618_10_Dimension_Reduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SI 618: Data Manipulation and Analysis\n",
    "## 10 - Dimension Reduction\n",
    "### Dr. Chris Teplovs, School of Information, University of Michigan\n",
    "<small><a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a> This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Dimension Reduction slides](resources/si618-dimensionality-reduction.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall:\n",
    "\n",
    "* Run factor analysis if you assume or wish to test a theoretical model of latent factors causing observed variables.\n",
    "\n",
    "* Run principal component analysis If you want to simply reduce your correlated observed variables to a smaller set of important independent composite variables.\n",
    "\n",
    "--Jeromy Anglim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis 1 (Heptathalon)\n",
    "\n",
    "* Be able to perform principcal component analysis (PCA) and exploratory factor analysis (EFA).\n",
    "* Be able to apply manifold learning methods, including multidimensional scaling (MDS)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "sns.set_context(\"notebook\")  # make figures fit\n",
    "from pylab import rcParams\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.graphics.mosaicplot import mosaic\n",
    "from IPython.display import Image\n",
    "from IPython.core.display import HTML \n",
    "import sklearn as sk\n",
    "import sklearn.cluster as skc\n",
    "import sklearn.decomposition as skd\n",
    "import sklearn.manifold as skm\n",
    "import sklearn.preprocessing as skp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load the Data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hurdles</th>\n",
       "      <th>HighJump</th>\n",
       "      <th>Shot</th>\n",
       "      <th>Run200m</th>\n",
       "      <th>LongJump</th>\n",
       "      <th>Javelin</th>\n",
       "      <th>Run800m</th>\n",
       "      <th>Score</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Athlete</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>Joyner-Kersee (USA)</th>\n",
       "      <td>12.69</td>\n",
       "      <td>1.86</td>\n",
       "      <td>15.80</td>\n",
       "      <td>22.56</td>\n",
       "      <td>7.27</td>\n",
       "      <td>45.66</td>\n",
       "      <td>128.51</td>\n",
       "      <td>7291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>John (GDR)</th>\n",
       "      <td>12.85</td>\n",
       "      <td>1.80</td>\n",
       "      <td>16.23</td>\n",
       "      <td>23.65</td>\n",
       "      <td>6.71</td>\n",
       "      <td>42.56</td>\n",
       "      <td>126.12</td>\n",
       "      <td>6897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Behmer (GDR)</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.83</td>\n",
       "      <td>14.20</td>\n",
       "      <td>23.10</td>\n",
       "      <td>6.68</td>\n",
       "      <td>44.54</td>\n",
       "      <td>124.20</td>\n",
       "      <td>6858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sablovskaite (URS)</th>\n",
       "      <td>13.61</td>\n",
       "      <td>1.80</td>\n",
       "      <td>15.23</td>\n",
       "      <td>23.92</td>\n",
       "      <td>6.25</td>\n",
       "      <td>42.78</td>\n",
       "      <td>132.24</td>\n",
       "      <td>6540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Choubenkova (URS)</th>\n",
       "      <td>13.51</td>\n",
       "      <td>1.74</td>\n",
       "      <td>14.76</td>\n",
       "      <td>23.93</td>\n",
       "      <td>6.32</td>\n",
       "      <td>47.46</td>\n",
       "      <td>127.90</td>\n",
       "      <td>6540</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "                     Hurdles  HighJump   Shot  Run200m  LongJump  Javelin  \\\n",
       "Athlete                                                                     \n",
       "Joyner-Kersee (USA)    12.69      1.86  15.80    22.56      7.27    45.66   \n",
       "John (GDR)             12.85      1.80  16.23    23.65      6.71    42.56   \n",
       "Behmer (GDR)           13.20      1.83  14.20    23.10      6.68    44.54   \n",
       "Sablovskaite (URS)     13.61      1.80  15.23    23.92      6.25    42.78   \n",
       "Choubenkova (URS)      13.51      1.74  14.76    23.93      6.32    47.46   \n",
       "\n",
       "                     Run800m  Score  \n",
       "Athlete                              \n",
       "Joyner-Kersee (USA)   128.51   7291  \n",
       "John (GDR)            126.12   6897  \n",
       "Behmer (GDR)          124.20   6858  \n",
       "Sablovskaite (URS)    132.24   6540  \n",
       "Choubenkova (URS)     127.90   6540  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hept = pd.read_csv('data/heptathlon.csv')\n",
    "df_hept = df_hept.set_index('Athlete')\n",
    "df_hept.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hurdles</th>\n",
       "      <th>HighJump</th>\n",
       "      <th>Shot</th>\n",
       "      <th>Run200m</th>\n",
       "      <th>LongJump</th>\n",
       "      <th>Javelin</th>\n",
       "      <th>Run800m</th>\n",
       "      <th>Score</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>13.840000</td>\n",
       "      <td>1.782000</td>\n",
       "      <td>13.117600</td>\n",
       "      <td>24.649200</td>\n",
       "      <td>6.152400</td>\n",
       "      <td>41.482400</td>\n",
       "      <td>136.054000</td>\n",
       "      <td>6090.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.736648</td>\n",
       "      <td>0.077942</td>\n",
       "      <td>1.491884</td>\n",
       "      <td>0.969557</td>\n",
       "      <td>0.474212</td>\n",
       "      <td>3.545656</td>\n",
       "      <td>8.291088</td>\n",
       "      <td>568.469729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>12.690000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>22.560000</td>\n",
       "      <td>4.880000</td>\n",
       "      <td>35.680000</td>\n",
       "      <td>124.200000</td>\n",
       "      <td>4566.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>13.470000</td>\n",
       "      <td>1.770000</td>\n",
       "      <td>12.320000</td>\n",
       "      <td>23.920000</td>\n",
       "      <td>6.050000</td>\n",
       "      <td>39.060000</td>\n",
       "      <td>132.240000</td>\n",
       "      <td>5746.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.750000</td>\n",
       "      <td>1.800000</td>\n",
       "      <td>12.880000</td>\n",
       "      <td>24.830000</td>\n",
       "      <td>6.250000</td>\n",
       "      <td>40.280000</td>\n",
       "      <td>134.740000</td>\n",
       "      <td>6137.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>14.070000</td>\n",
       "      <td>1.830000</td>\n",
       "      <td>14.200000</td>\n",
       "      <td>25.230000</td>\n",
       "      <td>6.370000</td>\n",
       "      <td>44.540000</td>\n",
       "      <td>138.480000</td>\n",
       "      <td>6351.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>16.420000</td>\n",
       "      <td>1.860000</td>\n",
       "      <td>16.230000</td>\n",
       "      <td>26.610000</td>\n",
       "      <td>7.270000</td>\n",
       "      <td>47.500000</td>\n",
       "      <td>163.430000</td>\n",
       "      <td>7291.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Hurdles   HighJump       Shot    Run200m   LongJump    Javelin  \\\n",
       "count  25.000000  25.000000  25.000000  25.000000  25.000000  25.000000   \n",
       "mean   13.840000   1.782000  13.117600  24.649200   6.152400  41.482400   \n",
       "std     0.736648   0.077942   1.491884   0.969557   0.474212   3.545656   \n",
       "min    12.690000   1.500000  10.000000  22.560000   4.880000  35.680000   \n",
       "25%    13.470000   1.770000  12.320000  23.920000   6.050000  39.060000   \n",
       "50%    13.750000   1.800000  12.880000  24.830000   6.250000  40.280000   \n",
       "75%    14.070000   1.830000  14.200000  25.230000   6.370000  44.540000   \n",
       "max    16.420000   1.860000  16.230000  26.610000   7.270000  47.500000   \n",
       "\n",
       "          Run800m        Score  \n",
       "count   25.000000    25.000000  \n",
       "mean   136.054000  6090.600000  \n",
       "std      8.291088   568.469729  \n",
       "min    124.200000  4566.000000  \n",
       "25%    132.240000  5746.000000  \n",
       "50%    134.740000  6137.000000  \n",
       "75%    138.480000  6351.000000  \n",
       "max    163.430000  7291.000000  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's print out summary information to check the data quality \n",
    "# and structure.\n",
    "df_hept.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question: Should \"score\" be included in these analyses?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For now, let's omit the \"score\" column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_hept.drop('Score',inplace=True, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Rescaling the Data\n",
    "Let us normalize the data by computing the \"[z-scores](https://en.wikipedia.org/wiki/Standard_score#Calculation_from_raw_score)\" of the values. This step of normalization (rescaling) is important to PCA.\n",
    "\n",
    "Given a column x, the z-scores of the elements in x is simply\n",
    "\n",
    "    (x - mean(x)) / std(x)\n",
    "    \n",
    "where, `std` means standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Hurdles</th>\n",
       "      <th>HighJump</th>\n",
       "      <th>Shot</th>\n",
       "      <th>Run200m</th>\n",
       "      <th>LongJump</th>\n",
       "      <th>Javelin</th>\n",
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       "    <tr>\n",
       "      <th>Athlete</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "    <tr>\n",
       "      <th>Joyner-Kersee (USA)</th>\n",
       "      <td>-1.593317</td>\n",
       "      <td>1.021376</td>\n",
       "      <td>1.835071</td>\n",
       "      <td>-2.199232</td>\n",
       "      <td>2.405348</td>\n",
       "      <td>1.202526</td>\n",
       "      <td>-0.928655</td>\n",
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       "    <tr>\n",
       "      <th>John (GDR)</th>\n",
       "      <td>-1.371639</td>\n",
       "      <td>0.235702</td>\n",
       "      <td>2.129240</td>\n",
       "      <td>-1.051825</td>\n",
       "      <td>1.200091</td>\n",
       "      <td>0.310188</td>\n",
       "      <td>-1.222861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Behmer (GDR)</th>\n",
       "      <td>-0.886716</td>\n",
       "      <td>0.628539</td>\n",
       "      <td>0.740486</td>\n",
       "      <td>-1.630792</td>\n",
       "      <td>1.135524</td>\n",
       "      <td>0.880133</td>\n",
       "      <td>-1.459210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sablovskaite (URS)</th>\n",
       "      <td>-0.318663</td>\n",
       "      <td>0.235702</td>\n",
       "      <td>1.445125</td>\n",
       "      <td>-0.767605</td>\n",
       "      <td>0.210059</td>\n",
       "      <td>0.373515</td>\n",
       "      <td>-0.469498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Choubenkova (URS)</th>\n",
       "      <td>-0.457213</td>\n",
       "      <td>-0.549972</td>\n",
       "      <td>1.123591</td>\n",
       "      <td>-0.757078</td>\n",
       "      <td>0.360716</td>\n",
       "      <td>1.720658</td>\n",
       "      <td>-1.003745</td>\n",
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      ],
      "text/plain": [
       "                      Hurdles  HighJump      Shot   Run200m  LongJump  \\\n",
       "Athlete                                                                 \n",
       "Joyner-Kersee (USA) -1.593317  1.021376  1.835071 -2.199232  2.405348   \n",
       "John (GDR)          -1.371639  0.235702  2.129240 -1.051825  1.200091   \n",
       "Behmer (GDR)        -0.886716  0.628539  0.740486 -1.630792  1.135524   \n",
       "Sablovskaite (URS)  -0.318663  0.235702  1.445125 -0.767605  0.210059   \n",
       "Choubenkova (URS)   -0.457213 -0.549972  1.123591 -0.757078  0.360716   \n",
       "\n",
       "                      Javelin   Run800m  \n",
       "Athlete                                  \n",
       "Joyner-Kersee (USA)  1.202526 -0.928655  \n",
       "John (GDR)           0.310188 -1.222861  \n",
       "Behmer (GDR)         0.880133 -1.459210  \n",
       "Sablovskaite (URS)   0.373515 -0.469498  \n",
