P33. Unsupervised ML - PCA Data Mining (Univ).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised ML - PCA Data Mining"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Univ</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brown</td>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CalTech</td>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>CMU</td>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Columbia</td>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cornell</td>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Dartmouth</td>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duke</td>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Georgetown</td>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Harvard</td>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>JohnsHopkins</td>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>MIT</td>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Northwestern</td>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NotreDame</td>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>PennState</td>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Princeton</td>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Purdue</td>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Stanford</td>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>TexasA&amp;M</td>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>UCBerkeley</td>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>UChicago</td>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>UMichigan</td>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>UPenn</td>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>UVA</td>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>UWisconsin</td>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Yale</td>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Univ   SAT  Top10  Accept  SFRatio  Expenses  GradRate\n",
       "0          Brown  1310     89      22       13     22704        94\n",
       "1        CalTech  1415    100      25        6     63575        81\n",
       "2            CMU  1260     62      59        9     25026        72\n",
       "3       Columbia  1310     76      24       12     31510        88\n",
       "4        Cornell  1280     83      33       13     21864        90\n",
       "5      Dartmouth  1340     89      23       10     32162        95\n",
       "6           Duke  1315     90      30       12     31585        95\n",
       "7     Georgetown  1255     74      24       12     20126        92\n",
       "8        Harvard  1400     91      14       11     39525        97\n",
       "9   JohnsHopkins  1305     75      44        7     58691        87\n",
       "10           MIT  1380     94      30       10     34870        91\n",
       "11  Northwestern  1260     85      39       11     28052        89\n",
       "12     NotreDame  1255     81      42       13     15122        94\n",
       "13     PennState  1081     38      54       18     10185        80\n",
       "14     Princeton  1375     91      14        8     30220        95\n",
       "15        Purdue  1005     28      90       19      9066        69\n",
       "16      Stanford  1360     90      20       12     36450        93\n",
       "17      TexasA&M  1075     49      67       25      8704        67\n",
       "18    UCBerkeley  1240     95      40       17     15140        78\n",
       "19      UChicago  1290     75      50       13     38380        87\n",
       "20     UMichigan  1180     65      68       16     15470        85\n",
       "21         UPenn  1285     80      36       11     27553        90\n",
       "22           UVA  1225     77      44       14     13349        92\n",
       "23    UWisconsin  1085     40      69       15     11857        71\n",
       "24          Yale  1375     95      19       11     43514        96"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import Dataset\n",
    "univ=pd.read_csv('Database/Universities.csv')\n",
    "univ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT  Top10  Accept  SFRatio  Expenses  GradRate\n",
       "0   1310     89      22       13     22704        94\n",
       "1   1415    100      25        6     63575        81\n",
       "2   1260     62      59        9     25026        72\n",
       "3   1310     76      24       12     31510        88\n",
       "4   1280     83      33       13     21864        90\n",
