrame(returns)\n",
    "returns.columns = ['Returns']\n",
    "returns['Volatility'] = df.pct_change().std() * sqrt(252)\n",
    "returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PROBLEM STATEMENT\n",
    "# 6.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from sklearn import metrics\n",
    "from scipy.spatial.distance import cdist\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "data = np.asarray([np.asarray(returns['Returns']), np.asarray(returns['Volatility'])]).T\n",
    "X = data\n",
    "distortions = []\n",
    "K = range(1,10)\n",
    "for k in K:\n",
    "    KmeanModel = KMeans(n_clusters=k).fit(X)\n",
    "    KmeanModel.fit(X)\n",
    "    distortions.append(sum(np.min(cdist(X, KmeanModel.cluster_centers_, 'euclidean'),axis=1)) // X.shape[0])\n",
    "    \n",
    "    \n",
    "#plot\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.plot(K, distortions, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Distortions')\n",
    "plt.title('The Elbow Method showing the optimal k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PROBLEM STATEMENT\n",
    "# 6.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1a2a798d0>]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# computing K-Means with K = 3 (3 clusters)\n",
    "centroids,_ = kmeans(X,3)\n",
    "idx,_ = vq(data,centroids)\n",
    "\n",
    "plot(data[idx==0,0],data[idx==0,1],'ob',\n",
    "     data[idx==1,0],data[idx==1,1],'oy',\n",
    "     data[idx==2,0],data[idx==2,1],'or',\n",
    "     data[idx==3,0],data[idx==3,1],'og',\n",
    "     data[idx==4,0],data[idx==4,1],'om')\n",
    "plot(centroids[:,0],centroids[:,1],'sg',markersize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Returns       Hdfc\n",
      "Volatility    Hdfc\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "#identify outlier\n",
    "print(returns.idxmax())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "#drop relevent stocks\n",
    "returns.drop('Hdfc',inplace=True)\n",
    "data = np.asarray([np.asarray(returns['Returns']),np.asarray(returns['Volatility'])]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#computing K-Means\n",
    "\n",
    "centroids,_ = kmeans(data,3)\n",
    "idx,_ = vq(data,centroids)\n",
    "plot(data[idx==0,0],data[idx==0,1],'ob',\n",
    "     data[idx==1,0],data[idx==1,1],'oy',\n",
    "     data[idx==2,0],data[idx==2,1],'or',\n",
    "     data[idx==3,0],data[idx==3,1],'og',\n",
    "     data[idx==4,0],data[idx==4,1],'om')\n",
    "plot(centroids[:,0],centroids[:,1],'sg',markersize=8)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1a2a47da0>]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centroids,_ = kmeans(X,3)\n",
    "idx,_ = vq(data,centroids)\n",
    "\n",
    "plot(data[idx==0,0],data[idx==0,1],'ob',\n",
    "     data[idx==1,0],data[idx==1,1],'oy',\n",
    "     data[idx==2,0],data[idx==2,1],'or',\n",
    "     data[idx==3,0],data[idx==3,1],'og',\n",
    "     data[idx==4,0],data[idx==4,1],'om')\n",
    "plot(centroids[:,0],centroids[:,1],'sg',markersize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Returns       Dhfl\n",
      "Volatility    Dhfl\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "print(returns.idxmax())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns.drop('Dhfl',inplace=True)\n",
    "data = np.asarray([np.asarray(returns['Returns']),np.asarray(returns['Volatility'])]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centroids,_ = kmeans(data,3)\n",
    "idx,_ = vq(data,centroids)\n",
    "\n",
    "plot(data[idx==0,0],data[idx==0,1],'ob',\n",
    "     data[idx==1,0],data[idx==1,1],'oy',\n",
    "     data[idx==2,0],data[idx==2,1],'or',\n",
    "     data[idx==3,0],data[idx==3,1],'og',\n",
    "     data[idx==4,0],data[idx==4,1],'om')\n",
    "plot(centroids[:,0],centroids[:,1],'sg',markersize=8)\n",
    "show()"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}