       "Choubenkova (URS)    1.720658 -1.003745  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hept_norm = df_hept.copy()\n",
    "df_hept_norm.ix[:,:7] = skp.scale(df_hept_norm.ix[:,:7].astype(np.float))\n",
    "df_hept_norm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "      <th>count</th>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>2.500000e+01</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.131628e-16</td>\n",
       "      <td>3.055334e-15</td>\n",
       "      <td>3.463896e-16</td>\n",
       "      <td>-4.352074e-16</td>\n",
       "      <td>-2.486900e-16</td>\n",
       "      <td>-1.589839e-15</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621e+00</td>\n",
       "      <td>1.020621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.593317e+00</td>\n",
       "      <td>-3.692669e+00</td>\n",
       "      <td>-2.132797e+00</td>\n",
       "      <td>-2.199232e+00</td>\n",
       "      <td>-2.738515e+00</td>\n",
       "      <td>-1.670227e+00</td>\n",
       "      <td>-1.459210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-5.126326e-01</td>\n",
       "      <td>-1.571348e-01</td>\n",
       "      <td>-5.456503e-01</td>\n",
       "      <td>-7.676047e-01</td>\n",
       "      <td>-2.203898e-01</td>\n",
       "      <td>-6.972903e-01</td>\n",
       "      <td>-0.469498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-1.246944e-01</td>\n",
       "      <td>2.357023e-01</td>\n",
       "      <td>-1.625458e-01</td>\n",
       "      <td>1.903222e-01</td>\n",
       "      <td>2.100590e-01</td>\n",
       "      <td>-3.461121e-01</td>\n",
       "      <td>-0.161751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.186635e-01</td>\n",
       "      <td>6.285394e-01</td>\n",
       "      <td>7.404863e-01</td>\n",
       "      <td>6.113890e-01</td>\n",
       "      <td>4.683283e-01</td>\n",
       "      <td>8.801333e-01</td>\n",
       "      <td>0.298637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.574573e+00</td>\n",
       "      <td>1.021376e+00</td>\n",
       "      <td>2.129240e+00</td>\n",
       "      <td>2.064069e+00</td>\n",
       "      <td>2.405348e+00</td>\n",
       "      <td>1.732172e+00</td>\n",
       "      <td>3.369945</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Hurdles      HighJump          Shot       Run200m      LongJump  \\\n",
       "count  2.500000e+01  2.500000e+01  2.500000e+01  2.500000e+01  2.500000e+01   \n",
       "mean   2.131628e-16  3.055334e-15  3.463896e-16 -4.352074e-16 -2.486900e-16   \n",
       "std    1.020621e+00  1.020621e+00  1.020621e+00  1.020621e+00  1.020621e+00   \n",
       "min   -1.593317e+00 -3.692669e+00 -2.132797e+00 -2.199232e+00 -2.738515e+00   \n",
       "25%   -5.126326e-01 -1.571348e-01 -5.456503e-01 -7.676047e-01 -2.203898e-01   \n",
       "50%   -1.246944e-01  2.357023e-01 -1.625458e-01  1.903222e-01  2.100590e-01   \n",
       "75%    3.186635e-01  6.285394e-01  7.404863e-01  6.113890e-01  4.683283e-01   \n",
       "max    3.574573e+00  1.021376e+00  2.129240e+00  2.064069e+00  2.405348e+00   \n",
       "\n",
       "            Javelin    Run800m  \n",
       "count  2.500000e+01  25.000000  \n",
       "mean  -1.589839e-15   0.000000  \n",
       "std    1.020621e+00   1.020621  \n",
       "min   -1.670227e+00  -1.459210  \n",
       "25%   -6.972903e-01  -0.469498  \n",
       "50%   -3.461121e-01  -0.161751  \n",
       "75%    8.801333e-01   0.298637  \n",
       "max    1.732172e+00   3.369945  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# confirm the mean/std are 0/1\n",
    "df_hept_norm.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Multidimensional Scaling (MDS)\n",
    "MDS seeks a low-dimensional representation of the data that preserves the distances in the high-dimensional space. It can take any kind of distance matrix as input.\n",
    "\n",
    "Note that each time you run MDS, you will get a different result, unless `random_state` is fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "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": [
    "# Use MDS to visualize brands.\n",
    "# Recall that df_bybrand is the mean-metric-by-brand \n",
    "# we created above.\n",
    "X = skm.MDS(n_components=2).fit_transform(df_hept_norm) # import sklearn.manifold as skm\n",
    "plt.scatter(X[:,0],X[:,1],s=50)\n",
    "\n",
    "plt.xlabel('MDS1')\n",
    "plt.ylabel('MDS2')\n",
    "plt.title('MDS')\n",
    "\n",
    "for i, s in enumerate(df_hept_norm.index):\n",
    "    plt.annotate(s, xy=X[i,:2]+0.05, fontsize=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jO4XL6XQSGxtLSkqKTxu0vHgnSVK3FIXcBh3KKJHuKUagi2PBFOiuYltUVNTrBbJ9+3buu+8+oFMoN295n4f+8Ta6OdfStOsdAKKnXYz5yHbebSninXfeYra2mrVr1xIbG4tGo6G6uprY2Fh0Oh1NTU00NTVx6623YjAYWLVqFddddx3PP/88kiQxd+5ccnNz+eijj1i6dCmbN2+mubmZ//qv/wJg8+bN3HrrrRw6dMhnPxcvXuxxC+vo6GDixInMmzcPrVbLSy+9xM033+zX53cyGenj1zUaDbGxsd2iP2/bTG+DILVa3aOh/EhvKZbp6OgY8baOoIiu3wSSXghWTtdsNlNWVuaX2Mp0vXBNyVOQNCrMzbVoYpLRZ0/BXnsEALco4nC42d3k4tVbbuXPf/4TLS0tTJ8+nba2NnQ6HVdffTWvv/46AOvWrWPTpk188cUXXHfddXz66afMnDmTN954A6vV6lnIrKio8Ly/w+Ho8aL96KOPaGlp4fnnn+fee+9l//79PPzwwzzxxBOeUqqhYiSmF4Lpl9Bf1KzT6UhISOjWeWe32z1iLKcnLBYLOp2uxzbokbRY53a7MRqNSqQ7FJysXNRQtfb29Fqz2UxpaSlNTU1+i61MUVERjz32GIIgcObZC/m6xogYHosgiLg6GnEd3k70tItx1B3H8v0ONLGpmDvauf9PTzB1TC4TJ07kxIkTjBs3jubmZh8h+M1vfsNzzz3HL37xC1544QUkSSI5OZmKigrS09P54osvaGtro6Ojw+Nxq9PpcLvdZGZm8te//tVzrIsXL2bq1Km89NJLpKWleUx3HA4HkZGRvR7fSGmOgJE5gQIGlqoQBIGwsDDCwsJ6XbyTzYEqKip8Fu+6ehifjGtU9tINhUhX6OfEGXGFl97zuIaT77//Hp1Ox5gxY/p9bXt7O0ePHuXMM8/s97UWi4WvvvqKBQsW+IhtTk4OOTk5g8qzffJ9E/e9+x0me/9fAFdNz+BPl072e9uSJNHS0sLx48dxu93k5OQgSZLPbavL5cJoNNLY2Mj555/vV+7wgw8+oLCwsMec7vHjx9Hr9YwaNcrv/eyJyspKnE4nY8eOHdR2LBYLBw8eZN68eYPaDkBxcTHh4eFkZ2cPelsHDhxg9OjRPpFssJEX72Qxlv/u8pdm15zxUA8gLS8vZ+rUqZSXlzN69Oghe58A6PVgT9lI9/HHH+9xcejwiQ5e/6qG8mYzYVo1S/JTWXJGGhG6zojOO+J4/PHHWbx4MZ9//jlLlizpFpH2Fp30FL2+8MILLFy4kP3797Ns2TIef/xxsrKyKC0txel0Eh8fz2uvvUZGRga33347L7744qDzmlan269WS+isjfSX1tZWjh8/jt1uZ9y4caSlpXk6AdPS0jyvczqdPeYOZdcubwtF+Xb1oosuCvQwAyaY6YVg3WKP1FRFb3RdvJNxuVw+QtzS0oLZbEYUxW5iHMzFO4PBAIz8qREQgqIL/pUOuVwuHnroISRJYvny5Rw9dpy1245SHzaaEx/8HX1KLlH5C/n4jb3cg8R91y+h/MAOCgoKuP7664HOiGjr1q3cf//9PPvss1RXVzNu3Dh0Oh0tLS2kpaVhMpmYO3cuH374IaIoMnv2bA4fPszRo0dpaGjgyiuvBMBoNHa7EBobG1Gr1UyYMIGIiAjGjh2LSqVCq9V6DJkHQ0ZsmF+3Klq1QG5iRL+vMxgMHD9+HLPZTF5eHhkZGX2KjlarJT4+vtv8M9m1y2Qy+dyuek95kH+GqrxppKUXThWXsb4W77zFuKGhAbPZ7CmD846K+/Mw7gmDwYAgCN3ar0ciISm6/uB2u1mwYAGiKGI0Gvmftz+jptVM3JmzCM+cSMyUhdhOHMNyopiIsbN44r19XJobyfXXX8+7775LUlIScXFxNDQ04HA4OHjwIHl5eZjNZnQ6HT/96U+xWCy8//772Gw2Dhw4wEUXXURDQwMHDhwgJSWFtrY2z/7ILcRy9FdfX8+SJUtwOp08/fTTPProoxw7dgyr1cqFF15IWFgYHR0dgzqJpmXHEq3XYOnH0UklCFw5vffOH6PRyPHjxzEYDOTl5ZGVlTXgi7o3166uUx6qqqowmUxIkuQRYLncaSSNrB/J1Qsjid4GkNrtds/fvb29ndraWs811jUq7mvxTnYYG2nH3ROnrOgCfPbZZ0iSxKW/uIMGpx5VTKexSKdRsoAkQVj6eCSHFSF5DLsqjgJwxRVXALBnzx5uu+02HnnkEWbPnk1JSQlTp06lubkZrVZLS0sL0dHRlJWVMWPGDIxGI/Pnz6ejo4NvvvmGCRMmePZFHkH+2WefsWPHDubMmePJ4cbHx/PRRx/x2GOPYbfbeemll3A6nYP+1hYEgfvOH8dD7x3B5uy5FjhMo+K8Sclkx4d3e85kMlFSUkJraytjxoxh6tSpQyZ2PRnFdJ0K3NbW5vEp0Ov1Phek7GXrj3CN1OqFUyHSDQTvxTvvAaSSJPl03nUdQNq1ksLpdNLe3h4SjREQoqLbX3qhuroao9HI6tWrAfjd+n1YGipIWtA5ZylhXmeBvzbux3lakiRhyxxHi8lBYlRnw4GcE/7LX/5CY2MjVVVVzJw50/M7aWlpPS6iTJ06la1bt3LWWWcBeGpRd+/ezf33309OTo7P7dPHH3/MggULUKlUhIeHc+utt7Ju3boBfTZdWVqQRovZwRMflyBKEk63PHG1U3DPHJPAqsvyfX7HYrFQUlJCU1MTo0ePZsqUKQHf7vXH448/TkREBCUlJTz55JNAp1iUNlv58EgTJU1m1CqB6dmxnDcxkVGjEnE4HGi1WrKzs7FarZhMJl5++WXy8/M5ePAg8+fPZ9OmTWRnZ9PS0sL48eO5+uqrefPNN9Hr9Sxbtox//etfLFq0aMQ1R4xUAT8ZCIJAREQEERERPQ4glb+E6+vrMZlM3HHHHdTV1aHRaLj99tuZMmUKixYtYtKkSQN6/3vuuYd33nmHiooKDh06xJQpU4J1aECIim5/ZGdnewQXoKrDTdK5N3VzMvJGEAS0GoETBptHdL0JpPZWdiXr6OigoqKClpYWrrvuum5iKyMvvHkvKgSzOWDFmaM4b1Iyr+6p5rPjLbjcIpPSo7nhzBymZsV4LnabzUZpaSn19fUBl6oNBO/P4qqrriLnnOv4+KOtCMDEhZdTf3QfW47sYcPSXzFRrKLhyG7y8/PJysri2muv9ZiD5+fnY7FYmD9/Pl988QVOp5PExESys7PZtWsXx44dQ6/XU1JSQkNDA3a7PSjHNVKFMtRFtze8B5B68+qrr7JmzRr27NlDXV0dH330EVardcCie9lll3HXXXdx9tlnB2O3uxGSohvoiR6m/cEwuZ9fEyV69fYMpE5XzkXu27eP0aNHk5+f32ekOBwjezLjwrn/gvHcf0H35+x2O2VlZZw4cWLY/HfVajW33HILa9euxWKxIKSMo9gWSWJqOmnjp9FedQTJbiQ1Zzw1n72Je/6VJEYls2zZMt59913Pdrxz5RqNhvDwcFauXMnRo0d5+umnuf3227FarTQ1NdHS0oLL5aKyshKdTkdzc3O3FEUgpU3BFt2RKOChwOTJk0lISOCMM85g48aNwOBSSPId6lARkqIbKBdMTuFovRGXu/c/hChJ6DUq8pJ6XsX3J9L1zoGq1WpmzpzpV54pEP+FYOJwOCgvL6empoaMjIxhnQYsDymsrq7GIqopb7MzIzWVb3Y3UL57K+MXXkFLxQZGz17MgbefJTVrNEe+/RSxy8Wk0WhIT0/n2LFjPPnkk+Tn5/PBBx9w/PhxUlJS2LZtG48//jh2u51XXnmFhIQExo0bhyRJpKSkeKooqqurfUqbvCsoeltND3Z6IRhCKZv5n06iC93NbkaKoU9PhKToBvqBXl6YwdPbShElqccUgyRJaNUqfj4nG42655O1L8Mbo9FIaWkpra2tnhyoPDvLHwKdwTZYnE4nFRUVVFVVkZqayrx58wgP776QNhB6ytXanW72VRn4v+8aqTfY0WtVnFV0DYsnJZMWo2fzdw2MOfc61GoV06+4jeOfbyI8NgFDfSWNxw8y+9q7OfDqX7C5JA5VNlNQUMBTTz3lKatbt24djzzyiM9+dK33DQ8P51e/+hX/+te/gM4vup7qTL0X7uSJwPJqelchDmZ0GiwBlwV3JIvOUGAwGMjNzT3Zu+EXISm6gRIdpuGJn57ByrcOYXeJqIQfhVv8QXALMmO4YV5Or9voSRh7Els5IjrZI3t6wuVyUVVVRUVFBUlJSZx55pmeOV/BxDsqvPzKqwibdQXlx49hriuj8Irb+GbrO9QULOK5l4+QajpObOY4altdJC36CQBOmxmV+ofPUatHrdWTMWUuRgc0tZsoKf2Gu+++2/Mer732Gu3t7X4Vxv/yl7+ktLS0V1HqzZdA7r6Sy/1MJhN2ux2VSsWRI0e61RYHSrCi09MxyoXQGdUDp4noAiwcn8QLP5/Gmo9L+e5EB1p1Z8mYRiWwfE42N581utd8LvwojKIoekq9Wltbyc3N7XF1fySNYXe73VRXV1NeXk58fDyzZ8/uthgRDCRJ8snVmsxmDFE5qOLzCBOO4NLpsLfWoVELxISpsKlVlNki+fl5V/LNur95tiP+8FmkjD2D8Qsuw9Rcx4nvdmNoayH28rMx/PC6p59+mhkzZpCSkkJNTU1AF10gkaAgCD362DY0NHgc2eTSJpPJ5FPwL/9ERET0WW4X7Ej3dCNUbB0hREV3oCfntOw4XrlhBnUGGycMNsI0KsanRqHtJaXQ9T1VKhUHDx6kvb29V7GVGa7pEX0hiiI1NTWUlZURExPDjBkzhrxjxztXW9rmwmCXyNHBCZMBSewc7mk3Gaja9wlRSZ0dbZWtNhB+FB5VD+KUOnkO6Qmj+Hr7e5yzoIinn366s+JEq6WyspJZs2YN6XH1hEqlQqfTkZn5Y2OJt1uXPGqnqqrKp8bUe/FOHs2uRLqDI5ii+5vf/IZ3332X+vp6zjvvPBITEzl8+HBQtg0hKrqDJT02jPTYML9fbzQaKSkpQRRFoqKiKCgo6LduNVAj82CKriiK1NXVUVJSQkREBIWFhcMWBXj7XTzxcRljzrsWrV7LGZfc5Hk8Pnuc59+jJImqNgsLfnojdQY78RFatOFRiG4XUy7qrKuOTEwjLiyRuekqLps0g9zcXM477zzPNr777ruAji9YUWVP2+nLrUuuMTWZTJ7OK5fLRVRUFHa7nYaGBhISEoiKihpwXfTpLLrBchh75plneOaZZ4KyrZ4ISdEdrkWCjo4OSktLaW9vZ/To0RiNRjIyMvy6IAIR3UCi4r6QJIm6ujpKS0vR6XScccYZQ+o01R9NJkefKRvo/FtqVCqum5XJCzuraTTaGXXmUlRqVWdnklPEZHdRkBnDkrE9b+vGG28cit3vl0DEu7caU7kt/NChQ1gsFlpbW7uZAsmRsT8etqej6IqiSEdHh9KRFsp0FduCggLUajV1dXUnfWTP+vXrqaysJC8vj6uuugqAZqOd1S+8yZ4qE9r0CcREhqM69G+e/PN/0Z/k9ubGtnXrVr799ttex/i8/fbbLFq0iH/961/ce++9PPHEEyQlJVFTU0N7ezurV69m75tPY1LHkFt4Jk0l3zK26LJu25EkCbckkREbxqpLJ/Lh4UY+ONJEq8WBJEFSpI5rZ2awcHwi1ZUVfn1G/RHMNuDBIpsCCYLA+PHj0el03dpgGxsbPQt38swz7xSFtynQ6Si6RqMRSZJCwksXFNH1wVtsc3NzPWIrE2iedigE2mAwMGrUKM4991xKS0v5x4uv8+HhBvRpeVjL9qMt3kvaJb/iUJOZn97zOPOz9cwYl0VdXR333nsvq1ev9lyoV1xxBQ6Hg0cffZQbbriBt99+m9LSUtasWcO3335LeXk5b731FpIkeRaMbrqpM01QU1Pj0y8v88tf/pJ///vfAKRGCJA8npj0XGwdbbTXlBCX5etha3a4yY4LIzW6UziWzcjg8sI0DFYXapVAXLjGJ5ocaSbmQ1Ey1lsbrLcpkLxwJ0/ZkAVY/gIfSaZAQ00o2TpCiIpusNMLHR0dlJSUeGr9uoqtTKBj2O12u1+vVavVOJ0wA9DcAAAgAElEQVROv1576623cuTIEX7729+y8LwL+ai4DVtrHTmTCnFPnYfb6cDaXEOETo3D0EDF7BXw3Wbmz5zKe++9R0FBAVqtlv379yNJEm+++SYvv/wy4eHhiKLomfwAkJuby1VXXcVvf/tbzwgfmd4+h3/+85/U1NQA8NwzT7Dskef55sPXGTPtLIwN1T6i6xYlbE6Rq6an+/xNtWoVST20Yo80hrsNuD9TINm/1mq1smPHDo8pkHdkfLImOwwlsugqke4QE4xx3F3Ftj8XraGaCKxWq/32z92wYQO7d+9GkiQOVbeijYxFK0ggCNQd3gtAev4c+G4XsSmZVHz6NlFj0lmyZAmLFy/m008/5b333gM6/XyXL1/O1q1bufrqq7FarTidTk+qIzMzkxdffJH58+d7Rvh4fxbQGX099dRTZGZmYrfbueWWW/jkk0/YuXMnu3fvZorOwMHULBrq64mL7zQYEiUJo82FS4QrCtM4M9e/i2WkjWCHk2/tKAgCer0evV5PYmIi4eHhNDQ0ePwo5EaPEydOeKZ5dLVMDPVJwLLohoKXLoTguB4Zh8Mx4IvHYDBQWlrqEdvs7Gy/bsUOHz5MdHS0X+NiamtraWlpoaCgoN/X1tTU0NbWxhlnnNHrazo6Ojh+/DhGo5G8vDwyMzP5zYZDNJscROp7/+50ixIGq5MNN8/yqzTOX9555x0WLlzoSTG43W6cTmeP0VqL2cFDq5/FNGYRNqeIBJyREc1lU1OZmhnjIzZvvvkmVVVVjBkzxmMAb3G4+fWDf6Il93zabG6iwnRcODmZZdPT0bnMVFRUMGPGDADWrFnDypUru+2DLGo7d+6kvb2dHTt2kJaWxty5c/nkk0948MEHufzyy9m4cSOrVq1Cr9dzxx138NZbb3Hdddf1+BnU1tZiNBqZOHHioD5LSZLYvn17UNzP6uvraWlpIT8/v8fnnU6nT4pC/re8cOctxCNt+GRvbN68mVtuucVzhzZCOHXG9cgMJOoxGAyUlJTQ0dExIH/YoRrD3lfJmOzn0NbWRm5uLoWFhZ59Nlhd/VYHqFWdn5PNKQZVdGVBhM4Luby8HKvV6mmt9fYrSIzU8Y8/rkSUJKwON1q1qtf9NhgMZGdns2jRIr799lveePf/+Lg1ltbKJsTStxBtJqInnc3T77/AM5LEn+69HW1LObt27UKv19Pe3s7bb79NTU2NZ4x8S0sLV111Fenp6ezfv58LLriArVu3MmnSJKZNm8aXX37JkSNHGDduHMXFxSQkJHhaf9vb23v9DIJdejYczRFarZa4uDif/GfXaR7Nzc0+wye7piiGet5ZoMgG5qFCyIpuIHQVW2/hCoShanjo6bWyp21zc3OvnrbxEVoajfY+xdQtdvpNhGt7f80FF1zA5s2b+fOf/+zxMGi3OHn+jY1832ynoc1MbFwcF59zFkumpBIb3nkr6na7qaqqory8nMTERI4ePYpOp+Pw4cMeo/GEhATOPfdcIiMj2bNnDwcPHuTSSy+ltbWVyspKYmNj6ejoQKfTMWrUKGJjYzl8+DAPPvggy66+hg2fH0ZIzUN02NDExYPbibV8P5qYJJztTTy+9RgrxjqxGI3ccccdPPLII+zatctnjPwVV1zhGXTpcrmQJInf/e53VFVVsWrVKoqKili3bh133nknTz31FDfccAPbt28H6DPXPhK7yAY6Cbi3aR7etcU9TfPwTlUE23PZX7qa3Yx0QlZ0/TnZgyW2MhqNBqvV6vdrB+K9YLVaKS0tpaGhgZycHIqKino9mS/MT+G5HZVE9mEMZrA6WDg+uVcjH4DCwkKWL1/OzJkzeeONN3jqr38ndtI8Dn21E3VkLCqVGoexjR0fbuSO8kOMyU7n8ovO5cMPP6S1tZXHHnuMl19+mbq6Os