       "5   1340     89      23       10     32162        95\n",
       "6   1315     90      30       12     31585        95\n",
       "7   1255     74      24       12     20126        92\n",
       "8   1400     91      14       11     39525        97\n",
       "9   1305     75      44        7     58691        87\n",
       "10  1380     94      30       10     34870        91\n",
       "11  1260     85      39       11     28052        89\n",
       "12  1255     81      42       13     15122        94\n",
       "13  1081     38      54       18     10185        80\n",
       "14  1375     91      14        8     30220        95\n",
       "15  1005     28      90       19      9066        69\n",
       "16  1360     90      20       12     36450        93\n",
       "17  1075     49      67       25      8704        67\n",
       "18  1240     95      40       17     15140        78\n",
       "19  1290     75      50       13     38380        87\n",
       "20  1180     65      68       16     15470        85\n",
       "21  1285     80      36       11     27553        90\n",
       "22  1225     77      44       14     13349        92\n",
       "23  1085     40      69       15     11857        71\n",
       "24  1375     95      19       11     43514        96"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Consider only numerical data\n",
    "univ2=univ.iloc[:,1:]\n",
    "univ2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1310,    89,    22,    13, 22704,    94],\n",
       "       [ 1415,   100,    25,     6, 63575,    81],\n",
       "       [ 1260,    62,    59,     9, 25026,    72],\n",
       "       [ 1310,    76,    24,    12, 31510,    88],\n",
       "       [ 1280,    83,    33,    13, 21864,    90],\n",
       "       [ 1340,    89,    23,    10, 32162,    95],\n",
       "       [ 1315,    90,    30,    12, 31585,    95],\n",
       "       [ 1255,    74,    24,    12, 20126,    92],\n",
       "       [ 1400,    91,    14,    11, 39525,    97],\n",
       "       [ 1305,    75,    44,     7, 58691,    87],\n",
       "       [ 1380,    94,    30,    10, 34870,    91],\n",
       "       [ 1260,    85,    39,    11, 28052,    89],\n",
       "       [ 1255,    81,    42,    13, 15122,    94],\n",
       "       [ 1081,    38,    54,    18, 10185,    80],\n",
       "       [ 1375,    91,    14,     8, 30220,    95],\n",
       "       [ 1005,    28,    90,    19,  9066,    69],\n",
       "       [ 1360,    90,    20,    12, 36450,    93],\n",
       "       [ 1075,    49,    67,    25,  8704,    67],\n",
       "       [ 1240,    95,    40,    17, 15140,    78],\n",
       "       [ 1290,    75,    50,    13, 38380,    87],\n",
       "       [ 1180,    65,    68,    16, 15470,    85],\n",
       "       [ 1285,    80,    36,    11, 27553,    90],\n",
       "       [ 1225,    77,    44,    14, 13349,    92],\n",
       "       [ 1085,    40,    69,    15, 11857,    71],\n",
       "       [ 1375,    95,    19,    11, 43514,    96]], dtype=int64)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Converting data to numpy array\n",
    "univ_ary=univ2.values\n",
    "univ_ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.41028362,  0.6575195 , -0.88986682,  0.07026045, -0.33141256,\n",
       "         0.82030265],\n",
       "       [ 1.39925928,  1.23521235, -0.73465749, -1.68625071,  2.56038138,\n",
       "        -0.64452351],\n",
       "       [-0.06065717, -0.76045386,  1.02438157, -0.93346022, -0.16712136,\n",
       "        -1.65863393],\n",
       "       [ 0.41028362, -0.02520842, -0.78639393, -0.18066972,  0.29164871,\n",
       "         0.14422904],\n",
       "       [ 0.12771914,  0.34241431, -0.32076595,  0.07026045, -0.39084607,\n",
       "         0.36958691],\n",
       "       [ 0.69284809,  0.6575195 , -0.83813038, -0.68253005,  0.33778044,\n",
       "         0.93298158],\n",
       "       [ 0.4573777 ,  0.71003703, -0.47597528, -0.18066972,  0.29695528,\n",
       "         0.93298158],\n",
       "       [-0.10775125, -0.13024348, -0.78639393, -0.18066972, -0.51381683,\n",
       "         0.59494478],\n",
       "       [ 1.25797704,  0.76255456, -1.30375836, -0.43159988,  0.85874344,\n",
       "         1.15833946],\n",
       "       [ 0.36318954, -0.07772595,  0.24833493, -1.43532055,  2.21481798,\n",
       "         0.0315501 ],\n",
       "       [ 1.06960072,  0.92010716, -0.47597528, -0.68253005,  0.52938275,\n",
       "         0.48226584],\n",
       "       [-0.06065717,  0.44744937, -0.01034729, -0.43159988,  0.04698077,\n",
       "         0.25690797],\n",
       "       [-0.10775125,  0.23737924,  0.14486204,  0.07026045, -0.86787073,\n",
       "         0.82030265],\n",
       "       [-1.7466252 , -2.02087462,  0.76569936,  1.32491127, -1.21718409,\n",
       "        -0.75720245],\n",
       "       [ 1.02250664,  0.76255456, -1.30375836, -1.18439038,  0.20037583,\n",
       "         0.93298158],\n",
       "       [-2.46245521, -2.54604994,  2.6282113 ,  1.57584144, -1.29635802,\n",
       "        -1.99667073],\n",
       "       [ 0.88122441,  0.71003703, -0.9933397 , -0.18066972,  0.64117435,\n",
       "         0.70762371],\n",
       "       [-1.8031381 , -1.44318177,  1.43827311,  3.08142243, -1.32197103,\n",
       "        -2.22202861],\n",
       "       [-0.24903349,  0.97262469,  0.04138915,  1.07398111, -0.86659715,\n",
       "        -0.98256032],\n",
       "       [ 0.2219073 , -0.07772595,  0.55875358,  0.07026045,  0.77772991,\n",
       "         0.0315501 ],\n",
       "       [-0.81416244, -0.60290126,  1.49000956,  0.82305094, -0.84324827,\n",
       "        -0.19380777],\n",
       "       [ 0.17481322,  0.18486171, -0.16555662, -0.43159988,  0.01167444,\n",
       "         0.36958691],\n",
       "       [-0.39031573,  0.02730912,  0.24833493,  0.32119061, -0.99331788,\n",
       "         0.59494478],\n",
       "       [-1.70894994, -1.91583956,  1.541746  ,  0.57212078, -1.09888311,\n",
       "        -1.77131286],\n",
       "       [ 1.02250664,  0.97262469, -1.04507615, -0.43159988,  1.14098185,\n",
       "         1.04566052]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Normalizing the numerical data \n",
    "univ_norm=scale(univ_ary)\n",
    "univ_norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.00987445e+00, -1.06430962e+00,  8.10663051e-02,\n",
       "         5.69506350e-02, -1.28754245e-01, -3.46496377e-02],\n",
       "       [-2.82223781e+00,  2.25904458e+00,  8.36828830e-01,\n",
       "         1.43844644e-01, -1.25961913e-01, -1.80703168e-01],\n",
       "       [ 1.11246577e+00,  1.63120889e+00, -2.66786839e-01,\n",
       "         1.07507502e+00, -1.91814148e-01,  3.45679459e-01],\n",
       "       [-7.41741217e-01, -4.21874699e-02,  6.05008649e-02,\n",
       "        -1.57208116e-01, -5.77611392e-01,  1.09163092e-01],\n",
       "       [-3.11912064e-01, -6.35243572e-01,  1.02405189e-02,\n",
       "         1.71363672e-01,  1.27261287e-02, -1.69212696e-02],\n",
       "       [-1.69669089e+00, -3.44363283e-01, -2.53407507e-01,\n",
       "         1.25643278e-02, -5.26606002e-02, -2.71661600e-02],\n",
       "       [-1.24682093e+00, -4.90983662e-01, -3.20938196e-02,\n",
       "        -2.05643780e-01,  2.93505340e-01, -7.80119838e-02],\n",
       "       [-3.38749784e-01, -7.85168589e-01, -4.93584829e-01,\n",
       "         3.98563085e-02, -5.44978619e-01, -1.55371653e-01],\n",
       "       [-2.37415013e+00, -3.86538883e-01,  1.16098392e-01,\n",
       "        -4.53365617e-01, -2.30108300e-01,  2.66983932e-01],\n",
       "       [-1.40327739e+00,  2.11951503e+00, -4.42827141e-01,\n",
       "        -6.32543273e-01,  2.30053526e-01, -2.35615124e-01],\n",
       "       [-1.72610332e+00,  8.82371161e-02,  1.70403663e-01,\n",
       "         2.60901913e-01,  2.33318380e-01,  2.38968449e-01],\n",
       "       [-4.50857480e-01, -1.11329480e-02, -1.75746046e-01,\n",
       "         2.36165626e-01,  2.63250697e-01, -3.14843521e-01],\n",
       "       [ 4.02381405e-02, -1.00920438e+00, -4.96517167e-01,\n",
       "         2.29298758e-01,  4.48031921e-01,  4.93921533e-03],\n",
       "       [ 3.23373034e+00, -3.74580487e-01, -4.95372816e-01,\n",
       "        -5.21237711e-01, -6.39294809e-01, -9.00477852e-02],\n",
       "       [-2.23626502e+00, -3.71793294e-01, -3.98993653e-01,\n",
       "         4.06966479e-01, -4.16760680e-01,  5.06186327e-02],\n",
       "       [ 5.17299212e+00,  7.79915346e-01, -3.85912331e-01,\n",
       "        -2.32211711e-01,  1.79286976e-01, -3.09046943e-02],\n",
       "       [-1.69964377e+00, -3.05597453e-01,  3.18507851e-01,\n",
       "        -2.97462682e-01, -1.63424678e-01,  1.14422592e-01],\n",
       "       [ 4.57814600e+00, -3.47591363e-01,  1.49964176e+00,\n",
       "        -4.54251714e-01, -1.91141971e-01,  1.04149297e-01],\n",