4//3z27dvHZZddRnV1NTExMTz44IO0tbV5pjiLosj48eOpr6+nvqGRlPHT0U2cywkJPlz/e5IitRQVFRGRU4CpYQthGj2a6EQsFQfRxqYSPWUhxqM70MYlY6w6zHYxkQvHxPPWW2/hcrmYN28edXV15OXl0dra6pOv1Gg0vP3229TV1XHs2DHGjRtHWVkZBw4c4IYbbkAURUaNGoXFYmHz5s195jqHsslioARTwHsbPum9cGcwGDymQHq9vlv783As3IWS7wKEsOj2RXt7O6WlpRiNxm635INhqMrA5OqFI0eOUFdXR3Z2tl+etkVjk1j/VQ0dNicxYd3FweZ0IyBwSUFaD7/9I0lJSZ7cbHVTG612aC6vJCo1B5XkIip1NJaWE4guB2EFRTSbO3j3w+3kJCeTkJBAR0cHCQkJJCcnU1lZyZlnnklFRQWTJk1i165d3Hjjjbz//vtERUWxc+dOCgsL2bBhAy5tBBVGAef2A4Ql/4fkmUuoKq4iMiGNORPS+XDPYSInFaHWalHrI7E3VhA/6yeYS/bitppInLeM1r2bOHpCxbyUGKqrq7nzzjv5+9//jiiK3HzzzVx//fWUlpaybNkyJk6cSG5uLjt37uScc84hKiqKhQsX0tLSwoYNG1i7di1JSUk4HA4efvhhnnnmmT6bS06VSDdQejIFEkXRM83De6qDPJK9p9riYBFKvgtwiomut9iOGTOGadOmBfUEHIr0gsPhoLq6mo6ODuLj4wPytI0K0/CHn0zi4feO0mKyE6HXoNeocLkljDYnGpXA/ReMIzcpss/tuN1u9uzZQ3Z2NrsPFWPsMBAZm4m1oQJtZDSG6mKsHc1EZY5DJUmo1RrsYZk4Xe00NTYwceJEqqqqEASBnJwcPv30U0976wcffMBdd93F+vXrKS8vx263s3jxYp569u+Yo7LQR8YiOK2EaVUY9m/G2d6AZvQZbNv7HbrkXCw1R1GHR6EJiwKVGkkUkVxOBLUaR1sdCAIq4Pyll7Pt/Y3s3LmTmJjOxbmmpiZmzZrFVVddxf79+5k4cSKpqame8StXXHEFs2fP5rXXXgN+XP02Go1Ap5AsX76818/tVI90A0E2+YmM9D3X5JHscmTc2NjomQLcU4piIPuupBeGCe+TtL29nZKSEkwm05CIrUwwF9K8PW0TExMJCwsjJ288bVYnEaKTmHD/SnjGJEXy7NVT+eT7Jt4/3ECbxUGEVs0lBelcmJ9KRlz/HhMPPPAAAK1mB3/dXsaXpc00ffk2EXEJjD1vOTabFVEU0YeFodPqsDrcOAxNjHZ8zznxOgoLCykoKOCzzz4jPj6ea6+91rPtu+66C4AFCxawcuVKHn/8caw2G+qsqbhqy4iKT0GfmgOCwOiiK9Ho9KTmzyIsMrpz8OfkBag1GizVhxHUndGR09SO6HYhuV1IkohbkogK73xu3rx5HDx4kOzsbJKSklCr1T6LrllZWezcubPXCpRrrrmGK664gt///vf9llGN1Eh3JJV/9TSSvaspUEtLi8cUKDw8vFtkLJsC9YbBYCArK2s4DicohGzJmNvtprm52UdsBzMa3B9aW1spLi5m7ty5/b7W5XKxfft2Fi9e7PP4X/7yF+x2O4cOHeIPf/gDeXl5FDdZ+J/NB/ni/XdIK7oatyhxRmYMN83PYV5e964vGe+L/oUXXmDFihU8/fTTaLVajEYj1113Hf/93/9Nfn4++fn5NDQ0UFVVRXt7O//zP//DunXrfGaxnWi38dftpRysMRChVWGz2XC5XOjD9Oh1P0bfdpeIACyZksotRZ3G0aIo4nA4/Pr8D9Z08NB73xOpU/d5MZ0w2LA5RVSqztdIYme5mSAIIElIgNstMTpG4u5pvl4FcslTT9v/05/+xA033ODjDtaVxsZG9u7dy9KlS3t9TVlZGYIgDNo822w2c+jQIb/Oq/44duwYERERZGdnD3pbw41sm+pdymYymbpN85D/La91LF26lHnz5rFq1aqTfAQ+nHolY42NjXz77beMGTOG6dOnD8stVdf0gtXh5mi9EbtLJCFSx/iUSM9FLqcXZGGUPW0rKipITk4mJSWFvLw8bv7d/2NHSSvRMy/D1lBO/ScvEjm6gK1b97H97QTGhZspzEnihhtuYPPmzYiiyOzZs3n//fcpKCjg+uuvBzpviYuLi5k4cSIXX3wxABUVFVxwwQUsW7aM1atXk56ezk033eSZI9W1IUOr7rQYtNvtiDY3er2O8OjobsIlSRJqlQq1amBRXnWbFbcfUWKYRoXd6cYt4vNegiB0jjOWJPQ6FSsvmsT0jHBMJhNGo5GGhgZKS0txOp3dFnaioqJ8yt16IyUlpU/BhZEb6YZq+29f0zxkEfae5mEwGHjkkUc8lqsffPABZ5xxBpmZmQP+uxQXF7NixQpaWlpITEzk5Zdf9mkKCgYhK7rJyckUFRUNi9jKpjByyuDR1Y+RctbP2HyoHpfYeTMgSRLJ0XpuOHMUxZ9vYsWKFWzcuJGjR49SV1fH9OnTefPNN3E4HFx55ZW8/vrr/Or2O3j/0z3EFy7G8NVGwlNySCu6hoYv30IXEUXq/J9S/Omr/PqS6/juu+84cOAAF110EQ0NDcTHx3sEF34shRIEgePHj7Nu3Tpuv/32bseydu1aqqurue222wgLC6Ojo4OYmBicTictJypwGRoQJTURUZFoerl4Owd4CkzNGlgeTSUICP1NCf3hdVfPzOSdg/U4XCJInZ13kiThFiV0GhW/PDObs/I6F3S6ljy5XC5PtGQymairq8NsNiMIAkajEYfD4RHi/m5he0LJ6Q4POp0OnU7n0+Yr+4FcddVVrF+/nsOHD3PZZZfhcDioq6sjLa3vxePeuPXWW/n1r3/N8uXLefXVV7nlllvYtm1bsA4FCGHRValUw3ZyuVwuHnroIZxOJ2cXLeClf/8H18ffMq7oEso/e5v4rPGodXp0My7g0a3Hyaw+wZzvv2fUqFFMmzaNs88+G71ezzXXXENZWRlr167F6XQy89p7UO050pl31OoRVGoElQokCUGlRiUIiIKGtw7UckmaxIwZMzAajcyfP5/q6mqffdRoNJ6hjOXl5YSFdeZyt27dSk1NDYWFhTQ0NHDbbbfx8ccf88UXX2Cz2YiMjKS8vJzy8nKSk5O5btFUmj6tot5gJTaiu+janW7UQmfDw0BFd2JqJCqhb7GRJAmNWuDCyclcOS2dl3ZXs+W7BkSpM+c1Y1Qcvzwzi7l9tBBrNJoeGwG+++47tFotoij6tMd6R8Nyg0d/0x5GmvH4qSi6PSEIAqNGjeLBBx/kueeeY+3atVx++eWUlJSQmpo6oG02NjZy4MABPvroI6Azv3/HHXfQ1NTk82U+WEJWdIezI8btdrNgwQKcTidbDpRB6jjy511Ie+X3RCakkbfgcr7f+goROjVaNXxRXM8ZuzoNZbRaLRs2bPBEnQ888IDnVv/Pr7+KNjqR5DmXUr/r3yRP6zTmTiu62vPemQuu5nuzxL+uuNCni6uwsNBnH2NiYnC5XNxzzz0+j7/wwgvdjmf58uWIosiuXbvYsWMHMTExzJo1i+joaCRJ4upZbv7+WTktZjtxYVrUahVuUeq81ZcgOUrHnYvy+u2G64285EhGJ0ZQ0WIhqpcWZrPDTXpsGJPSohAEgYeXjOe6SToMZjuTJ4wlTDuwW2hBEFCr1cTGxnoaJqB77WltbS0Wi8Vn2oMsxrKVYjAtIpVId2BIkuQpGdNqtUyaNGnA26quriYzM9PzRatWq8nIyKC6uloR3ZPBZ599hiiKVMSciV5zHJVK3Xm36znBJZwOBxartTMHmTubuoN72b17d69RZ8KsS5C+/wpTxSFElxOVvntplyAIqAQJq9Pdp8j98pe/9Os4JEmisbGR4uJiioqKGD9+vM9tmyAIXJSfSk5CBM9/UcE3tYYfZsmpiNSrmZUVw/Vzc8hL7nlf/eW+xXn87u0jGG0uovQ/LqhJkoTJ3nmsD5yf1819LFqvGrDg9kVvtacWiwWj0egZ024ymQCIiory5IyNRuOAy53k91Ei3YFhNptxu91Kne5wMFyRbnV1NUajkdWrV9NssnPV33aQf9FyVCo1kYnpgITT6SBj7qVYrVYiIsKJjU/g23oLK5YvZ9KkSZ4TomvU+d5ze3Hpz0OrVmGqK+vx/UVRQi0IROoGLzQtLS0UFxcjiiITJ04kKSmpx89REATyM2J4clkBbRYH5c0W1AKkxAQ25qgvchLCeeqnk3nm0woO1xk787yChCjBhLQo7lwwmjFJwZ9UHAg9TXvwtlIsLy/HYrFw+PBhbDabj8F4IJOBlUh34MjeGMEQ3ezsbGpraz1exG63mxMnTgS9EiRkRReCZ/XXF9nZ2axevRqQfQx+fM7ldGKxWpEkifDwcHQ6LSCQM+8niKj7rdW9ZmYmj39UAkDCzIvozFb6XnwuSeSygow+23j7o6Ojg+LiYsxmM+PGjSM9Pd3vizw+Qkf8KP+6hwIVj1EJ4fzPFZOobbdR2tRpxp2bFEF2fLjf2xgIgxE5byvFxsZGYmJiyMzM7GYw3tTU5GkCiI6O7rOUTYl0B04wvXRTUlIoLCxk/fr1LF++nPXr1zNt2rSgphYgxEV3uImP0KFWCVjtTkSXGdEtEh4R/kM08+NFZHW6mZMaiVrt7rMr7cL8VJ77opIWs73HtXynW0SvVvPzuQP7pjWbzRw/fpy2trZhKa0bqJBlxoWR6UcTBwTXCzcYeJcI9mQw7u3e1djYSGlpqU9rbHR0NHa7PWjHdbqKbrA60v7xj3+wYsUK/vjHPxIfH8/LL78clO16o4huANgsJqYlSexusJIaG4Fe7yu20GnQDbD0jDTsDZY+RTdSr+H55YXc9OpBWoxWHC4RjVpAlDqdwfRaFc8sK2BUQmC32TabjdLSUurr63t1KAs2w5HuGUl2gtB/xNybe1fXUrbW1lbsdjs7d+7stmgXaCnb6TSmBzpFNyIiImheDhMnTmTPnj1B2VZvhLToDkd6AX4cwd7e3k5RlpZyuw6bG3SdZaMeREmizeLg7LGJTEiN4nBz//4L2QkRbLptDv/csoedDQIGu0SkXs2lU9O5pCCduAj/WzplX1t5FdYf05zTEemHbrZgbGcgXwRdS9lqa2sxGAyeidNyTfHx48e7lbLJP70J6+kY6YaS7wKEuOgONWazmZKSElpaWjyz07755hv+KzeFtXtbqGq1IEqgFuToFC6YnMJtRWM8pUn+mN6EadUU5YTzs7npAyrq9va1TU5OZt68eYSH+5cX7Wm6MMAf/vwo4xZfx66yVpxuiXGpkVxSkI7W0szevXtZtmyZz3ZMJhMbN25k3LhxnkqPefPm8eGHH5Kenk5LSwv3338/t956K+np6Vx44YV0dHQwbdo0n9KtYLB//36ffZg3bx7Q2VZ8oMrAjsNmdHo3mUl2ZufEMSk9ivAuFRF79uxh0qRJfZpjf/zxx1xwwQU89NBDFBQUeJos5Fbr1atXU11dzapVq/j73//Oa6+9xpVXXumpZpGRJAm1Wu0ZRuldZyqPaO+vlC0qKgq9Xq+IbggQ0qI7VLeb3p62o0ePJj8/33N7rlarSQgT+NvVBRytN7KrtBWT3U1arJ6F45NJjfnRo2CorCBl5OL+kpISYmJimD17ts9Kuz94Txf+5ptv2LJlC6qUcbzxVRXC12sQbSYiEjP4ftxMnv/b01xy2RUU6iU2bdrExo0bufPOO5kxYwZbtmxhwYIFvP7669x9992e7e/evZvbbruNAwcO8Pnnn5Ofn8+KFSvYtm0bl156KS+99JKP/0Mw+PTTT3324fnnn+dodRNNQhyG+irC9HqS0zI4VlvFByJMyC/EWb4XyeVg7NjOwZnx8fGMHj2ad955h++++46HH36YNWvWMG3aNC67rHOUfENDAwkJCajVatra2jw+vN4TkT/77DMuv/xyKioqmDdvHtu2bWPJkiU++9tXxCyPaPdeKJJL2WQxlkvZJEnC5XJRVlZGTEzMoJy7QoX29vaQKheDEBfdYGOz2SgrK/N42hYVFXVzbJKHUwqCwOT0GCan9x4JaTQav6f89jWypyuSJNHQ0MDx48fR6TpdvgZ64snThe+77z4mTZrEmZf8nFWfVKJRqZhw3s8o+fh1dBoV0Xo1rSr4srSNeqmBP9x4CXV1dZ7ZZLW1tT4R2uuvv94tohMEgcOHD3P33Xdz++23o9PpPCPE/SWQdJK8D9u/3I07dRJRms5mjCkLLmTnplfJzptAW2MdNpebmPHziG4v5vbbb+fJJ58EOu8gbDYbWq2WqqoqUlNTPbaPgOc8mDhxIitXruSJJ54gLS3NZyLygQMHyM3Npby8nJ///Od8+OGH3fYz0Oi0p1I26Dx/d+7ciV6vp7W11ce5S84RB1LKFgqE2qgeCHHRDVak63A4KCsro7a2tt9caKCeuv5O+fWeHtEX/tba+suWLVsoLi4mNTWVc889l5v/uBp16ljUalVn44cAMZljqdq1BUP1MTJnnMe3JQZW3ns/F194PpWVleTk5JCZmUl9fT0LFy7kiSeeIDY2lqioKNrb21m7dq0nvXDw4EF+/etf8+CDD1JYWNjNf7Uv/D3OrvsQmT2JDqOFjLwzKDvyNSqVmrEFs2iqKSM5M4eYcC3tdhHB0dnWK7+PSqWipaUFl8uFKIpoNBpqa2s97yPbRh4+fJg1a9Z4UkPyROQvvviCc845h6VLl/L0009TV1dHTk5Ot/0VRTEo57LcKTd69GjPY11L2ZqbmzGZTD7CLQtyeHh4yEXFoTY1AkLY2hE6Tyh/b997wnvhKT09nTFjxnSLzrpSUlLiGTfTH/5M+ZUpLi5GrVaTl5fX4/MGg4Hi4mIsFkvAtbb+UtJo4o43vvXpEOuJdquTFXNHsXzOj6VsRqORjRs3cvXVV/f6e1354IMPKCws9DunW1NTg9lsZsKECX6/h8HqZO2OStJjfhymWHfiBNE/3H7LtJgdjE+J5OIp/vftP/nkk/zkJz/xpCT6o7ecbrAsIl0uF19++SULFizo83VdS9nkH7vd3qMr20jy5+3K9ddfT2pqKv/85z9P9q505dSzdhwMLpeLyspKKioqSE1NDWjhKZA5acHI6XrX2ubl5Q2pZ3CTyYFK6D+iVAmd9ozeREVF8bOf/Syg97vooosC3sdAcbjEH7rd+j4mrVqFyR5YTn3hwoV9jvPpSm+j3OUoerD4m6boq5RNjopli0yz2YxWq+0mxMMx+8wfOjo6AvoSHgmEtOgG+kfvOr127ty5Ad3ewo85XX8IdE6aPLgRTk6trU6j8uvWRhQJSlvyQAi0RFCvVXc6k/VT3uVwicSGB/b5BtPwJhhfpG63e1Db6W3Kgzz7zGQyUV9fj9FoxOVyERkZ2a3bbrhrhENtPhqEuOj6iyiKVFdXU1ZWRlxcnMdRayAEEr0Gkv+VF9JOZq1tfno0KkHA5Rb7bDtWqQTOGtv7RIuhYiCRVUyYhpyEMBqNDuJ/qHnuSSodbpH89MDOiZFmYj4UBuaCIHhK2VJSUjyPe5eyeRuL6/V6nzyxXMo2VFGxIrrDTH9/SO+SqujoaKZPnz7omr6hGE4JncdiMBjYsWNHwLW2wSJMq+YnBWm88/UJYsN6viU32V2kROsoHKCX7sngrLwEXtlbS6RO7XFq8z62RqODzNgwsvxsRZYZaSbmw1mj608pW01NjWfcTtdFu4iIiKB8QSiiO0KQJIm6ujpKSkoICwtj6tSpQTHEgODX3oqiSG1tLcXFxahUqgHV2gLs27eP7du3I4oi8+fP56yzzsLudFPSZGZPeRttVieNx7/l4qKZzBqXSXgv6YEbzhzF0Tojh+uMdBz5jPRJs6jc+X/knnsdRz58hZQxk5mgqeV///cbbrzxRt555x1aW1u56aabeOGFF7jpppsC3vehJjs+nKVTUnj/cBNqAZzuzskTRpuLDpuTtJgwLi9MG5DwjSSxPNmNEb2VsjkcDk+nXVtbG9XV1T6lbF29iv3F20s3lDilRFeuXy0pKfFMUkhMDO5tcKCRbm8C7V1rq9frycvLo7m5eUCCC7Bt2zbuu+8+z//f+duVtIdnYnYL2NsaiYqJAZWWd8MT+d1v72JJ0WwWzpvtGVk/evRoT+nYw5dfycelRlbvbsauicThFrG7RCamRnHZjERsHYKnwL+9vR21Wo0kSYSFhQ15sfpA86gFmTFkxIbxbW0H2w420WF3kxWt4ZwJiYxNjkQ7ABe30znSDQSdTkdiYqLPteh2u328iltaWnosZZNd2Xo6LpvNhtPpVER3OPE2vm5qaqKkpNMmccKECYOuX+2NQBbSehNoudZWkiRPrW1bWxsNDQ2D3r9XX30VjVZPuUnFrPOW8PlLj5M1Lh+r0UB4tJ7UmDBSRuWhmXYZO/e+R2XpcYqKimhra0OlUrFixQrUajU/mxlL5Yx0rl0+jbWtn/LQr2bzt6e/4IbrfkZ5eTkPPPAAjz32GHv37iUpKYk9e/aQnJxMTU3NiL0IkqJ0nDMhiQRrDdnZaYP+Qh5pYjlSRbcn1Gp1tyGUXUezNzU1UV5e3mMpmyiKnkaVYN3FDhchLbrwo4C53W7GjRtHSkrKkJayDCa9INfaWq1Wxo0bR1raj7e0A2kD9uacc87hscceIy4uDqtahc0NSVF6cqfMoKO5geSs0ZgMbQCE67Q43RKNrRbmzJmDwWCgsLCQ3bt3++TZdFotWfHhROtVPPf3v5KZmcmOHTvYv38/0dHR/N///R+rVq0iPj6eJ554gri4OGbMmOHpwpMbDYIlBCOhRMkbJdINLoIgEBYWRlhYGElJSZ7H3W63Tz1xY2Mj69at44033iAiIoKHHnqIOXPmMG/ePM4666xB78err77KY489xpEjR3jqqae44447Br1Nb0JadCVJora2lpycnCFpFuiJQCsSoLNxoLS0tM9a28GK7syZM5k5cyYA//y8nHMzOttzpy3oXgt77s9uxuES0S+8hpuWTPB8bmeffTiJcBwAACAASURBVLbP67Kzs2lpaeGBBx7weVx+nSRJiKKIy+Xirrvu4oUXXiApKQlRFDudvH54Xj4u2djFu+PrZHCqiuVgS8ZGKvJMO+9F8NGjR1NQUMAf/vAHwsLCeO211/j666+DIrqFhYW88cYbPProo4PeVk+EtOgKgkBhYaFf7bPBQqVSecSkvxNcbgHeu3dvv7W2gXgv9EerxdHvHDGdRoXVLHaKby+vvfLKK3t8XD5+WViFH5oPZOMa72hZ/tuIouj5Hfkx+Xjl3/cnKh5JJuanqniHAomJiYwdOxZRFHnttdeA4J0bU6ZMAYYuKAhp0T0ZyJaNLper15VWp9NJWVkZNTU1qFQqZs2a1a8ph7/eC/4QrlXjcIl9DrJ0ixIqCGgMkHxSu91uj1D0d2LKz3d9nbcAD1aITxYjTSyHok53JNPe3u4T/Y609FNvhLzonowPurcUg9vtprKykvLyclJTU5k/fz5fffWVXxfUYNML3szMieODw41E9jLeHDq9BgqyYlCr/Pv8ZGGUzVnkn4EifyZdo2Lv9+kqxN7PD0akRlqEOtLEO1To6OgYUN399OnTqaqq6vG5hoaGIf/iCnnRPRl0XUyTa21LSkqIi4tjzpw5ntIvf8VUfl0wLsCpWXH88c+riIiIIHd8PpXff8O5P+u89Xe4RSqbLVS2WQnTqPjk+ybmjI7HbjZQXl7uyQvLeIsgwM6dO4mPj2fMmDGsWLGCN954gzVr1nDPPfewd+9ebDYbW7ZsISMjg8WLF7Nr1y5uvPFGv/a7NyGW27erqqrIzc31GB1554ZPRp54pInl6Sa6Ay1PPHDgwBDsjf8oojsA5EhXrrUtLi4mLCyMadOmdTsJ/BVd+TY6GLeI0WEaCrNi+a7RjlUIQxQlDC2NvPPK8zR2WElZtIKGd/9MaWom/07KxNpaz4P3/A5VcxkbNmxg4sSJmM1mcnJyKC8vZ9++ffzv//4vgiCwf/9+7rrrLjZt2sQ999zDF1980e39bTYb06ZNY9KkSTQ2NnLo0CG/nNa6IkkSzc3NFBcXExkZyezZs4mMjPSJgL0X7LwfU6lUvaY2goUS6Z5cQnFqBJwConuy0gutra0cOXIEgMmTJ5OYmNjjvgykxGwwovvoo48SFRXFN3u/5K/rXmT9lk85YnHy2qaPaLOqsJ0oQbQYMNSUkjrnJ9Rsf5XErDze2F9LWPGXZKQkMOv8K3jj+Wdpbf2ahx56iIcffthzbPKx7N+/n9LSUqKjoykpKaGyspJFixbxj3/8g2uuuYZ//vOfvPLKKx4nq9WrVzN69Gjuvfde1q1bxz333IPD4WDFihVcfPHFLFmyhJ/+9Kds27YNgJqmNj7Zf4wNr79KZFQUt911N1s+2s6yy5b2KKZdRddoNLJlyxby8vLYsWOHZ3TP1q1bcblcSJLE3Xffzd69e1m6dOmAPuuRJpaiKI5oG8ZgM1TdaOvXr+fee++lra2NTZs28eijj/Kf//yHyZMnB2X7IS+6w43BYKCjowOj0cikSZN8am17YiCmN4NBrVZzxx130NzczOf/2YKprp6mE1V02Eqx1haD6Maw99+otDoMDTWYTEaEukra1q/BbrOgsrTw8ec7MbW3EBERwa69+2mqr+XAgQNYLBag01M4PT2d2NhY9u3bx6RJk9i9ezdtbW2MHTuWjz/+mK+//prc3FxSU1PRarX893//Nzt37mTjxo2efdXpdDgcDjo6Ovjggw84++yz+eSTTzhQWsen+49SMO8cYuPiEQQ4Wm/io6072fblXmZOGEVTUxNLly7l3//+N6Io8otf/IJVq1Zx2223MXXqVD755BMWL17MK6+8wr333uvJB2/atAlRFNHr9cTHx1NeXo7b7R7Qgp0S6Z5cDAZDQNaa/nLNNddwzTXXBH27MiH/FxquSNdsNnPw4EEOHDhAREQE48eP96s2OFB7x2AtpnUWdAvsKW8je+ZikgrPJ/mMInKX3kpH5WHSZl+Mre44MWNnoMmdRXT2RBLGzyQ+JYM7//gUCfHxJKWP4mhpJZMKphMVFcUFF1xAVFQUc+fOJScnh/DwcMaNG8eFF17IunXryMvLIzExkQsvvJBly5Zx8803097eTlpaGunp6Z4RNt643W4yMjIoLy/H5XLx2f7DHG12kZ2ayJiMJLQaFRq1iuRoPdFhGuqNTiYvuhytVstHH31EZmYmgiBgt9spKipi6tSpQOf4IPkLUa1W88orr/DMM8/gcrl46KGHSEpKQq1W43Q6PXljp9OJ0+nE5XLhdrv7rSYJVomSUqc7MEJxagScAqI71NhsNr777jt2795NdHQ0Z599NjExMUMipMEoG3O73Tz77LM8++yzTJq3GKvTjUolgEqFoFITM2oKDlMr2qg4LA2VCGo91rZGVGo1ICCi4uMN/0tKZg654/9/e2ceH1V97v/3TDKZbJN9zyQkIXvYEkJARGsV1LbUqtUqLtdi/dUo7mLVW71oxRYULVpUEJRWuWL1KvZKtbcCvdW2LGHRhJAVyL5PkslMMvuc3x+5M85knSQz2Tjv12te8ILJOd9Z8jnPeb7P83myCAgIQJYwn56eHgRBICoqiuTkZCIiImhqasJisfDFF1/w/vvvk5eXh8lk4sCBA/j7+wP95XO1tbU899xzlJSUcN1111FfX8+2bds4duwYXl5eLF68mHnz5tGn0xGYmk9n9Smqi4sGvTaJRILCT8bxOjUmi8CqVatobGxEqVQil8udbq1t44MuvfRSHn/8ccrKyggODiYoKIj3338fo9GITCbDz88PX19ffHx8kMlk9uaNgUJsMpnsQuz4GYmR7tQxE81uYIaP64H+L5qrwx/HgmOtrVKpJDk52V6XW1FRgbe397CjdRwZy3OPHDlCRkaG23rJPy1u5o/HG/GSSqhq0zqNGRcAq1VAYzAjCODTVoaxT8vq1atJj3Y23Wno1nHtwljSopwN33fu3Ok0yddqtbJ79+4hqxX27NnDDTfc4DSqRqVS8dprr7Fy5UoyMjIwegfwxxNNxI9isdis1rMqM5KsEfxvNRoN7777Ljk5OURERJCamopcLnd6TmtrK8eOHeOHP/zhkMcYasPO9vtiMpk4cuQIK1assDe8jFfw/v73v3PxxRdP2KS+pKSE6OhoJ9/b2Ux+fj7333+/29t03cTsHdfj7vTCULW2A2dajSVP6yn/XVeR0G/kDQOuoIKA1eGCG5yyAAEJUUGDGz7kXlKa1fpBojtwdLpUKh22POy2226z/91oNFJdXU17eztr164lPj4eqVTKuY5eXPk4pRIJGsPwm5Pd3d1UVFSQn59PRkbGsDvc0dHRwwqu7fU4/gn934/GxkbOnTtHQkICEonE/pmNt7FDjHTHh1qtnnFmNzALRNddWK1WGhoaOHv27KBa24F4eXlhMBhcOu7AMTyjPdedojsn3B+pVIKvzIsQfxnqPhNybylIJP0PbJGbBLNVIDZYTojf0F12ghtueqxWK3V1ddTU1BAbG8vy5cudUgLeUqlL91ZWQUAuGywuBoOBqqoqOjs7SU1NdbsfR3d3N+Xl5faUiKND1kgddrYStqGE2B3NHo5ruNBEVywZmwIm+kslCAItLS1UVVXh6+vr0nQJT0Wv7vRfAMiJDSLYzxut3kRKuD+nDRr0Zity734B8JJKsFjBWyoQKPfm4rlD7wQbrVbigsc/xcJmvWmrt12yZMmQs+liguTIvCSYLNZh/W37RUogMfTb9VitVmpra6mtrSU+Pp7ly5e7dZ6co5gPdIezMZ4OO/j2+ytGumNDr9ej1+tnZE53xosu9H9hx7OTbCu8h5FrbQcy1trbsTzXXf4LgiCAYOVnFyWw5cBZAuTeLFAGUd+po01jRBCsWKwCEgnMjQzgisxIAnwGfx10Jgu+3l4khTuLrkZvxmix4i2VEOTrPez7ptFoqKiowGg0kpWVNaKHrY+3lNyEYI6c7yI+xHfIY7ZpjKRE+hPq72NvnqioqBhRzMeL7e7n3LlzxMXFjVnMRxNi2zw8X19f+77ERJzYLiTR7enpAWaely7MEtEdKyP52rqCJycCTzTSHdi2mxMXxC+uTOOtf9Wh6jUSIPcmwdsLk9VKtMKH25YqOVmnRme04i9zzi1+8s4b5F/zU+ZaGzj8z3ouvfRSmtU6TjdpUfUakCBBoD9nnBOnIDH027Hcjnnb5ORklEolhw8fJiQkhLKyMhobG+nu7qawsJAnnniCBQsWoFAoiIqOJjwgkcZuCPGXEfh//hF6k4WOXiNRgXJWZkbxm9/8huXLl7N79242btyIUqnEbLWy55P/obzDgG98Jt4SCTlxCsyNp4kPD6KgoGDQ+7Vz504yMjLYv38/ubm5mM1mVq1axXXXXcczzzzDX/7yF+6//35KS0tJT0+f0GcD37rUtbW1UVlZSWRkJAUFBchksgl32F1Iotvd3Q0gRrpThauRrlarpaqqiu7u7mF9bV1hOm6kDWe3CJAdq+DF67P5xX9sxCiR0VR3ns0vvkxKhD8SiQRliB9/OFzP8bouQEJYgIzIABlWiwXdyf/miKqF1atX8+qudzj4j6Nce8vP+NdfPkYRHIJe14cg9eaFkq8J8ZdRsDAHnU7H4cOHkUql+Pv7s3TpUn72s5/xH//xH6xevZq+vj5iYmJ48MEH7a+7q6uLOXPmcPVVV/H27t1c/aNbOFnXTZNaj4T+ke/fTQ8nNdyP+vPVdi+G1157jf/6r//iiiuv5tHnX8XgE0xvRyNZi3WcLz3BIZOVmPSFrEgXOH/+j5w8eZL77ruPhIQEmpubnVJJoaGhNDU1UV5eTmZmJsePHyc+Pp6UlBQ+++yzcX0uA9FqtZSXl2M2m1m4cKGTaAzlxOYYGY+2YXchia4Y6U5z9Ho91dXVtLa2kpyczIIFCybUauvu4ZTjea4jgiCMarcolUiIUsgJCgpCovYl2k/g6aefpqGrD/Pc76Cqr8YvKByz1IsjBz4g7ZIfQut5ehVWLrnkEna/8w41bT0YtGq++vMHnD5xhFvufpjK0m8w6XqZvyiPr48f48Df/s4Vl11qH6+yefNm9u/fb799vvLKK/n8889Rq9U899xz/OQnPyEzM5P169fz4osv4uPjQ19vL1kxCjKjA9GbrQgCyL0ltDQ3c+LYN0RERJCUlIRGo6Gzs5Nrr72WBzf+jh6zFxlpc5Clp3P+9Aku//Fa/vbhLoL9ZPzzXCep3irCwsIoLi4mISGBhoYGYmNjEQSB66+/npiYGL766iuys7PJzs5GLpejUqkARt0MNVmsdPaasAgCAT5eBPs5t+OazWbOnTtHU1MTKSkp9sqHkXCMbm0Mt2Fnmxdm+y5MZ0tMd9Dd3W2vs55pzN5Phf5flIqKCv75z38ik8m45JJLSElJmbChjKei17GKru0XzOYlMJrdolQqpbCwkIyMDE6dOkVURi4dijS8jVpC/LwJ9fciLtiP5LQMFi69hOrWHgxe/lRXV6PVWwiPjEUCGPQ6/AMV7P/jH+xrLjl+BKPRwJzM/jRBTEwMfX19bNmyBaPRSHx8PCtXruSjjz7CarVy/PhxLBYLPj4+lJaWsmXLFmJjYzEajfaqEYlE0u8N3KfheFERjY2NLFq0iJycHLy8vNiwYQO/+93vaOnuo/TMGZZ/9ypCIqI5c/gQqQuX8uW+P+DtLcNbKkEh9+ZISbVTp5lSqaS5uZmenh5Onz5NZ2cnKSkpJCUlIZFIuPXWWzl48CCAvUZ7y5YtTu+pyWKlqKaL3x+u56NTTez7upk9xxr4tLiFdo3Bbop0+PBh7rvvPsLDwyktLeXJJ5/kyJEj9ojNarXy1ltv8e6771JXV8dTTz1FW1sbzz77LFu3buWDDz7gyy+/5PHHH+f+++9HKpXyzjvvIJfL6ejo4MSJE8TExCCXy0ds7Jgt2CoXZoqHriOzItId+MZbLBZqamqoqakZttZ2Iow1p+vqc12tXhiYt3XV29ZqtbJt2zbq6uq46ZZbeeJ3j+MlgYU3/D/+8cF2kEjIWn4lUi9vfGVexMxJpaRRzXeX5fJ1TTsKRRCxMVH957ZYqDtXRWR8Ej49aipLv+HqH/6Y0yXF9PT0UFhYyMGDB1m/fj2PP/44dXV1tLa2olKpeP755/H397cXte/evdu+xs8++8xeO2u7QxmqamD9+vUAvPDCC+z5ooiQyFhCo+MA+N7ahwFQpuU4vWdBc7JZe1kyscH934WQkBBKS0tZtWoVS5cuJSIigry8PKfj/+Mf/6C1tZU5c+bYj/Pv//7vSKVS7ll3H4/96kXUOjM/+Mm/8fGbL5KYmsmc9BwOV5TxHl54qc5z78/vJCcnhyuuuILDhw9jtVqJiIigqqqKpKQkgoKCKCoqYt68eVRWVvLrX/+a5557juPHj3P99dczf/58XnzxRWJiYrjxxhspLS21f6f+9re/ERAQQF5enpNR/sCIeLqOThovM7VcDGaJ6NpwrLUNDQ0dsdZ2IoxFSN0ZFY9XbG04jmgvbuxh4XX32gVo5drH7P8Xn74AgCtuvY9mtZ7sZSmUtJuo/qaIZd9ZSXrOAtrbO2htayUsNIzomGikZgOXfe9aslZ8jxvz4vCSSsjNzQVg8+bNAGzdutV+juFuC7///e9jtVo5f/68yyVg/hFKVtz48xFfu0QiQSqBPqPF3gBTV1fHHXfcwZw5c0a8+3FsorD5MsTHx3Po+BkkikiuvnI5NWdOEZ+cxg9u/Tn79+ygr7uLBZdfx+E/19Hwf+3SXl5e9jInrVbrdI76+noKCgqorKwkKCiIxsZG+7od+eCDD6irq2PZsmV0d3djtVopKChwuYTN9udIEzs8bYnpDgZOjZhJzBrRbW5upqqqCj8/P5dqbSeC7cvoysaFO7wXRtokGy8dWgOuVtl1aI1ceullzMtfDoY+ysrL8ZX7kpaWhq+8X7S/f+Pt6EwWFHJvl6ZRDNW55ljPGxgYSEFBgd3DYSQCfb0wWUa/dRYE6O3p5nDFeRQKBUuXLh1zTtAWIUq9vOiQBGPobuWf//MnVl5/K+3N9Wi1Wjo6VPj6+dFSdgwvbxl5l15NalQgR48e5eabb8bf35/t27c7HTchIYGmpiYAHnnkEXbs2MGaNWvYu3cvBw4csEfaV155JdXV1Xz66adERkaSn5/v8ndhpNFJjt+viXbYTQZipDvF1NfXU1NTQ3Z2ttPoZk/hypw0G7ZdZVdaPYcSaFc2ycaDt1SCIHFNdb2lEiJ9BQ4Xn0fhbUGpVBKkGDzzTa0zsTR5fLvJWq2WyspK9Ho9mZmZY/occ2IV/K2yY8T3WN2rR6/pQt2sImuMx7fR0NBAT08PmzZtQtVr5I/HG7nl3v67B5PRyMLvfJ+W5hZuvOsBWurOUvF1EWnz86jp1JEaFWhPWQBOfwdYsmSJk2/Fhg0bnP7U6/VUVlbS09PDT37yEyIiIti1a5dbSqbGsmE3WofdZDFTHcZgloiuUqmctBHsNmx53dFE1ybQFotl1MJ6R9GdaCphNFIiAvrrbEcQKqsgYBWsmDobqFN3MDc2BpMsEEXg4Px4Z6+R0AAZytCxRY42Y6Hm5maSk5NJSEgY8y9xXLAvcyMCqO3UEa1wNrURBCuqzi7Ot2u4YVEMFxdkjFsklEqlfSy31dp/wRKsAipVByqVirDwcHsZYmrOIlJzFtGtM9mfOxLD+VYIgkB9fT3nzp1DqVTaNxEB7rrrrnG9DlcYrbFjqNSE7ecmQ4hnqsMYzBLRdWcnl6uMtVbXbDa7LLqOO83uFlsb8SG+zI3wp75LR0SgfND/C4JAXVs34dI+wgPiSJm/AkHqRVFNF3WdOrylEmReUkwWAbPVSrRCzkVzw/BxcbqwIAg0NjZy9uxZIiMjWb58+agXsOGQSCTctDiet/9VR0O3jlA/Gf4+UrS9vdS1qLB6ybm2IJXVuUq3vZeBvt7odDqqWuvwlctJTk7BR+68fkEQ0BstRCrG97p6eno4c+YM3t7e5Ofne2R/Yiy4IsSTtWGnVqtJSEhwy7Emm1khulOBu2t1bbdsGo2G4uJigoKCCA4ORqFQuNVHwIZEIuGOZQm8dOAsLT16IgPleEklCAhoe/uoa1MT6u/Ngz/IJT7i24ji4rnh5MSZaOjS0We04CuTogzxI9Rf5rKg2YxjpFIpubm5o46ndwWFrzd3XzKH4sYeDp5poeS8CqvFQl5KHKvmK0mN9Heb4Or1eqoqK/nXH3dw8U/uwdhRy1lVM1l5yzBZrNR16vjfg18QmJqP0SzwzaE/cdfNP2JJVvKIx929ezfp6el8+OGH9Pb2snjxYmJjYykpKSE/P58tW7Zw++23j2hHOdlMZMNuIukJMdKdYqbTGPahGEl0HaMEPz8/CgoK0Gg09PT00NbWhkajwc/Pj6CgIPtDoVC4ZUx0pELOY1em8ufTrRyr6cZiNqPRarBarVyeHctNy1IGFfkDhPjJCBni30dDr9dTVVVFV1fXuNqvR8NbIhBibOci/1ZuujyZxAQl3m4cp221Wqmvr+f8+fPEx8czPyWOkwf20d3WxEXfvZKPd7+Bf8H1nPj0D8ikEoLTC0iJ9OVslZHfH67jP576d1Yuzyc3N5fS0lL8/Pyoqalh48aNQH9km5qaSmpqKhEREVx//fX853/+J2lpafT29gL9lRS1tbVue02eYKQNu5HSE2MR4vGOX58OzArRnQrc4b8w1CaZQqFAoVAQF9dfc2q1Wunt7aWnp4eenh6am5vRarVuE+LwAB9uzo0my1dNdWM3iQsSWZiWSKCv+wYc2kao19bWolQqycrKcmv07ugUFxYWxkUXXTTIsHyidHd3U1ZWho+Pj91YJ9BPztaHH+D1D/+Hdk0fVe1aErR6pBKwAv59zTSWFhMk9yUiUE5pQBxX3nwXf31/FwaDgfvvv5+nn34aAJ1OR11dHWfPniU5OZnIyEikUilHjx4lOTmZv/71r/a1uGoVOt0YjxPbcEI8U710YZaI7lREuhNxGhvLJpmjEMfHxwP9X1StVmsX4qamJnp7e/H393cS4sDAwBGFeKC/7Q2rVrh1mux4S8DGgkajoby8HIvFwoIFC9x+y2k0GqmqqkKlUpGenk50dLTTZxUR6MOV2VGcPN/Bv8wmtMV/JcTfBz+ZlHnZ2ZCdzckDn+DtJcVfLuNguQpBEFAoFOzcuROLxWKvSbbNn7ONtT906JB90OZvf/tb+znHm/uejoxnw85qtaJSqWZkCzDMEtGdCsZjeuOuigSpVGoXVhtWq9Welujp6aGxsZHe3l4CAgKcomGFQoFEInHJ33YiaLVaKioqMBgMo1o6DsRstaLR91+kAuTeQ27OmUwmzp49S0tLi928yJ0XX0EQ7I02NsP1gdG5rexr2dKlNPo0sfLWFKIUgyPsvJXXArDq5v9HU4+exwrvp6asmC+++IKwsDC6u7tZunQpNTU1WK1WLr300kHHePjh/i47x+642cpIeeKqqirWrVuHyWSis7NzStY3UWaN6I7XU3e8jLW91zZlFjxTkSCVSgkODnbKc1ksFntErFarqa+vp6+vz37+2NhY4uLi3BoxOJaApaSkDOvktmXLFtavX8+xY8fQ6/VceumlGM1WzrRoKG3S2Jsdvnh/Jw89/Ag5cUH4+3ghCAJNTU1UV1dPqOpBq9Xy6aefUl9fj79/v7/E1q1bueGGG1i2bBlpaWn87W9/47nnnqOvr4/PP/98xM2rHr0ZH++R85ASiQQpoO0z4O/vz4oVK8jIyCAqKgqJRMJPf/rTUdc92oih2czrr7/OM888Q0FBAdXV1aSkpEz1ksbFrBHdycaVSNdWQuPn50d5eTmNjY1Ot//+/u7bUR8KLy8vuxDb/G31ej3x8fHI5XI0Gg2nT59Gp9MRGBjotLaAgIAx7SqPtQTM0Qdi9erV/OfevXxy4F8s++GtnPnHX7hh7b3s+8MbtNVV8cdPPqVX1Uq0jxF/uYz6+noyMjLQaDTcdNNNfP7555jNZsLCwli1ahV79uwhOzubpKQk/vd//5drrrmG7du3Y7Va2bBhA3K5nM8++4zLLruMd999F29vbwRBwGQyodVqaWxsZNWqVSiVSvvdwWibVyF+MqrMvSO/R1YrvX19nP7mJOmJQ0fPIoOpqqrinnvuoaSkhC1btlBYWDhtOuPGw6z5xKci0h1pTprjJllKSgqJiYn2W/+2tjaqq6sxm81OQhcUFISv79ATE8bLwLztihWD87Zms9memujq6qK2thadTodCoRh0kRjqy+44O8zVEjCpVMp9991nj3TL6juQ+gXS23y2f4zQ/13QktOy+M53V7LpiftJSc9kUWIYiYmJrFu3jpdeeom+vj58fHwoLy9n6dKl9hTOypUr2b59O0ajkaNHj9rvANrb21EqlTQ2NhITE4NUKuXuu+9m06ZNHDp0iIULF7Jx40ZkMhlffPGFfb2jbV7lJgRz+FznsM0mRqOR2uYOgnwELi3InbE775OJxWLhtdde49lnn2X58uWUlJSQlJQ01cuaMLNGdCeb4aoXhsvbymQywsPDnXKbRqMRtVpt3wwrLy/vd8MaQojHiqtzyWyvJTQ01Gk32FGIVSoV58+fx2AwOEXEvr6+NDQ00N3dPaESMIPZSvnZWgL95AhWAZPRyME//REEAQvwyXu7Sc+eh1HwImfhYk5/fdx+nnPnzuHv74/BYGD+/Pn84Q9/4NSpU/j4+NDe3s7ixYtZunQpp06dIjEx0d7+Gx8fT0tLCzqdjscff5yWlhbuuecedu7cyY4dO/je975HaWkp27Zt44orrhg1hTEnzI+kCH/qO/VEB32b1xWsVrrV3XR2a7DKArjjikyCgydelzzbqaiooLCwkLKyMrZu3crPf/7zGWnjOBSSUaLDyQsdJ4jN/WmyaGlpobm52e6k5a5NMr1eb4+IbQ+JREJwcLCTbs1c4wAAGyRJREFUEI8kAhqNhsrKSgwGA+np6W7zozCZTGg0Grq7u2ltbUWr1SKRSOyNHONNmzR06fiivJ2YoG8vLn29vTQ2NSKVSomPi+83kOnRc3FKKOnRihGO5hrd3d28/fbb5OXljboR19ra6lJDgkZvtnfFKXy9kZqNtKlUGJChUARxfV48y1OGHv4p0o/FYuHVV19l48aNrFixgl27ds3UjcNhfwFE0R0n7e3t1NTUkJ+f71GPBEEQhhRib2/vQRGxIAicPXuW1tbWETexJrIWW/SsUChIS0tDJpMNWpvZbB6UmvDz8xv2fant7ONQRQcxQb6YTSaaW/prkWNjYvtLwP7v51p7DBQkhZAdO37RtZmKV1ZWEh4eTlpamltLsIwWK9/UqvhT0Vlae/SEh4VyUWoUBUmhdhtNkaEpLy+nsLCQiooKtmzZwl133TWTo9thFy6mF8aJl5eXxysSbMf18/PDz8+P6OhooF84+vr67CJ37tw51Go1giDg7+9PYmIiCoXCrTOzRioBGyptYktNtLa2UlVV5ZS/tgmyTYj9ffq9M1Qd/R69oaGhZKRnIB1QYywIVvugyvHQ29tLeXk5RqOR+fPnu724XhAEWpsa6a07y08XK0lOTnZL5+Bsx2w288orr/D888/zne98h5KSEhITE6d6WR5j1kS6trE1k4EgCPT29nLixAmMRuOg22t3b4aNtA5b5Onv709CQgImk8kuxu5oIXash51I9Gw0GgdFxBaLhaCgIGQyGZ+Vd+Ht5c3cOUp8hyhhM1ms9OhN3LQ4HpmLpjo2bA0IDQ0N43YyG42enh7KysqQSqVkZWVNuTnNTOHMmTMUFhZSXV3Nyy+/zNq1a2dydOvI7E8vTIboDpW3tYmcbUOsp6fHvhnmKMTubkt1JW9rayF2XNvAzrXg4GACAwMHidDAErDU1FS3d0L19PRQUVGBVqtFK8g50mhA4QNBAX74+/n3R/j+fkgkXrRojXwnLYz0qLGlFtra2qioqCA4OJj09HS3jm2C/ijNdlFKTU0lLi5utoiGRzGbzbz88sv85je/4fLLL2fnzp0olcqpXpY7mf2ia7Va7RNn3c1YNskEQcBgMAwS4qFysONpuTUajRPK2zo2TNgefX19TlUJAHV1dXh7e5ORkeEWFzBHHMvYlMpvb8NrVL0cKmujV6cDswGDwYBaqwMgLz6Q+QmhLld06HQ6ysvL6evrIzMzc0wdca4gCIJd0D2RG57NnD59msLCQs6fP89vf/tb7rjjjtl4oRJFdzy4qyJBEAR0Op2TCGs0GuRyuVPEOdKtv6PDVUxMDHPnznWbT4LFYkGj0aBSqWhqasJgMCCRSJw2w4KDg93SzKFSqSgvL8ff35+MjIxBXgwGs4W6Th1Naj0CEBXoQ2yAFyZ9r9OFwlY14fiwTcKtqamhrq6OOXPmMGfOHLenEmyCrtPpyMrKmrHGK5ONyWTi5ZdfZtOmTaxcuZI333zT7icyC5n9oisIgtvclxzNmN01k2wgA93Denp60Gq1g279AwICUKlU9nrbtLQ0t+cLHQc12iJPQRAG5WBt+WtXqxIc0el0VFZWotFoyMjIIDIyctzrHa6iQyKRYLVakcvlJCUlERkZ6dbo02q1UltbS21trccEfbZSUlJCYWEhtbW1bN26ldtvv302RreOiKI7luM42i1O5hdjoGlNV1cXOp0OqVRKWFgY0dHR9hZdd6zLdotsm0Cbnp4+og+D4yadY3nYSF11joKemJg46uTd8aDX66moqECtVhMbGwswZFrHFrmPR4i7u7s5c+YMvr6+ZGZmut0tbbZiNBp56aWX2Lx5M1dddRU7duyw25bOckTRdeXnPVlvOxYc87ZJSUkoFAq0Wq09PWE0GlEoFE4bda5GnDYcS8AyMzMJCxtf0b4tf+34AAgKCsLLy4uuri4UCgVZWVlut+IbLjdsw5bWcVybRqMZU37dZDJRVVVFR0eHkzmNyOgUFxdz991309DQwCuvvMKtt956Ib13s190gRG9EIZjOomtq3nboSomrFarS+3D7ioBGw5BEOju7qaiogKdToefnx96vd7JjtKVrrrR6OrqoqysDF9fXzIyMly2phxY42wTYh8fn0Glde3t7VRVVREdHe3WHPpsx2AwsGXLFl544QV+8IMf8MYbb9jvQC4gLgzRNRqNLpveTCexHVhvm56ePua8rcFgcBLhnp6eQUKn1Wqpra0lKiqKuXPnun233bEeNikpicTERKRSqVMO1rZGW8TpGK0rFIpRhc1gMFBVVUVnZ6fbIk9b3bVtXV1dXWg0GiQSCaGhoYSHh9vXKLqCjczXX39NYWEhTU1N/O53v+Pmm2++kKJbR0TRtTEZm2RjwVM+CTahU6vVtLW10d7ebt9kCgkJcevgS8fccEhICGlpaaOWdA0XcTpWdNgeXl5eTqbicXFxpKSkuF0ABzZRhIWFOeXYbc0mjlUdnhocOtMwGAxs3ryZl156iR/+8Ie88cYb9g7KC5QLQ3RNJtOIo9incpNsIBOtt3UFnU5HVVUVarWatLQ0oqKihhQ6Pz+/QRGnq2ux5YaNRiMZGRnjzg1Df3rFcX1qtRqtVotcLsdkMiGTyZg7dy5RUVFu34xTqVSUlZWhUCjIyMgY8qIxXMWJpwaHzhROnjxJYWEhra2tbNu2jZtuummqlzQduLBFdzqlEjxZb2vDYrFQU1NDfX09CQkJJCUljVj/6zhdwtYsERAQ4CTEA03NzWYz586do6mpyWMXDdt8sra2NvugRltXneMYIts8uPGc32Aw2CsfMjMzx1zKNnBe3VBdf7b1zTYh1uv1bNq0iZdffpnrrruO1157jaioqKle1nThwhTd6SS2giDQ0dFBZWUlfn5+48rbunKOsZSADYetWcJRiA0Gg32Kgs2pKyIigrS0NLe3ODuO5BlqE8uVrjpbM8dwQuyYroiPjyclJcVtouiqEI/ljmK6ceLECe6++246Ojp47bXXuPHGG6d6SdONC0N0bfaO00lswXN524HnqKiowGQyTfg2fyhMJhOtra2cP38es9mMVCodVDERHByMXC6f0Hut0WgoKytDEASysrJcbkF2NF23PWwXioHTL2znmExzmuEuFO6K2CcLnU7Hr3/9a1555RV+/OMfs23btgk1usxiLgzRtVktTpdNssnI2w6cihsfH++xc7S2ttrPIZFIBtXoqtVqp/ZcW3rClSoJm3FMc3Mzqamp9nNMdN2OQqxWq+1lhWFhYcTFxY2rxtldON5R2P50jNhttdhjnVfnKY4dO0ZhYSFdXV28/vrr/PjHP57qJU1nZr/o6vV60tLSmD9/Pvn5+SxZsoS8vLwp6YsfmLdNSUlxe3mW1WqlsbGRc+fOeawEbODk3dGcxkYzXHfMEdt2/AVBoKWlhaqqKo8Zx9hK8mxuYwM3FIeqcZ5oxD5eHIXY9rDNq3OM2idTiHU6HRs3buTVV1/lpptu4tVXX/XI3dosY/aLrk6nY+/evRw9epTjx49TXFyM2WwmLS2N/Px8+2PBggUec4OajLwtQGdnJxUVFchkMjIyMlAoJj6+ZiBqtZqKigoAMjMzx+00NrA0zFaR4Ovri5+fH729/RN0s7Oz3Z4SAWdzmuE670aL2D1lz+kqw6VOhprg7O4LxdGjRyksLEStVvPGG29w3XXXufX4s5jZL7oD0el0nDp1iiNHjnDs2DGOHTvG+fPn8fHxYcGCBSxZsoTFixeTn59PamrqhL+sjm21nsrbOpaApaene6Ql1Taqvb29nbS0NGJjY91+DpPJRGVlJa2trQQGBtpLsRzzmxO9rXZsEU5MTCQpKcnlYw1nz2kbaT9Re053MDB14tgePjCHPZ7Pr6+vj+eee45t27axZs0aXnnlFbfbY85yLjzRHYr29naOHTvG0aNHOXbsGEVFRXR2dhIaGmoX4Pz8fBYvXuxy6ctk5G3HUgI2Xhx38z1VyuZ4mx8SEkJ6ero9erRtNDmKnF6vH7IiYTQR6e7upqysDLlc7jZzmuF8HGQy2aCIeKqaJdwlxIcPH6awsBCtVsv27dv50Y9+NImvYtYgiu5Q2AY5OkbDX3/9NQaDgaSkJPLy8liyZAn5+fnk5uY6lV9ZLBYaGho8mrd1LAELDg4mLS3N7aYx0C9S5eXleHl5kZmZ6ZF0RV9fH+Xl5ej1epcNdsxm86D8sMlkGmT2Y3M1czSnSU9PJzo62qN52eFSJ7auOtsap7JZYjhnOEchlkqleHt7I5fLefbZZ3n99de5/fbb+e1vf+uRlM8Fgii6rmI0GikuLrYLcVFRkV2Q5s2bx6JFi9DpdJw8eZLt27czf/58j+RtPV0CBs4+BmlpacTExLhdpByjdHd40A6ctWYbyCmXy+nr6+sfajkGAxx344pP8lTX6A58D/ft28eWLVsICgrCaDSyZs0abr/9dr773e9OyfpmCaLoToTu7m6Kiop455132LdvHwaDgZiYGLq7u8nLy2Px4sX2iHiiTvi2dEVbWxspKSkeKQGzWq00NDRw7tw5j/kYAHR0dFBeXo5CoRh3o8Zo9Pb2cubMGfR6PaGhofZc7HTKvw7XLOHOHPZ40Wq1PP3007z33nvk5eWhVCopKSmx7x+IjBtRdN3BrbfeSlhYGBs2bKCvr4+jR4/a88MnT56kt7eXuLg4p/xwXl6eSzv/thIwT+ZU4dvKBx8fHzIzMz0SEdpMxTUaDZmZmR7ZVHSMoAdO+HXMvzq6mg1npjMVjFQa5umKBBtfffUV99xzD0ajkTfffJPvf//79v8zm82ikc/EEEXXHdgaLobCYrFQWlrK0aNHOXLkCMePH+f06dMIgkBmZqZTNJyTk2MXVIvFQmdnJ9XV1R4tAdPr9VRWVnq08sFxnI2nNvzg2zlrgYGBw5rTDMRm3+i4UTfUeKSp7AgbS1fdRD47rVbLhg0b2LFjB2vXruWll14iJCTEja9EBFF0pwatVsuJEyfsFRNFRUXU1dXh5+fHwoULUSqVnDhxgquvvpr169d7ZONntOkK7qKzs5Py8nKPjrMxGAxUVlbS3d09LnOagQwcjzSwI8yWnvBktDka4xmRNBJ///vfuffeezGbzezcuZOrr756El7FBYkoutOF5uZm/vKXv7BlyxbOnDlDQkICLS0tBAcH29MStm66idZFjjZ51x04CqFt4KS7BcqT5jQDsVgsgzbq3DEeyZ0M3AhzZXKIRqPh6aefZteuXdx555289NJLBAcHT8n6LxBE0Z1OVFZWsnbtWrZs2cLSpUuprKy0pyWKioooLi7GZDIxd+5cJyFeuHChS11R7py8OxyOm3GeFEKbOQ1AVlaWR1IvozEw2lSr1S6PR5os9Hr9IGc4iUTC888/j6+vL8XFxUilUnbt2sXq1aunbJ0XEKLoziQMBgOnTp2yb9QVFRXZc77z5893EuK0tDR7DrK3t5fW1laPTt6Fb+t6vb29yczM9EjJnKNfr7sMcNzJUB1r7p4DNxFsjSh33XUX1dXVdHV12X0w3n33XW6++eYpWdcFhCi6Mx2VSmVv4LAJcUdHByEhISxcuBBfX18OHz7MG2+8wVVXXeWR8iybqbhKpfJYXS9AW1sbFRUVhIaGkp6ePmXCNRaGmwPn2LHmrvFIrnDo0CHWrVuHRCJh165drFy5ks7OTk6cOEFWVhZKpdLja7jAEUV3tiEIAjU1Nbz99tu8/vrr9PT0EB8fb68csLUzL1myhEWLFk0oGhUEgcbGRqqrq4mNjSUlJcUj5Ww6nY6Kigp6e3vJysqa8d1QjgMvB45HGtix5q6KCbVazS9/+Ut+//vfU1hYyObNm6ckJSMiiu6sZfv27Zw8eZLnn3+ekJAQSkpK7LXDx44ds5t1Z2dns3jxYrsQZ2dnu5R66Onpoby8HPBcTtWxwiIhIYHk5ORp4R/rCQY2SqjVaiczc8eKibG+BwcOHGDdunXIZDJ27drF5Zdf7qFXIeICouheqPT09FBUVGQX4WPHjtHU1ERAQACLFi2yN3EsWbIEpVJpTxdoNBoaGxtpbW0lNTWVuLg4j6QSbOY0nmzWmO4MbJSwma27Wp/b3d3Nk08+ybvvvsu9997Lpk2bJmUahsiIiKIr8i0NDQ32aPjo0aOcOHECrVZLdHQ0ubm5mM1mTp06xXvvvUdBQYFHcqo2c5r29nbS09M9lh+eqTg6htlyxI71uefPn8fb2xuNRsNjjz2GXC7nrbfe4rLLLpuU9a1fv56PPvqImpoaSkpKmDdv3qScdwYhiq7I8FgsFsrLy3nzzTfZvXs3RqORsLAwmpubSU9PdzKBnz9//oRE2DYporKykqioKFJTU6fME2GmYTQa7QL8zDPPsG/fPgRBICwsjO9973v86Ec/mrQBkf/4xz+YM2cOl1xyCfv37xdFdzDDiq7YXC2Cl5cXOTk5KBQK7rzzTp599ll8fHw4efKk3W3t1VdfpaamBrlc7mQCv2TJElJSUlyKUnt7eykvL8doNLJw4UKx9XSM+Pj4EBkZyfHjxzl8+DDJyck8+OCDmEwme333ZInuihUrJuU8sxEx0h2BdevWcfDgQeRyOYGBgbzyyivk5+dP9bI8xkjeEtBfyuVoAn/8+HG7CbxjNLx48WKnhgyj0Uh9ff2Q5jQirtPZ2cnjjz/O+++/zwMPPMDGjRunPAeelJQkRrpDI6YXxsP+/fu56qqrkMlk7N+/nwcffJCzZ89O9bKmDYIgUF1d7WQC/8033ziZwHt5efHll1+yY8cOVqxY4ZH64QuBP//5zzzwwAMoFArefvvtaRNpiqI7LKLoThSVSkVcXBw6nU6M0kbAaDTyzTff8NFHH/HWW2/R2dlJfHw8TU1NTt10+fn5ZGZmiu/lKKhUKn7xi1/wwQcf8NBDD/Hcc895xENjvIiiOyxiTneibNu2jR/84AeiSIyCj48PS5Ys4cCBA1x88cW8+uqrKBQKioqK7GmJDRs20NbWhkKhIC8vzyk1ERcXN9UvYdrw6aef8uCDDxISEsJXX33F8uXLp3pJIm7ggo508/LyqKurG/L/Wltb7c0D77//Phs2bODLL78kOjp6zOfZs2cPL7zwAmfOnGHr1q3cd999E1r3TMBqtQ57gRIEgbq6ukEm8H19fcTHxw8ygb/QOqo6OjrsJVmPPPIIv/rVryY1LVNZWckdd9yBSqUiPDycd955h7S0NKfnPPDAA3z88ce0tLQQERFBeHg4paWlk7bGGYCYXhgv+/btY/369Rw8eJCkpKRxHeP06dNIpVI2bdpEQUHBBSG6Y8VsNttN4G3eErZfYpsJvK2JIycnZ9ZONfjTn/7EQw89RHh4OG+//TbLli2b9DVcfvnl3Hnnndx2223s2bOHt99+m0OHDk36OmY4ouiOh/3793P//ffzxRdfkJqaOuHj/fSnPyU/P18UXRfRaDSDTODr6+vx8/Nj0aJFTtM45syZM6ObK9rb23n00Uf55JNPePTRR3nmmWemZNOxra2N9PR0VCoVXl5eWCwWwsPDqaqq8ohF6CxGzOmOh7Vr1+Lj48MNN9xg/7eDBw9O2FxcxDUUCgWXXXaZU5dVU1OTk9vau+++i1qtJjIycpAJ/EwxzPn44495+OGHiYqK4l//+hcFBQVTtpb6+nri4+PtqTUvLy/i4uKor68XRddNiKI7Au3t7S49z9Xc8HhxJcd2oRAXF8e1117LtddeC/TnjisqKuwm8J999hmbN2/GZDKRmprqJMQLFixwyQR+smhra+ORRx7hv//7v3nsscfYsGHDlBqhi0wOYnphEhlvekHMsY0NvV4/yAT+7Nmz+Pj42MvWbGmJtLS0KUlLfPTRRzz88MPExsaye/fuadN0I6YX3MawXyqx/mma09bWxsmTJ1mzZg0Aa9as4eTJky5H4Rcivr6+XHTRRTz00EPs3buX6upq2tvb2bdvH6tXr6auro4nn3yS3NxclEol11xzDc8++yyfffYZra2tHl1bS0sLt9xyC3feeSeFhYUcP358ygR3z549LFiwAG9vb7Zt2wZAVFQUixYtYu/evQDs3buX3NxcUXDdiBjpTgJ79+7lscceo6urCx8fHwICAvjrX/9Kdnb2qD974sQJ/u3f/s2pHCc7O5s9e/aQl5fnyWXPagRB4Ny5c05ua19//TV6vZ7ExEQnE/jc3NwJNyQIgsCHH37Io48+ilKpZPfu3VP++Q1XVVNeXs4dd9xBV1cXoaGhvPPOO2RkZEzpWmcg4kbaVLJmzRp7pDrViJZ8/UgkEubOncvcuXO55ZZbgH47xeLiYrsQ79mzh6eeegqpVEpOTo6TCXxWVpbLufqWlhYeeughPv/8c5588kl++ctfTovcsu2zH1hPnZmZydGjR6diSRcEouhOcxISEmhsbMRisdhzbE1NTSQkJIzreNdeey0PPvggl1xyiZtXOvORyWR2Yb333nuB/vE3jibwzz//PM3NzQQGBpKbm+u0UTdweKYgCHzwwQc8+uijJCYmUlRUxKJFi6bq5YlME0TRneY45thuu+22CefYpotRykwhODiYlStXsnLlSvu/NTQ0OJn87Nq1C61WS0xMjD0tkZKSwnvvvcehQ4d46qmneOKJJyZ9wKanq2pExocoujOA7du3c8cdd/CrX/3KnmMTmTqUSiU33HCDvX7bYrFQVlbGkSNHOHr0KJ988gnffPMN0dHRHD9+nAULFkzJOk+ePDkl5xUZGVF0ZwDTMcemUqm4/fbbOXv2LHK5nNTUVHbs2HFB7nJ7eXkxb9485s2bx1133QVAdXU1CoViXF4dIrMbsWRMZFxIJBJ+8YtfUFFRQXFxMXPnzuWJJ56Y6mVNG1JTU6e94O7duxelUsmHH37I008/jVKp5MyZM1O9rFmPKLoi4yIsLMypPXfZsmXU1tZO3YJExsyaNWtoaGigt7eXrq4uGhoaXCpjFJkYouheYDzwwAMolUoaGhpYuXIlOTk5Ez6m1WrljTfe4JprrnHDCkVEZjdic4TIhFm3bh2NjY18/PHHosm7iEg/YnOEiGdYv349VVVVfPrpp6Lgioi4gCi6IuPml7/8JSdOnODPf/7ztOiwEhGZCYjpBZFxUVpayrx580hPT7ebbScnJ7Nv374pXpmIyLRAnBwhIiIiMomI1o4iIiIi0wFRdEVEREQmEVF0RURERCYRUXRFREREJpHRSsZm7kxrERERkWmIGOmKiIiITCKi6IqIiIhMIqLoioiIiEwiouiKiIiITCKi6IqIiIhMIqLoioiIiEwi/x8sk4JrNijoLwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can also create 3d scatterplots.\n",
    "X = skm.MDS(n_components=3).fit_transform(df_hept_norm)\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X[:,0], X[:,1], X[:,2], s=100)\n",
    "\n",
    "ax.set_xticks([-2,-1,0,1,2])\n",
    "ax.set_yticks([-1,0,1])\n",
    "ax.set_zticks([-1,0,1])\n",
    "\n",
    "for i, s in enumerate(df_hept_norm.index):\n",
    "    x, y, _ = proj3d.proj_transform(X[i,0],X[i,1],X[i,2],\n",
    "                                    ax.get_proj())\n",
    "    plt.annotate(s, xy=(x-0.005,y+0.002), fontsize=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We can also create 3d scatterplots.\n",
    "X = skm.MDS(n_components=3).fit_transform(df_hept_norm)\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X[:,0], X[:,1], X[:,2], s=100)\n",
    "\n",
    "ax.set_xticks([-2,-1,0,1,2])\n",
    "ax.set_yticks([-1,0,1])\n",
    "ax.set_zticks([-1,0,1])\n",
    "\n",
    "for i, s in enumerate(df_hept_norm.index):\n",
    "    x, y, _ = proj3d.proj_transform(X[i,0],X[i,1],X[i,2],\n",
    "                                    ax.get_proj())\n",
    "    plt.annotate(s, xy=(x-0.005,y+0.002), fontsize=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Bivariate Analysis (Quick Review)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Bivariate Analysis\n",
    "For initial inspection of bivariate relationships among the variables, let us create a correlation plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "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>Hurdles</th>\n",
       "      <th>HighJump</th>\n",
       "      <th>Shot</th>\n",
       "      <th>Run200m</th>\n",
       "      <th>LongJump</th>\n",
       "      <th>Javelin</th>\n",
       "      <th>Run800m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Hurdles</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.811403</td>\n",
       "      <td>-0.651335</td>\n",
       "      <td>0.773721</td>\n",
       "      <td>-0.912134</td>\n",
       "      <td>-0.007763</td>\n",
       "      <td>0.779257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HighJump</th>\n",
       "      <td>-0.811403</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.440786</td>\n",
       "      <td>-0.487664</td>\n",
       "      <td>0.782442</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>-0.591163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Shot</th>\n",
       "      <td>-0.651335</td>\n",
       "      <td>0.440786</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.682670</td>\n",
       "      <td>0.743073</td>\n",
       "      <td>0.268989</td>\n",
       "      <td>-0.419620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run200m</th>\n",
       "      <td>0.773721</td>\n",
       "      <td>-0.487664</td>\n",
       "      <td>-0.682670</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.817205</td>\n",
       "      <td>-0.333043</td>\n",
       "      <td>0.616810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LongJump</th>\n",
       "      <td>-0.912134</td>\n",
       "      <td>0.782442</td>\n",
       "      <td>0.743073</td>\n",
       "      <td>-0.817205</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.067108</td>\n",
       "      <td>-0.699511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Javelin</th>\n",
       "      <td>-0.007763</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>0.268989</td>\n",
       "      <td>-0.333043</td>\n",
       "      <td>0.067108</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.020049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run800m</th>\n",
       "      <td>0.779257</td>\n",
       "      <td>-0.591163</td>\n",
       "      <td>-0.419620</td>\n",
       "      <td>0.616810</td>\n",
       "      <td>-0.699511</td>\n",
       "      <td>0.020049</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Hurdles  HighJump      Shot   Run200m  LongJump   Javelin   Run800m\n",
       "Hurdles   1.000000 -0.811403 -0.651335  0.773721 -0.912134 -0.007763  0.779257\n",
       "HighJump -0.811403  1.000000  0.440786 -0.487664  0.782442  0.002153 -0.591163\n",
       "Shot     -0.651335  0.440786  1.000000 -0.682670  0.743073  0.268989 -0.419620\n",
       "Run200m   0.773721 -0.487664 -0.682670  1.000000 -0.817205 -0.333043  0.616810\n",
       "LongJump -0.912134  0.782442  0.743073 -0.817205  1.000000  0.067108 -0.699511\n",
       "Javelin  -0.007763  0.002153  0.268989 -0.333043  0.067108  1.000000  0.020049\n",
       "Run800m   0.779257 -0.591163 -0.419620  0.616810 -0.699511  0.020049  1.000000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test for correlations\n",
    "df_hept_norm.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x1c1af24400>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw a \"clustered\" heatmap\n",
    "sns.clustermap(df_hept_norm.corr(),cmap=plt.cm.OrRd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x1c1b2b1438>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1260x1260 with 56 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pairplot\n",
    "sns.pairplot(df_hept_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Principal Component Analysis\n",
    "\n",
    "We have demonstrated how to use principal component analysis (PCA) to do dimensionality reduction for visualization in the previous lab. Now let us look at PCA in greater details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a PCA model\n",
    "pca_model = skd.PCA().fit(df_hept_norm.ix[:,:7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 7)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# There are 7 components extracted from the data; each component is\n",
    "# a 7-dimensional vector.\n",
    "pca_model.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.64611996, 1.24408391, 0.54272305, 0.47621544, 0.25548619,\n",
       "       0.0759954 , 0.05104272])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at the variances explained by each component.\n",
    "# These values equal to the eigenvalues of the correlation matrix.\n",
    "pca_model.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way of determining the number of principal components to retain is to look at the explained variance as shown above, and drop those principal components whose explained variance is smaller than 1.\n",
    "\n",
    "Another way is to create a __Scree Plot__ as below, and find the \"elbow\" point on the plotted curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1c933f28>]"
      ]
     },
     "execution_count": 23,
     "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": [
    "# A \"scree\" plot.\n",
    "plt.plot(range(1,8),pca_model.explained_variance_,'b-o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will create a __biplot__, which is 2-D scatterplot showing all the data points as well as the data variables in the space defined by the first two principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatterplot of disaggregated data\n",
    "X = pca_model.transform(df_hept_norm.ix[:,:7])\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.title('PCA biplot')\n",
    "plt.ylim(-4, 10)\n",
    "\n",
    "# Add variable unit vector projections\n",
    "V = pca_model.transform(np.identity(X.shape[1]))\n",
    "for i, v in enumerate(V):\n",
    "    plt.annotate(df_hept_norm.columns[i], \n",
    "                 xy=(0,0), xytext=v[:2]*10, \n",
    "                 fontsize=13, color='orange',\n",
    "                 arrowprops=dict(\n",
    "                    arrowstyle='<-', linewidth=2, color='orange'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q1: What's the correlation between PC1 and *Score* from the original data?</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.20643487e+00, -2.94161870e+00, -2.70427114e+00, -1.37105209e+00,\n",
       "       -1.38704979e+00, -1.06537236e+00, -1.12307639e+00, -9.42210150e-01,\n",
       "       -5.41184843e-01, -7.75487044e-01, -5.67738958e-01, -1.21091937e+00,\n",
       "        1.57800481e-02,  3.85204977e-03,  9.26189926e-02, -1.40055128e-01,\n",
       "        1.74657449e-01,  5.29960012e-01,  1.14869009e+00,  1.10808552e+00,\n",
       "        1.47689483e+00,  2.05556037e+00,  2.93969248e+00,  3.03136461e+00,\n",
       "        6.39931438e+00])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:, 0] # for PC1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reload the dataframe in the first part of df_hept\n",
    "df_hept_temp = pd.read_csv('data/heptathlon.csv')\n",
    "df_hept_temp['pc1'] = X[:,0] \n",