       "       [ 8.22603117e-01, -6.98906146e-01,  1.42781145e+00,\n",
       "         7.60778800e-01,  1.84260335e-01, -2.51103268e-01],\n",
       "       [-9.77621343e-02,  6.50446454e-01,  1.00508440e-01,\n",
       "        -5.00097185e-01,  4.87217823e-01,  2.19242132e-01],\n",
       "       [ 1.96318260e+00, -2.24767561e-01, -2.55881433e-01,\n",
       "        -4.84741049e-02,  8.22745655e-01,  1.52246521e-01],\n",
       "       [-5.42288939e-01, -7.95888376e-02, -3.05393475e-01,\n",
       "         1.31698758e-01,  5.27399148e-02, -3.67264440e-02],\n",
       "       [ 5.32220920e-01, -1.01716720e+00, -4.23716362e-01,\n",
       "         1.69535706e-01,  3.57813210e-01, -6.60989993e-02],\n",
       "       [ 3.54869664e+00,  7.78461666e-01, -4.49363319e-01,\n",
       "         3.23678618e-01, -3.58332564e-01, -7.74564151e-02],\n",
       "       [-2.30590032e+00, -1.17704318e-01,  2.53988661e-01,\n",
       "        -5.16183372e-01,  5.58940129e-02, -1.07932007e-02]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Applying PCA Fit Transform to dataset\n",
    "\n",
    "pca=PCA(n_components=6)  # n_components is no. of features\n",
    "\n",
    "univ_pca=pca.fit_transform(univ_norm)\n",
    "univ_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.45774863, -0.42714437,  0.42430805,  0.39064831, -0.36252316,\n",
       "        -0.37940403],\n",
       "       [ 0.03968044, -0.19993153,  0.32089297, -0.43256441,  0.6344864 ,\n",
       "        -0.51555367],\n",
       "       [ 0.1870388 ,  0.49780855, -0.15627899,  0.60608085,  0.20474114,\n",
       "        -0.53247261],\n",
       "       [ 0.13124033,  0.37489567,  0.0612872 , -0.50739095, -0.62340055,\n",
       "        -0.43863341],\n",
       "       [ 0.02064583,  0.4820162 ,  0.8010936 ,  0.07682369,  0.07254775,\n",
       "         0.33810965],\n",
       "       [ 0.8580547 , -0.39607492,  0.21693361,  0.1720479 , -0.17376309,\n",
       "        -0.00353754]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# PCA Components matrix or covariance Matrix\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76868084, 0.13113602, 0.04776031, 0.02729668, 0.0207177 ,\n",
       "       0.00440844])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The amount of variance that each PCA has\n",
    "var=pca.explained_variance_ratio_\n",
    "var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 76.87,  89.98,  94.76,  97.49,  99.56, 100.  ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cummulative variance of each PCA\n",
    "var1 = np.cumsum(np.round(var,4)*100)\n",
    "var1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18fddcba880>]"
      ]
     },
     "execution_count": 10,
     "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": [
    "# Variance plot for PCA components obtained \n",
    "plt.plot(var1,color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Univ</th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brown</td>\n",
       "      <td>-1.009874</td>\n",
       "      <td>-1.064310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CalTech</td>\n",
       "      <td>-2.822238</td>\n",
       "      <td>2.259045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>CMU</td>\n",
       "      <td>1.112466</td>\n",
       "      <td>1.631209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Columbia</td>\n",
       "      <td>-0.741741</td>\n",
       "      <td>-0.042187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cornell</td>\n",
       "      <td>-0.311912</td>\n",
       "      <td>-0.635244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Dartmouth</td>\n",
       "      <td>-1.696691</td>\n",
       "      <td>-0.344363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duke</td>\n",
       "      <td>-1.246821</td>\n",
       "      <td>-0.490984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Georgetown</td>\n",
       "      <td>-0.338750</td>\n",
       "      <td>-0.785169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Harvard</td>\n",
       "      <td>-2.374150</td>\n",
       "      <td>-0.386539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>JohnsHopkins</td>\n",
       "      <td>-1.403277</td>\n",
       "      <td>2.119515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>MIT</td>\n",
       "      <td>-1.726103</td>\n",
       "      <td>0.088237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Northwestern</td>\n",
       "      <td>-0.450857</td>\n",
       "      <td>-0.011133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NotreDame</td>\n",
       "      <td>0.040238</td>\n",
       "      <td>-1.009204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>PennState</td>\n",
       "      <td>3.233730</td>\n",
       "      <td>-0.374580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Princeton</td>\n",
       "      <td>-2.236265</td>\n",
       "      <td>-0.371793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Purdue</td>\n",
       "      <td>5.172992</td>\n",
       "      <td>0.779915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Stanford</td>\n",
       "      <td>-1.699644</td>\n",
       "      <td>-0.305597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>TexasA&amp;M</td>\n",
       "      <td>4.578146</td>\n",
       "      <td>-0.347591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>UCBerkeley</td>\n",
       "      <td>0.822603</td>\n",
       "      <td>-0.698906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>UChicago</td>\n",
       "      <td>-0.097762</td>\n",
       "      <td>0.650446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>UMichigan</td>\n",
       "      <td>1.963183</td>\n",
       "      <td>-0.224768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>UPenn</td>\n",
       "      <td>-0.542289</td>\n",
       "      <td>-0.079589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>UVA</td>\n",
       "      <td>0.532221</td>\n",
       "      <td>-1.017167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>UWisconsin</td>\n",
       "      <td>3.548697</td>\n",
       "      <td>0.778462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Yale</td>\n",
       "      <td>-2.305900</td>\n",
       "      <td>-0.117704</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Univ       PC1       PC2\n",
       "0          Brown -1.009874 -1.064310\n",
       "1        CalTech -2.822238  2.259045\n",
       "2            CMU  1.112466  1.631209\n",
       "3       Columbia -0.741741 -0.042187\n",
       "4        Cornell -0.311912 -0.635244\n",
       "5      Dartmouth -1.696691 -0.344363\n",
       "6           Duke -1.246821 -0.490984\n",
       "7     Georgetown -0.338750 -0.785169\n",
       "8        Harvard -2.374150 -0.386539\n",
       "9   JohnsHopkins -1.403277  2.119515\n",
       "10           MIT -1.726103  0.088237\n",
       "11  Northwestern -0.450857 -0.011133\n",
       "12     NotreDame  0.040238 -1.009204\n",
       "13     PennState  3.233730 -0.374580\n",
       "14     Princeton -2.236265 -0.371793\n",
       "15        Purdue  5.172992  0.779915\n",
       "16      Stanford -1.699644 -0.305597\n",
       "17      TexasA&M  4.578146 -0.347591\n",
       "18    UCBerkeley  0.822603 -0.698906\n",
       "19      UChicago -0.097762  0.650446\n",
       "20     UMichigan  1.963183 -0.224768\n",
       "21         UPenn -0.542289 -0.079589\n",
       "22           UVA  0.532221 -1.017167\n",
       "23    UWisconsin  3.548697  0.778462\n",
       "24          Yale -2.305900 -0.117704"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Final Dataframe\n",
    "final_df=pd.concat([univ['Univ'],pd.DataFrame(univ_pca[:,0:2],columns=['PC1','PC2'])],axis=1)\n",
    "final_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18fdb5d7400>"
      ]
     },
     "execution_count": 12,
     "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": [
    "# Visualization of PCAs\n",
    "sns.scatterplot(data=final_df,x='PC1',y='PC2',hue='Univ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### OPTIONAL STEPS ####"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#How to compute Eigen vector and eigen values for a given matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  0],\n",
       "       [ 0, -2]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Suppose the given matrix A is\n",
    "A = np.array([[1,0],[0,-2]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvals, eigvecs = la.eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1., -2.])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Eigen value (λ)\n",
    "eigvals = eigvals.real\n",
    "eigvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0\n"
     ]
    }
   ],
   "source": [
    "lambda1 = eigvals[1]\n",
    "print(lambda1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Eigen Vector (V)\n",
    "eigvecs"
   ]
  },
  {
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}