    "df_hept_temp['pc2'] = X[:,1] # pc2 has same direction with Javelin, from the above plots, also found below for correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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>Hurdles</th>\n",
       "      <th>HighJump</th>\n",
       "      <th>Shot</th>\n",
       "      <th>Run200m</th>\n",
       "      <th>LongJump</th>\n",
       "      <th>Javelin</th>\n",
       "      <th>Run800m</th>\n",
       "      <th>Score</th>\n",
       "      <th>pc1</th>\n",
       "      <th>pc2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Hurdles</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.811403</td>\n",
       "      <td>-0.651335</td>\n",
       "      <td>0.773721</td>\n",
       "      <td>-0.912134</td>\n",
       "      <td>-0.007763</td>\n",
       "      <td>0.779257</td>\n",
       "      <td>-0.923198</td>\n",
       "      <td>9.564348e-01</td>\n",
       "      <td>1.725835e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HighJump</th>\n",
       "      <td>-0.811403</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.440786</td>\n",
       "      <td>-0.487664</td>\n",
       "      <td>0.782442</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>-0.591163</td>\n",
       "      <td>0.767359</td>\n",
       "      <td>-7.966208e-01</td>\n",
       "      <td>-2.711075e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Shot</th>\n",
       "      <td>-0.651335</td>\n",
       "      <td>0.440786</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.682670</td>\n",
       "      <td>0.743073</td>\n",
       "      <td>0.268989</td>\n",
       "      <td>-0.419620</td>\n",
       "      <td>0.799699</td>\n",
       "      <td>-7.667860e-01</td>\n",
       "      <td>3.162788e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run200m</th>\n",
       "      <td>0.773721</td>\n",
       "      <td>-0.487664</td>\n",
       "      <td>-0.682670</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.817205</td>\n",
       "      <td>-0.333043</td>\n",
       "      <td>0.616810</td>\n",
       "      <td>-0.864883</td>\n",
       "      <td>8.614484e-01</td>\n",
       "      <td>-2.845622e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LongJump</th>\n",
       "      <td>-0.912134</td>\n",
       "      <td>0.782442</td>\n",
       "      <td>0.743073</td>\n",
       "      <td>-0.817205</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.067108</td>\n",
       "      <td>-0.699511</td>\n",
       "      <td>0.950437</td>\n",
       "      <td>-9.635326e-01</td>\n",
       "      <td>-6.106182e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Javelin</th>\n",
       "      <td>-0.007763</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>0.268989</td>\n",
       "      <td>-0.333043</td>\n",
       "      <td>0.067108</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.020049</td>\n",
       "      <td>0.253147</td>\n",
       "      <td>-1.592590e-01</td>\n",
       "      <td>9.198430e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run800m</th>\n",
       "      <td>0.779257</td>\n",
       "      <td>-0.591163</td>\n",
       "      <td>-0.419620</td>\n",
       "      <td>0.616810</td>\n",
       "      <td>-0.699511</td>\n",
       "      <td>0.020049</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.772776</td>\n",
       "      <td>7.918903e-01</td>\n",
       "      <td>2.453337e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Score</th>\n",
       "      <td>-0.923198</td>\n",
       "      <td>0.767359</td>\n",
       "      <td>0.799699</td>\n",
       "      <td>-0.864883</td>\n",
       "      <td>0.950437</td>\n",
       "      <td>0.253147</td>\n",
       "      <td>-0.772776</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-9.910978e-01</td>\n",
       "      <td>9.788578e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pc1</th>\n",
       "      <td>0.956435</td>\n",
       "      <td>-0.796621</td>\n",
       "      <td>-0.766786</td>\n",
       "      <td>0.861448</td>\n",
       "      <td>-0.963533</td>\n",
       "      <td>-0.159259</td>\n",
       "      <td>0.791890</td>\n",
       "      <td>-0.991098</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>3.694283e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pc2</th>\n",
       "      <td>0.172583</td>\n",
       "      <td>-0.271107</td>\n",
       "      <td>0.316279</td>\n",
       "      <td>-0.284562</td>\n",
       "      <td>-0.061062</td>\n",
       "      <td>0.919843</td>\n",
       "      <td>0.245334</td>\n",
       "      <td>0.097886</td>\n",
       "      <td>3.694283e-16</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Hurdles  HighJump      Shot   Run200m  LongJump   Javelin  \\\n",
       "Hurdles   1.000000 -0.811403 -0.651335  0.773721 -0.912134 -0.007763   \n",
       "HighJump -0.811403  1.000000  0.440786 -0.487664  0.782442  0.002153   \n",
       "Shot     -0.651335  0.440786  1.000000 -0.682670  0.743073  0.268989   \n",
       "Run200m   0.773721 -0.487664 -0.682670  1.000000 -0.817205 -0.333043   \n",
       "LongJump -0.912134  0.782442  0.743073 -0.817205  1.000000  0.067108   \n",
       "Javelin  -0.007763  0.002153  0.268989 -0.333043  0.067108  1.000000   \n",
       "Run800m   0.779257 -0.591163 -0.419620  0.616810 -0.699511  0.020049   \n",
       "Score    -0.923198  0.767359  0.799699 -0.864883  0.950437  0.253147   \n",
       "pc1       0.956435 -0.796621 -0.766786  0.861448 -0.963533 -0.159259   \n",
       "pc2       0.172583 -0.271107  0.316279 -0.284562 -0.061062  0.919843   \n",
       "\n",
       "           Run800m     Score           pc1           pc2  \n",
       "Hurdles   0.779257 -0.923198  9.564348e-01  1.725835e-01  \n",
       "HighJump -0.591163  0.767359 -7.966208e-01 -2.711075e-01  \n",
       "Shot     -0.419620  0.799699 -7.667860e-01  3.162788e-01  \n",
       "Run200m   0.616810 -0.864883  8.614484e-01 -2.845622e-01  \n",
       "LongJump -0.699511  0.950437 -9.635326e-01 -6.106182e-02  \n",
       "Javelin   0.020049  0.253147 -1.592590e-01  9.198430e-01  \n",
       "Run800m   1.000000 -0.772776  7.918903e-01  2.453337e-01  \n",
       "Score    -0.772776  1.000000 -9.910978e-01  9.788578e-02  \n",
       "pc1       0.791890 -0.991098  1.000000e+00  3.694283e-16  \n",
       "pc2       0.245334  0.097886  3.694283e-16  1.000000e+00  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hept_temp.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pc1 has high correlation with score, -0.99, which is highly negatively correlated with score. PC2 has same direction with Javelin, from the above plots, also they are correlated significantly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Factor Analysis\n",
    "\n",
    "We didn't cover factor analysis in class but it is in the readings. Factor analysis is similar to PCA but we have a little bit more control over the factors and how they relate to each other.\n",
    "\n",
    "Below, we'll create 3 factors for the events and then print out their loadings.  That tells us how much each event contributs to each factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "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>Factor1</th>\n",
       "      <th>Factor2</th>\n",
       "      <th>Factor3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Hurdles</th>\n",
       "      <td>0.951275</td>\n",
       "      <td>0.187302</td>\n",
       "      <td>0.109397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HighJump</th>\n",
       "      <td>-0.763002</td>\n",
       "      <td>-0.446091</td>\n",
       "      <td>0.050968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Shot</th>\n",
       "      <td>-0.732991</td>\n",
       "      <td>0.160497</td>\n",
       "      <td>0.303633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run200m</th>\n",
       "      <td>0.885045</td>\n",
       "      <td>-0.403132</td>\n",
       "      <td>0.056832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LongJump</th>\n",
       "      <td>-0.964212</td>\n",
       "      <td>-0.076056</td>\n",
       "      <td>0.140774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Javelin</th>\n",
       "      <td>-0.129255</td>\n",
       "      <td>0.511201</td>\n",
       "      <td>0.092702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run800m</th>\n",
       "      <td>0.750836</td>\n",
       "      <td>0.151658</td>\n",
       "      <td>0.308775</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Factor1   Factor2   Factor3\n",
       "Hurdles   0.951275  0.187302  0.109397\n",
       "HighJump -0.763002 -0.446091  0.050968\n",
       "Shot     -0.732991  0.160497  0.303633\n",
       "Run200m   0.885045 -0.403132  0.056832\n",
       "LongJump -0.964212 -0.076056  0.140774\n",
       "Javelin  -0.129255  0.511201  0.092702\n",
       "Run800m   0.750836  0.151658  0.308775"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a three-factor model\n",
    "fa_model = skd.FactorAnalysis(n_components=3) \\\n",
    "              .fit(df_hept_norm.ix[:,:7])\n",
    "\n",
    "# Show the loadings\n",
    "df_loadings = pd.DataFrame(fa_model.components_[:3,:].T, \n",
    "                   index=df_hept.columns,\n",
    "                   columns=['Factor1', 'Factor2', 'Factor3'])\n",
    "df_loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x1c24041d68>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FADDtiiQXVtVbklyz1GhNFQDA2nx8/FoToQoAYEJ3n75InVAFADChqp4/q33e9J+F6gAA066eeO3L6HcAHjOvyEgVAMCE5dN/VfWbSc6dV2ekCgBgZVclOW7eRUaqAAAmLFtTdViSk7KKbwMKVQAA066eeL83ydlJ3jmvSKgCABirqlsneVOSD3X33qo6JskvJXlZkpuvVDtoqKqqU5PsGPKeh6hjN7oDAMDaVNVPJDkryVeTXD7ONX+Y5C0ZTQGuaOiRqh3dvWvgex5yqmrXRvcBAFizZyY5sbs/WlXfm+StSX60u1+3mmLf/gMAGLmuuz+aJN39riSfWm2gSqypAgBYclRVnZCkxsfXTx5390UrFQtVAAAjRyc5f1nb0nEnufNKxUIVAECS7j72QOqtqQIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADMDmnwDAllZVO5PsnHFqT3fvGeo5QtUhpKpOTbJjiHt1964h7gMAh4BTkpw2o/30JLuGeohQdWjZIQwBwJqdkWT3jPaZo1RV9cIkz01ydZK3JjkxydO7+9yVHmJNFQCwpXX3nu7+zIzX/qb+HtrdVyT5/iSfT3LXJM+a9xyhCgBgtu9L8obuvixJz7tYqAIAmPbFqnplkv+e5G+q6oisYsmUUAUAMO1Hk3w0yWO7+6tJvj3JC+cVCVUAABO6+/Ikr05y7fj4M929e16dUAUAMKGqTs5opOoN4+OTquqN8+qEKgCAaacnuW+SryZJd1+Y5C7zioQqAIBluvsLy5q+Ma9GqAIAmHZlVX1bxtsoVNWDsp+NQifZUR0AYNqpSf4yyZ2q6m0Zbf75yHlFQhUAwITufl9VPTjJ9ySpJP+wml+8LFQBACwz/jU1f7mWGqEKACBJVV2e2b+OppJ0d99qpXqhCgBg5KQDKRaqAACSdPclB1IvVAEAZMXpvySJ6T8AgNVZmv77iSS3TPKKjNZTPSXJ5+YVC1UAALlh+q+qHtjdD5w49XNV9fYkz1+p3o7qAADTbltV37p0MH5/m3lFRqoAAKadkeSDVfXm8fHJSX5zXpFQBQAwobvPrKoLkjwoozVVL+3uj8yrE6oAAMaq6vAkf97d/zXJ3CA1yZoqAICx7t6X5Fuqas0ZyUgVAMC09yZ5Q1X9UZKrlhq7+/yVioQqAIBp3zP++VMTbZ1EqAIAWK3ufvAidUIVAMCEqjp5VrvpPwCAtfmFifc7knxXkvfH9B8AwOotn/6rqu9I8sx5dULV+rimqnatw32PHfqG+z7+7qFvyTa19xt2aGE4tzixN7oL8E3dfVFV3WvedULVOuju563HfdcpqAEAE5atqTosyf2yir09hSoAgGmTa6r2JvlkkkfPKxKqAACSVNX3jd+eNuP07ZN8eqV6oQoAYOSFE+9PSHJRRr9QORlt/nm/lYqFKgCAJN1936X3VfWB7l4xRC3n6zoAAP/Rmr+CKlQBAAzA9B8AQL65yeeSHVV1Qm5YU5XuvmileqEKAGDkzcuOJ38tTSe580rFQhUAQJLuvtOB1FtTBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAoQoAYABCFQDAAIQqAIABCFUAAAMQqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAjtjoDgAArKeq2plk54xTe7p7z1DPEaoOLddU1a4hbtTdg9wHAA4BpyQ5bUb76Ul2zSqoqrskuUsmslJ3n7/SQ4SqQ0h3P2+j+wAAh6Azkuye0T5zlKqqnp/kSUk+nmTfuLmTCFUAwPY1nuJbyzTfo5Lcqbu/vpbnWKgOADDt0iTXrrXISBUAwLT/meSNVfU3Sa5Zauzus1YqEqoAAKadmuQ2Sb4r02uqViRUAQBMu0+S47t7bpCaZE0VAMC0TyS58VqLjFQBAEz7WpJ/qqq3ZHpN1bNXKhKqAACmfWz8WhOhCgBgQnefvkidUAUAMFZVD0jy2CS3Hzd9Nslru/ud82otVAcASFJVv5rkzCSfSfKH49dnkpxZVf9rXr2RKgCAkScluWd3XzPZWFVnJflIkl9bqdhIFQDASCW5fkb7rLb/wEgVAMDIOUneV1W/n+SScdsdkzwxye/PKxaqAACSdPevVdXbkzwmyYPGzZcm+fnufvu8eqEKAGCsuy9IcsEitUIVAMDYfrZU+NPufse8WgvVAQCy4pYKL7WlAgDA6tlSAQBgALZUAAAYgC0VAAAOlC0VAAAGciBbKlhTBQCQpKpuXFXPqqrHjo+fWVVvrKrfqqqbzKs3UgUAMPKqjLLRQ6rqvyW5UZI/SPLwJGcnecJKxUIVAMDId3b3PavqqCT/luQ23X1tVb0uyYfmFZv+AwCY1hltr9BJ0t3Xj49XZKQKAGDkQ1X12iRHJ3lLknOq6g1Jvj/Jx+cVC1UAACNPTfK0jEaoXp7kYUmenuTT4/YVCVXb3Ft++M0b3QW2iIf90vEb3QW2kH975ac3ugtsITdb5XXd/e9Jfnei6U3j16oIVQAAE6pqR5LHJ7lLJrJSdz97pTqhCgBg2nlJjkry3iTfWG2RUAUAMO247j5hrUW2VAAAmPapqrrpWouMVAEATLsiyYVV9ZYk1yw1WlMFALA2H88q9qVaTqgCAJjQ3acvUidUAQBMqKrnz2qfN/1noToAwLSrJ177kjwiyTHzioxUAQBMWD79V1W/meTceXVGqgAAVnZVkuPmXWSkCgBgwrI1VYclOSmr+DagUAUAMO3qifd7k5yd5J3zioQqAICxqrp1kjcl+VB3762qY5L8UpKXJbn5SrXWVAEAJKmqn0hySZI3J/lAVf1AkouT3C6jKcAVGakCABh5ZpITu/ujVfW9Sd6a5Ee7+3WrKTZSBQAwcl13fzRJuvtdST612kCVGKkCAFhyVFWdkKTGx9dPHnf3RSsVC1UAACNHJzl/WdvScSe580rFQhUAQJLuPvZA6q2pAgAYgFAFADAAoQoAYABCFQDAAIQqAIABCFUAAAMQqgAABiBUAQAMwOafAABJqupWSZ6R5C6ZyEjd/ZjV1AtVAMCWVlU7k+yccWpPd++ZOH59kn9J8rdJ9q31OdsyVFXVqUl2bHQ/NlJ379roPgDAQXJKktNmtJ+eZNfE8c27+2mLPmRbhqokO4QKANg2zkiye0b7nmXH/1xVt+3uyxZ5yHYNVQDANjGe4lseoGa5eZKPVNW7klwzUW9NFQDAGvzR+LUQoQoAIEl3n3Mg9UIVALCtVdXPd/fvVtXzZ53v7mev5j5CFQCw3S2tn7r6QG4iVAEA21p3v3z88/QDuY9QBQBsa1X10yud7+6zVnMfoQoA2O7uu8K5Xu1NhCoAYFvr7icPcZ/DhrgJAMChrqqOrqpfq6o/HB/fvap+cLX1QhUAwMjLkhyZ5LvGx5/L7N8ZOJNQBQAwcs/uPjXJtUnS3VdlDVlJqAIAGLl28qCqdkSoAgBYswuq6peT3KiqHpTkT5P8xWqLhSoAgJFfSVJJrkzy/CTvS7JrtcW2VAAAGDmiu38jyW8sUmykCgBg5LNV9aqq+p5FioUqAICR45N8MMlLquoTVfXLVfXtqy0WqgAAknT3V7r7pd19UpJHJblrkk+vtt6aKgCAsao6LMnJSX48yfcl2b3aWqEKACBJVb0oyX9P8tEk5yT5se7+99XWC1UAACNfSXL/7v7sIsVCFQBAku7+9QOpt1AdACBJVd2rqt5dVV+vqn1Lr9XWG6kCABh5WZJfTfKiJA9P8jMZ7a6+KkaqAABGdnT33yU5rLv/rbt/NckjVlssVAEAjOwd//xKVd27qm6Z5I6rLTb9BwAw8tpxkPqtJO9McniS56y2WKja5n7x+os3ugtsEW958Z02ugtsIT97uP974uCpqu8Yv/2rJN+W5NIkS7//7+qqulF3f2PefXxqAYDt7s0z2nr888gkN6mq/9ndr17pJkIVALCtdfeKQ+1VdZskf5dkxVBloToAwAq6+98y2m5hRUIVAMAc3f17864RqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAAxCqAAAGIFQBAAxAqAIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYwBED3++aqto18D3Xw7Eb3QEAYGsZNFR19/OGvN96OUSCHwBwCDH9BwAwAKEKAGAAQhUAwACEKgCAAQhVAAADGHpLBQCATaWqdibZOePUnu7eM9RzhKqDoKpOTbJjo/sxqbt3bXQfAOAgOSXJaTPaT0+ya3ljVR2R5GlJHpKkk7w1ySu6e+9KDxGqDo4dQgwAbJgzkuye0b6/UaozM9oo/JwkleQJSe6V5CdXeohQBQBsaeMpvrVM831fknt09/VJUlWvTfKReUUWqgMATPtckhtNHB+Z5LPzioxUAQBM+3SSd49HqJLk0UkuqKqfTpLuPmtWkVAFADDtyCQfSHL8+PhDSW6W5L4ZLVyfSagCAJjQ3U9epE6oAgBYpqoekuS4TGSl/U37LRGqAAAmVNW5Se6Z0bTfvnHzfqf9lghVAADTTspoS4V9c6+cYEsFAIBpn0zyLWstMlIFADDtFzLaQuGdSa5ZauzuZ69UJFQBAEx7SZLPZ7QL+6qnAIUqAIBp397dJ6y1yJoqAIBpH66q26y1yEgVAMC0nUn+uarelek1VY9ZqUioAgCY9kfj15oIVQAAE7r7nEXqhCoAgAlVdV5m7KBu+g8AYG3eNPF+R5IfSXLRvCKhCgBgwvLpv6p6TZL/M6/OlgoAACvrJHead5GRKgCACcvWVB2W5F5J/nZenVAFADBtck3V3iS/093vmVckVAEATLClAgDAAdjfVgpj1yS5OMnLuvtLsy4QqgAARt60wrkjkvynJH+S5KH7uwAAYNtbzbRfVX1of+eEKgCACVW1I8njk9wlE1mpu5+d5KT91QlVAADTzktyVJL3JvnG5Inuvm5/RULVNnfUYT4CDONXb3v5RneBLeTGd7U3NRvquO4+Ya1FPrUAANM+VVU3XWuRYQoAgCRV9fzx2yuSXFhVb8loK4Uk31xTtV9CFQDAyNXjnx8fv9ZEqAIASNLdpx9IvVAFADBhYhpw0hVJ3t3df7+/OgvVAQCmfVuSH8lo8OmIJD+c5PgkL66qX9lfkVAFADDttknu093P7O5nZrTh5y2SPCCjTUFnEqoAAKbdrru/unQwfn9sd1+ZZZuBTrKmCgBg2kVV9Yokr0nSSX48ySeq6kZJ9u2vyEgVAMC0pyT5WpKXJjkro60WnpJRoHrE/oqMVAEATOjuryV51n5O7/d3cglVAABJqurR3X1eVf30rPPdfdZK9UIVAMDIdyY5L8l9Z5zrecVCFQDAyN9V1fdltEB9zYQqAICRF068PyHJRUlqfNxJ7rdS8XYNVddU1a6D+LxjD+KzAIAFdPc3p/2q6gPdvWKIWm5bhqruft7BfN5BDnAAwIGbu4ZqOftUAQAMYFuOVAEALFdV3zFxuKOqTsgNa6rS3RetVC9UAQCMvHnZ8fkT7zvJnVcqFqoAAJJ0950OpN6aKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAoQoAYABCFQDAAIQqAGBLq6qdVXXsjNfOGdf+6WraZrGj+iZUVacm2bGez+juXet5fwDYRE5JctqM9tOT7FrWdtyM6+6+mocIVZvTDqEHAAZzRpLdM9r3LL2pqqcmeVqS46vqfRPX3CzJx1fzEKEKANjSuntPJgLUfvx1kouTvDTJL0y0fy3Jh1fzHKEKANj2uvuSJJck+c4kqaobj9uvXu09LFQHABirqjtX1XuSfDnJl6rqH6rqzqupFaoAAG7w8iSvSPItSY5O8spx21xCFQDADY7p7lf3DV6T5JjVFApVAAA3uL6q7rZ0UFXHJ9m3mkIL1QEAbvDLSd5RVR8cH987yY+tplCoAgAY6+6/qqrvTHK/JJXk3d39pdXUClUAABO6+4tV9dcZ56SqOrq7vz6vzpoqAICxqvqhqvpckn9PcmWSq8Y/5xKqAABu8Pwkj0lyZHcf3t2Hdffhqyk0/QcAcIOvdPc/LFJopAoA2PaFHR/sAAAI7ElEQVSq6uiqOjrJn1XVT1XVLZbaxu1zGakCABitneqMvvGXJGdOHHeSuVOAQhUAsO1199TsXVXdPMmDknyquz+0mnuY/gMAtr2qOreq7jV+f4skH07y60n+uqr+v9XcQ6gCAEju090fHr//sST/0t33SHKfJD+7mhsIVQAAo32pljwgyZ8lSXd/LqM1VXMJVQAASarqtlX1LRmtpXr7xKkdq6m3UB0AIPmtJB9Mcm2Sd3b3RUlSVd+d5NLV3ECoAgC2ve4+r6rekeTWSSa/7Xdpkqeu5h5CFQBAku7+QpIvLGu7bLX11lQBAAxAqAIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADsE/VwXFNVe1aw/XHrlM//oOLvrKqTWJhrn/pB2x0F9hCjr/uSxvdBbaQmx2k5whVB0F3P28t168xgAEAm4DpPwCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAoQoAYABCFQDAAIQqAIABCFUAAAMQqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAAxCqAAAGIFQBAAxAqAIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADOCIje4AAMB6qqqdSXbOOLWnu/cM9RyhanO6pqp2recDuntd7w8Am8gpSU6b0X56kl37K6qqmyRJd1+1mocIVZtQdz9vo/sAAFvIGUl2z2ifOUpVVXdP8gdJ7pmkq+ojSZ7Y3R9b6SFCFQCwpY2n+NYyzbc7ye9lFKyS5PHjtu9eqchCdQCAaUd29+/3Dc7NKgaihCoAgGkfqqoHLB1U1fcmec+8ItN/AADTTkzypKr65Pj4uCQfrKr3JUl3329WkVAFADDt5xcpEqoAACZ099sXqROqAAAmVNXdkvxKRtN+38xK+5v2WyJUAQBMOy+j7RR2J9m32iKhCgBg2t7ufsFai2ypAAAw7a+q6uFrLTJSBQAw7W+T/EVVXZ/kG0kqSXf3rVYqEqoAAKa9IsmTk7w/1lQBACzsK939urUWWVMFADDtz6vqJ6vqFlV19NJrXpGRKgCAab8+/nlWks54TVWSw1cqEqoAACZ090IzeUIVAMCE/U31dffXV6oTqgAApl2V6Wm/Jab/AABWa3L6r6p2JPnRJN86r863/wAA9qO7r+nuVyf5gXnXGqkCAJiwbE3VYUnum+S28+qEKgCAaZNrqvYl+WSSn5tXJFQBAEywpQIAwAGYs2v6td29d6V6C9UBAEauSnLl+Ofy1zVV9a9VdfL+io1UAQBk5Wm/qjo8yYlJXpPk/FnXGKkCAJiju/d19z8medP+rjFSBQAwoaouz/RO6klyRZJ3J3n2/uqEKgCAaWcmuVlGU32V5IkZhapK8ookj5xVVN3Lgxgwqap2JjklyRndvWej+8Ohy2eJIfk8rZ+qem93339Z29u7+4FV9dHuvsesOmuqYL6dSU4b/4QD4bPEkHye1s/Nq+oWSwdVdcsktx4fXru/ItN/AADTXpLkQ1V1fkZrq05O8vyqukmSd+2vSKgCAJjQ3S+tqguSPDCjdVRndfeHx6d/dn91QhUAwDLjEPXhuRdOsKYKAGBCVX1PVb2zqi6rqi9W1eVV9cV5dUaqYL49SU4f/4QD4bPEkHye1s//TvJrSd6TZN9qi2ypAAAwoare390nrrXO9B8AwLTzq+oRay0yUgUAMGH8a2pumeTKJN/I6BuA3d23WqnOmiq2pKr6TJJrxq8keWt3/48F7vOUJBd09ycX7MeLkzwqyR2TnNDdH1vkPmyszfB5qqpbJTknyZ0z+kv+E0me3t1fXuu92Dib4bM0rn9jkjskuT6j4PCzE1sGkJy0SJFQxVb2I939zwd4j6ckuSzJmv7iqqojuntvktcneWFGix05tG3o5ymjxbK/1d0XjNtenOQ3kzz9APvEwbcZ/m56QndfMW774SSvSnK/A+zTltHdl4z/d3e3jDb//MT4v9uKhCq2jar6sYw2bTsqo/+RPLO73zY+d48kv5vkmIyGeZ+fZEeS70pyZlVdmeR/JHlHkhck+S/je5yf5Je6e19VnZvky0nunuTmSe7X3e8c3/8g/Sk5WA7256m775fkgokuvCfJk9f5j8lBsEF/N10x0YWbZTRixVhVnZTRP4qXpv6OqKof7u73r1jY3V5eW+6V5DNJPpbkg+PX9ye55cT570hy6fj9UUn+Ncmjxse1dG2SdyZ5+ETdM5K8JcmRSW6U5G1Jnjo+d26S9yY5ekZ/Ppfk7hv938Vry3yeDk/y1iQ/vdH/bbwO3c9Sktck+WySSzJanrDh/302yyujX0XzkInjByd517w6I1VsZVND7FX13VX1x0lum2RvkttV1bcmuV2Sfd39Z8loJWJG/6qb5aFJXtPd143vuTvJI5K8cnz+vO7++nr8Ydhwm+nzdGaSryQ5+4D/VGyETfFZ6u4nj699cpLfTvLIYf54W8KNu/vvlw66+61VdeN5RbZUYDt5bZKXdPd3JrlPRmtUdmT0r7/VqoyG1idNHl91QD3kULIhn6fxWqo7Jnlcd5uy2Ro2+u+m3UkeXlU3W8PztrqvV9WDlw6q6oFJ5v6DWahiO7lZkk+P3z8to2HyJLkoyeFV9agkqZFbjs99bVy35G+SPLmqjqiqo5I8McnfrnvP2YwO+uepqn47yT2T/FB3XzvYn4SNdlA/S1V106q63UTTDyb5Qk+vs9rufj7J7qr6RFV9PKNv3j5jXpFQxXZySpI3VdU7ktwmyRVJMv4/p0cmeUZVfTg3rHNIkpcneW5VfXD8r5aXJfmX8TXvT/JPGa1LmKmqzqyqzyW5dZK3je/P1nBQP09Vde8kz07y7UnePb7H69brD8dBdbD/brppkjdU1Ueq6kNJfiam/qZ09z8mOS7JDyX5kSTHJ/mzeXU2/wQAmKOqPtvdt1/pGiNVAADzzR2F8u0/AIAkVfUdK5yem5lM/wEAJKmqT69wurv7zivWC1UAAAfOmioAgAEIVQAAAxCqAAAGIFQBAAzg/wdWT4lsxDTUbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the factor loading matrix\n",
    "sns.clustermap(df_loadings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you read down Factor 1 you can see that Hurdles, Run200m and Run800m seem to have high loadings.  We might name this the \"running\" factor.  Factor 3 has relatively high values for the jumping events.  Factor 2 is a bit of a mishmash.  We see high values for shot and javelin, which makes sense, but also for Run800m.  We might not have a great story for this.  Given our experience with PCA above we might try a two factor model instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "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>Factor1</th>\n",
       "      <th>Factor2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Hurdles</th>\n",
       "      <td>0.956422</td>\n",
       "      <td>0.173830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HighJump</th>\n",
       "      <td>-0.769389</td>\n",
       "      <td>-0.433264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Shot</th>\n",
       "      <td>-0.721458</td>\n",
       "      <td>0.186360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run200m</th>\n",
       "      <td>0.877247</td>\n",
       "      <td>-0.401455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LongJump</th>\n",
       "      <td>-0.953748</td>\n",
       "      <td>-0.051143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Javelin</th>\n",
       "      <td>-0.126044</td>\n",
       "      <td>0.508433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run800m</th>\n",
       "      <td>0.756286</td>\n",
       "      <td>0.140128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Factor1   Factor2\n",
       "Hurdles   0.956422  0.173830\n",
       "HighJump -0.769389 -0.433264\n",
       "Shot     -0.721458  0.186360\n",
       "Run200m   0.877247 -0.401455\n",
       "LongJump -0.953748 -0.051143\n",
       "Javelin  -0.126044  0.508433\n",
       "Run800m   0.756286  0.140128"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a three-factor model\n",
    "fa_model = skd.FactorAnalysis(n_components=2) \\\n",
    "              .fit(df_hept_norm.ix[:,:7])\n",
    "\n",
    "# Show the loadings\n",
    "df_loadings = pd.DataFrame(fa_model.components_[:2,:].T, \n",
    "                   index=df_hept.columns,\n",
    "                   columns=['Factor1', 'Factor2'])\n",
    "df_loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x1c1d960f98>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6z0J1AIBp10y89mf0HYC3nVdkpAoAYMLy6b+q+rUk586rM1IFALC6q5McO+8iI1UAABOWrak6LMn9s4ZPAwpVAADTrpl4vy/JWUneM69IqAIAGKuq2yd5c5IPd/e+qrptkp9P8ookt1qtdtBQVVUnJ9k15D0PckdvdQcAgLWpqp9McmaSLye5cpxrfjvJ2zKaAlzV0CNVu7p7z8D3PGhV1Z6t7gMAsGbPTnJCd3+sqr47yduT/Fh3v3EtxT79BwAwcn13fyxJuvu9ST611kCVWFMFALDkJlV1fJIaH98wedzdF61WLFQBAIwcleT8ZW1Lx53kmNWKhSoAgCTdffSB1FtTBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgM0/AYBDWlXtTrJ7xqm93b13qOcIVQe5qjo5ya711nX3nuF7AwDb0klJTp3RflqSPUM9RKg6+O0SkABgVacnOXtG+8xRqqp6cZLnJ7kmyduTnJDkGd197moPsaYKADikdffe7v7MjNdKU3/f291fSfIDSS5Pcs8kz5n3HKEKAGC2hyR5U3dfkaTnXSxUAQBM+3xVvTrJf0ry51V1RNawZEqoAgCY9mNJPpbkcd395SR3TvLieUVCFQDAhO6+Mslrk1w3Pv5Md589r06oAgCYUFUnZjRS9abx8f2r6k/m1QlVAADTTkvygCRfTpLuviDJPeYVCVUAAMt09z8va/r6vBqhCgBg2lVV9S0Zb6NQVQ/LChuFTrKjOgDAtJOT/GmSu1fVOzLa/PPR84qEKgCACd39gap6eJIHJ6kkf72WL14WqgAAlhl/Tc2frqdGqAIASFJVV2b219FUku7u261WL1QBAIzc/0CKhSoAgCTdfemB1AtVAABZdfovSWL6DwBgbZam/34yyW2SvCqj9VRPTfK5ecVCFQBAbpz+q6qHdvdDJ079bFW9M8kLV6u3ozoAwLQ7VtU3Lx2M399hXpGRKgCAaacnubCq3jI+PjHJr80rEqoAACZ09xlV9a4kD8toTdXLu/uj8+qEKgCAsao6PMkfdfe/TzI3SE2ypgoAYKy79yf5pqpad0YyUgUAMO1vkrypqn4nydVLjd19/mpFQhUAwLQHj3/+1ERbJxGqAADWqrsfvkidUAUAMKGqTpzVbvoPAGB9njvxfleS70zywZj+AwBYu+XTf1X1bUmePa9OqNpY11bVng1+xtEHUrz/4vcN1A1gLa6/1k42cLDp7ouq6j7zrhOqNlB3v2Cjn7EJoQ0AdpRla6oOS/LArGFvT6EKAGDa5JqqfUk+meSx84qEKgCAJFX1kPHbU2ecvkuST69WL1QBAIy8eOL98UkuyugLlZPR5p8PXK1YqAIASNLdD1h6X1Uf6u5VQ9RyPoYCAPCv9XoLhCoAgAGY/gMAyDc2+Vyyq6qOz41rqtLdF61WL1QBAIy8Zdnx5NfSdJJjVisWqgAAknT33Q+k3poqAIABCFUAAAMQqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAAxCqAAAGIFQBAAxAqAIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAZwxFZ3AABgI1XV7iS7Z5za2917h3qOUHXwu7aq9qy3qLvXXQMAB6mTkpw6o/20JHtmFVTVPZLcIxNZqbvPX+0hQtVBrrtfsNV9AIBt7vQkZ89onzlKVVUvTPLkJBcn2T9u7iRCFQCwc42n+NYzzfeYJHfv7q+t5zkWqgMATLssyXXrLTJSBQAw7b8l+ZOq+vMk1y41dveZqxUJVQAA005Ocock35npNVWrEqoAAKbdL8lx3T03SE2ypgoAYNonktxsvUVGqgAApn01yd9V1dsyvabqeasVCVUAANM+Pn6ti1AFADChu09bpE6oAgAYq6rvSfK4JHcZN302yRu6+z3zai1UBwBIUlW/lOSMJJ9J8tvj12eSnFFV/2NevZEqAICRJye5d3dfO9lYVWcm+WiSX16t2EgVAMBIJblhRvustn/FSBUAwMg5ST5QVb+V5NJx292SPCnJb80rFqoAAJJ09y9X1TuT/GiSh42bL0vyc939znn1QhUAwFh3vyvJuxapFaoAAMZW2FLh97v73fNqLVQHAMiqWyq83JYKAABrZ0sFAIAB2FIBAGAAtlQAADhQtlQAABjIgWypYE0VAECSqrpZVT2nqh43Pn52Vf1JVf16Vd18Xr2RKgCAkddklI0eUVX/IclNk7w+ySOTnJXkiasVC1UAACPf0d33rqqbJPmnJHfo7uuq6o1JPjyv2PQfAMC0zmh7hU6S7r5hfLwqI1UAACMfrqo3JDkqyduSnFNVb0ryA0kunlcsVAEAjDwtydMzGqF6ZZLvS/KMJJ8et69KqNrh3vrDb9nqLsCO8v3PO2aruwCsoLv/JclvTDS9efxaE6EKAGBCVe1K8oQk98hEVuru561WJ1QBAEw7L8lNkvxNkq+vtUioAgCYdmx3H7/eIlsqAABM+1RV3WK9RUaqAACmfSXJBVX1tiTXLjVaUwUAsD4XZw37Ui0nVAEATOju0xapE6oAACZU1Qtntc+b/rNQHQBg2jUTr/1JHpXktvOKjFQBAExYPv1XVb+W5Nx5dUaqAABWd3WSY+ddZKQKAGDCsjVVhyW5f9bwaUChCgBg2jUT7/clOSvJe+YVCVUAAGNVdfskb07y4e7eV1W3TfLzSV6R5Far1VpTBQCQpKp+MsmlSd6S5ENV9YNJLklyp4ymAFdlpAoAYOTZSU7o7o9V1XcneXuSH+vuN66l2EgVAMDI9d39sSTp7vcm+dRaA1VipAoAYMlNqur4JDU+vmHyuLsvWq1YqAIAGDkqyfnL2paOO8kxqxULVQAASbr76AOpt6YKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAm38CACSpqtsleVaSe2QiI3X3j66lXqgCAA5pVbU7ye4Zp/Z2996J4z9I8g9J/iLJ/vU+Z8eGqqo6Ocmure7HVunuPVvdBwDYJCclOXVG+2lJ9kwc36q7n77oQ3ZsqEqyS7AAgB3h9CRnz2jfu+z476vqjt19xSIP2cmhCgDYAcZTfMsD1Cy3SvLRqnpvkmsn6q2pAgBYh98ZvxYiVAEAJOnucw6kXqgCAHa0qvq57v6NqnrhrPPd/by13EeoAgB2uqX1U9ccyE2EKgBgR+vuV45/nnYg9xGqAIAdrap+erXz3X3mWu4jVAEAO90DVjnXa72JUAUA7Gjd/ZQh7nPYEDcBADjYVdVRVfXLVfXb4+Nvrar/uNZ6oQoAYOQVSY5M8p3j489l9ncGziRUAQCM3Lu7T05yXZJ099VZR1YSqgAARq6bPKiqXRGqAADW7V1V9QtJblpVD0vy+0n+eK3FQhUAwMgvJqkkVyV5YZIPJNmz1mJbKgAAjBzR3b+a5FcXKTZSBQAw8tmqek1VPXiRYqEKAGDkuCQXJnlZVX2iqn6hqu681mKhCgAgSXd/qbtf3t33T/KYJPdM8um11ltTBQAwVlWHJTkxyU8keUiSs9daK1QBACSpqpck+U9JPpbknCQ/3t3/stZ6oQoAYORLSR7U3Z9dpFioAgBI0t2/ciD1FqoDACSpqvtU1fuq6mtVtX/ptdZ6I1UAACOvSPJLSV6S5JFJ/ktGu6uviZEqAICRXd39l0kO6+5/6u5fSvKotRYLVQAAI/vGP79UVfetqtskudtai03/AQCMvGEcpH49yXuSHJ7klLUWC1U73HP3X7zVXYAd5c9edo+t7gLsOGc+e/XzVfVt47dvTfItSS5LsvT9f9dU1U27++vzniNUAQA73VtmtPX455FJbl5V/627X7vaTYQqAGBH6+67r3a+qu6Q5C+TrBqqLFQHAFhFd/9TRtstrEqoAgCYo7t/c941QhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAoQoAYABCFQDAAIQqAIABCFUAAAMQqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAAzhi4PtdW1V7Br7nRjl6qzsAABw6Bg1V3f2CIe+3kQ6i8AcAHARM/wEADECoAgAYgFAFADAAoQoAYABCFQDAAIbeUgEAYFupqt1Jds84tbe79w71HKFqk1TVyUl2bXU/lnT3nq3uAwBskpOSnDqj/bQke5Y3VtURSZ6e5BFJOsnbk7yqu/et9hChavPsEmQAYEucnuTsGe0rjVKdkdEm4eckqSRPTHKfJM9c7SFCFQBwSBtP8a1nmu8hSb69u29Ikqp6Q5KPziuyUB0AYNrnktx04vjIJJ+dV2SkCgBg2qeTvG88QpUkj03yrqr66STp7jNnFQlVAADTjkzyoSTHjY8/nOSWSR6Q0cL1mYQqAIAJ3f2UReqEKgCAZarqEUmOzURWWmnab4lQBQAwoarOTXLvjKb99o+bV5z2WyJUAQBMu39GWyrsn3vlBFsqAABM+2SSb1pvkZEqAIBpz81oC4X3JLl2qbG7n7dakVAFADDtZUkuz2gX9jVPAQpVAADT7tzdx6+3yJoqAIBpH6mqO6y3yEgVAMC03Un+vqrem+k1VT+6WpFQBQAw7XfGr3URqgAAJnT3OYvUCVUAABOq6rzM2EHd9B8AwPq8eeL9riQ/kuSieUVCFQDAhOXTf1X1uiT/Z16dLRUAAFbXSe4+7yIjVQAAE5atqTosyX2S/MW8OqEKAGDa5JqqfUn+V3e/f16RUAUAMMGWCgAAB2ClrRTGrk1ySZJXdPcXZl0gVAEAjLx5lXNHJPk3SX4vyfeudAEAwI63lmm/qvrwSueEKgCACVW1K8kTktwjE1mpu5+X5P4r1QlVAADTzktykyR/k+Trkye6+/qVioSqHe6ow2+61V2AHeWUu35+q7sAzHdsdx+/3iI7qgMATPtUVd1ivUVGqgAAklTVC8dvv5Lkgqp6W0ZbKST5xpqqFQlVAAAj14x/Xjx+rYtQBQCQpLtPO5B6oQoAYMLENOCkryR5X3f/1Up1FqoDAEz7liQ/ktHg0xFJfjjJcUleWlW/uFKRUAUAMO2OSe7X3c/u7mdntOHnrZN8T0abgs4kVAEATLtTd3956WD8/ujuvirLNgOdZE0VAMC0i6rqVUlel6ST/ESST1TVTZPsX6nISBUAwLSnJvlqkpcnOTOjrRaemlGgetRKRUaqAAAmdPdXkzxnhdNXrlQnVAEAJKmqx3b3eVX107POd/eZq9ULVQAAI9+R5LwkD5hxrucVC1UAACN/WVUPyWiB+roJVQAAIy+eeH98kouS1Pi4kzxwteKdHKqurao9m/i8ozfxWQDAOnX3N6b9qupD3b1qiFpux4aq7n7BZj5vkwMcAHBg5q6hWs4+VQAAA9ixI1UAAJOq6tsmDndV1fG5cU1Vuvui1eqFKgCAkbcsOz5/4n0nOWa1YqEKACBJd9/9QOqtqQIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAOaVW1u6qOnvHaPePa319L2yx2VN/GqurkJLs24t7dvWcj7gsA29BJSU6d0X5akj3L2o6dcd23ruUhQtX2tkv4AYADdnqSs2e07116U1VPS/L0JMdV1QcmrrllkovX8hChCgA4pHX33kwEqBX8WZJLkrw8yXMn2r+a5CNreY5QBQDseN19aZJLk3xHklTVzcbt16z1HhaqAwCMVdUxVfX+JF9M8oWq+uuqOmYttUIVAMCNXpnkVUm+KclRSV49bptLqAIAuNFtu/u1faPXJbntWgqFKgCAG91QVfdaOqiq45LsX0uhheoAADf6hSTvrqoLx8f3TfLjaykUqgAAxrr7rVX1HUkemKSSvK+7v7CWWqEKAGBCd3++qv4s45xUVUd199fm1VlTBQAwVlU/VFWfS/IvSa5KcvX451xCFQDAjV6Y5EeTHNndh3f3Yd19+FoKTf8BANzoS93914sUGqkCAHa8qjqqqo5K8odV9VNVdeultnH7XEaqAABGa6c6o0/8JckZE8edZO4UoFAFAOx43T01e1dVt0rysCSf6u4Pr+Uepv8AgB2vqs6tqvu1ruMbAAAIFUlEQVSM3986yUeS/EqSP6uq/7yWewhVAADJ/br7I+P3P57kH7r725PcL8nPrOUGQhUAwGhfqiXfk+QPk6S7P5fRmqq5hCoAgCRVdceq+qaM1lK9c+LUrrXUW6gOAJD8epILk1yX5D3dfVGSVNV3JblsLTcQqgCAHa+7z6uqdye5fZLJT/tdluRpa7mHUAUAkKS7/znJPy9ru2Kt9dZUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAA7BP1ea5tqr2rLPm6A3ox5SPfenSjX4EMOHjFz94q7sAO87tN+k5QtUm6e4XrLdmgRAGAGwR038AAAMQqgAABiBUAQAMQKgCABiAUAUAMAChCgBgAEIVAMAAhCoAgAEIVQAAAxCqAAAGIFQBAAxAqAIAGIBQBQAwAKEKAGAAQhUAwACEKgCAAQhVAAADEKoAAAYgVAEADECoAgAYgFAFADAAoQoAYABCFQDAAIQqAIABCFUAAAMQqgAABiBUAQAMQKgCABjAEVvdAQCAjVRVu5PsnnFqb3fvHeo5QtX2dm1V7dmIG3f3htwXALahk5KcOqP9tCR7ViqqqpsnSXdfvZaHCFXbWHe/YKv7AACHgNOTnD2jfeYoVVV9a5LXJ7l3kq6qjyZ5Und/fLWHCFUAwCFtPMW3nmm+s5P8ZkbBKkmeMG77rtWKLFQHAJh2ZHf/Vt/o3KxhIEqoAgCY9uGq+p6lg6r67iTvn1dk+g8AYNoJSZ5cVZ8cHx+b5MKq+kCSdPcDZxUJVQAA035ukSKhCgBgQne/c5E6oQoAYEJV3SvJL2Y07feNrLTStN8SoQoAYNp5GW2ncHaS/WstEqoAAKbt6+4XrbfIlgoAANPeWlWPXG+RkSoAgGl/keSPq+qGJF9PUkm6u2+3WpFQBQAw7VVJnpLkg7GmCgBgYV/q7jeut8iaKgCAaX9UVc+sqltX1VFLr3lFRqoAAKb9yvjnmUk64zVVSQ5frUioAgCY0N0LzeQJVQAAE1aa6uvur61WJ1QBAEy7OtPTfktM/wEArNXk9F9V7UryY0m+eV6dT/8BAKygu6/t7tcm+cF51xqpAgCYsGxN1WFJHpDkjvPqhCoAgGmTa6r2J/lkkp+dVyRUAQBMsKUCAMABmLNr+nXdvW+1egvVAQBGrk5y1fjn8te1VfWPVXXiSsVGqgAAsvq0X1UdnuSEJK9Lcv6sa4xUAQDM0d37u/tvk7x5pWuMVAEATKiqKzO9k3qSfCXJ+5I8b6U6oQoAYNoZSW6Z0VRfJXlSRqGqkrwqyaNnFVX38iAGbHdVtTvJSUlO7+69W90fONT5ndtZqupvuvtBy9re2d0PraqPdfe3z6qzpgoOTruTnDr+CWw8v3M7y62q6tZLB1V1myS3Hx9et1KR6T8AgGkvS/Lhqjo/o7VVJyZ5YVXdPMl7Vyoy/QcHoao6Osmnk9y9uz+zpZ2BHcDv3M5TVfdJ8tCM1lG9o7s/Mq/GSBUAwDLjEDU3SE2ypgoAYEJVPbiq3lNVV1TV56vqyqr6/Lw6I1VwcNqb5LTxT2Dj+Z3bWf53kl9O8v4k+9daZE0VAMCEqvpgd5+w3jrTfwAA086vqkett8hIFQDAhPHX1NwmyVVJvp7RJwC7u2+3Wp01VbBJquozSa4dv5Lk7d39Xxe4z1OTvKu7P7lgP16a5DFJ7pbk+O7++CL3gYPBdvi9q6rbJTknyTEZ/Q/6E0me0d1fXO+92DT3X6RIqILN9SPd/fcHeI+nJrkiybr+cq+qI7p7X5I/SPLijBZgwk6wpb93GS10/vXufte47aVJfi3JMw6wT2yQ7r50/N/uXhlt/vmJ8d+fqxKqYAtV1Y8n+ZkkN8noF/fZ3f2O8blvT/IbSW6b0dDzC5PsSvKdSc6oqquS/Nck707yoiTfP77H+Ul+vrv3V9W5Sb6Y5FuT3CrJA7v7PeP7b9KfEraXzf696+4HJnnXRBfen+QpG/zH5ABU1f0z+gfo0tTfEVX1w939wdXqhCrYXG+sqqVpiP+e5Pzufn2SVNW3JXlrkrtW1U2S/J8kz+nuP6xRArp1d3+xqn4iya9091vHdc9K8m0Z/aV/WJK3ZfSv6lePn/NdSR7e3V/blD8hbD/b5veuqg5P8swk523Yn5Yh/EaSp3T3XyVJVT08yW8m+e7VioQq2FxT0xBV9V1V9btJ7phkX5I7VdU3J7lTkv3d/YfJaHVkRv/yneV7k7yuu68f3/PsJI/KjX+5nydQscNtp9+7M5J8KclZB/ynYiPdbClQJUl3v72qbjavyJYKsLXekORl3f0dSe6X0dqLXRkNN69VZTT9MGny+OoD6iEcerbk9268lupuSR7f3Tesq8dstq+NR6eSJFX10CRz/3EqVMHWumVGX9KaJE9PcuT4/UVJDq+qxyRJjdxmfO6r47olf57kKVV1xHj64klJ/mLDew4Hr03/vauq/5nk3kl+qLuvG+xPwkb5uSRnV9UnqurijD69+ax5RUIVbK2Tkry5qt6d5A5JvpIk4790H53kWVX1kSQXJvmBcc0rkzy/qi4c/0vqFUn+YXzNB5P8XZLXrfTAqjqjqj6X5PZJ3jG+P+wkm/p7V1X3TfK8JHdO8r7xPd64UX84Dlx3/22SY5P8UJIfSXJckj+cV2fzTwCAOarqs919l9WuMVIFADDf3FEon/4DAMg3tthYydzMZPoPACBJVX16ldPd3cesWi9UAQAcOGuqAAAGIFQBAAxAqAIAGIBQBQAwgP8LWCm94Kfm5N8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the factor loading matrix\n",
    "sns.clustermap(df_loadings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis 2 (Products)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "sns.set_context(\"notebook\")  # make figures fit\n",
    "from pylab import rcParams\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.graphics.mosaicplot import mosaic\n",
    "from IPython.display import Image\n",
    "from IPython.core.display import HTML \n",
    "import sklearn as sk\n",
    "import sklearn.cluster as skc\n",
    "import sklearn.decomposition as skd\n",
    "import sklearn.manifold as skm\n",
    "import sklearn.preprocessing as skp\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Bivariate Analysis (Quick Review)\n",
    "\n",
    "In this lab, we will mostly follow the analytic procedure in the following book chapter:\n",
    "\n",
    "> Chapman and Feit, \"Reducing Data Complexity\", _R for Marketing Research and Analytics_, Chapter 8, (2015).\n",
    "\n",
    "Many of the text descriptions below are taken from this chapter. Of course, you will see example code given in python instead of R. We will use the dataset in the book, customer brand perception surveys. For exercise questions, you will work on the iris dataset.\n",
    "\n",
    "This section involves data importing and some descriptive analysis, serving as a quick review of previous weeks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "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>perform</th>\n",
       "      <th>leader</th>\n",
       "      <th>latest</th>\n",
       "      <th>fun</th>\n",
       "      <th>serious</th>\n",
       "      <th>bargain</th>\n",
       "      <th>value</th>\n",
       "      <th>trendy</th>\n",
       "      <th>rebuy</th>\n",
       "      <th>brand</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   perform  leader  latest  fun  serious  bargain  value  trendy  rebuy brand\n",
       "0        2       4       8    8        2        9      7       4      6     a\n",
       "1        1       1       4    7        1        1      1       2      2     a\n",
       "2        2       3       5    9        2        9      5       1      6     a\n",
       "3        1       6      10    8        3        4      5       2      1     a\n",
       "4        1       1       5    8        1        9      9       1      1     a"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Loads dataframe from a remote URL\n",
    "df_survey = pd.read_csv('data/products.csv')\n",
    "df_survey.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>perform</th>\n",
       "      <th>leader</th>\n",
       "      <th>latest</th>\n",
       "      <th>fun</th>\n",
       "      <th>serious</th>\n",
       "      <th>bargain</th>\n",
       "      <th>value</th>\n",
       "      <th>trendy</th>\n",
       "      <th>rebuy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.00000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.00000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.488000</td>\n",
       "      <td>4.417000</td>\n",
       "      <td>6.195000</td>\n",
       "      <td>6.06800</td>\n",
       "      <td>4.323000</td>\n",
       "      <td>4.259000</td>\n",
       "      <td>4.33700</td>\n",
       "      <td>5.220000</td>\n",
       "      <td>3.727000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.203454</td>\n",
       "      <td>2.608432</td>\n",
       "      <td>3.078059</td>\n",
       "      <td>2.74425</td>\n",
       "      <td>2.778199</td>\n",
       "      <td>2.667027</td>\n",
       "      <td>2.39858</td>\n",
       "      <td>2.742101</td>\n",
       "      <td>2.544592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.00000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>6.00000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.00000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.00000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.00000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           perform       leader       latest         fun      serious  \\\n",
       "count  1000.000000  1000.000000  1000.000000  1000.00000  1000.000000   \n",
       "mean      4.488000     4.417000     6.195000     6.06800     4.323000   \n",
       "std       3.203454     2.608432     3.078059     2.74425     2.778199   \n",
       "min       1.000000     1.000000     1.000000     1.00000     1.000000   \n",
       "25%       1.000000     2.000000     4.000000     4.00000     2.000000   \n",
       "50%       4.000000     4.000000     7.000000     6.00000     4.000000   \n",
       "75%       7.000000     6.000000     9.000000     8.00000     6.000000   \n",
       "max      10.000000    10.000000    10.000000    10.00000    10.000000   \n",
       "\n",
       "           bargain       value       trendy        rebuy  \n",
       "count  1000.000000  1000.00000  1000.000000  1000.000000  \n",
       "mean      4.259000     4.33700     5.220000     3.727000  \n",
       "std       2.667027     2.39858     2.742101     2.544592  \n",
       "min       1.000000     1.00000     1.000000     1.000000  \n",
       "25%       2.000000     2.00000     3.000000     1.000000  \n",
       "50%       4.000000     4.00000     5.000000     3.000000  \n",
       "75%       6.000000     6.00000     7.000000     5.000000  \n",
       "max      10.000000    10.00000    10.000000    10.000000  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's print out summary information to check the data quality \n",
    "# and structure.\n",
    "df_survey.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    100\n",
       "g    100\n",
       "c    100\n",
       "i    100\n",
       "b    100\n",
       "e    100\n",
       "j    100\n",
       "f    100\n",
       "h    100\n",
       "d    100\n",
       "Name: brand, dtype: int64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's check how many records we have per brand.\n",
    "df_survey.brand.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the above summary information, we can tell that the data are clean and are formatted appropriately."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Rescaling the Data\n",
    "Let us normalize the data by computing the \"[z-scores](https://en.wikipedia.org/wiki/Standard_score#Calculation_from_raw_score)\" of the values. This step of normalization (rescaling) is important to PCA.\n",
    "\n",
    "Given a column x, the z-scores of the elements in x is simply\n",
    "\n",
    "    (x - mean(x)) / std(x)\n",
    "    \n",
    "where, `std` means standard deviation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q2. Rescale the data</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "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>perform</th>\n",
       "      <th>leader</th>\n",
       "      <th>latest</th>\n",
       "      <th>fun</th>\n",
       "      <th>serious</th>\n",
       "      <th>bargain</th>\n",
       "      <th>value</th>\n",
       "      <th>trendy</th>\n",
       "      <th>rebuy</th>\n",
       "      <th>brand</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.77705</td>\n",
       "      <td>-0.159946</td>\n",
       "      <td>0.586702</td>\n",
       "      <td>0.704370</td>\n",
       "      <td>-0.836572</td>\n",
       "      <td>1.778524</td>\n",
       "      <td>1.110796</td>\n",
       "      <td>-0.445137</td>\n",
       "      <td>0.893714</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.08937</td>\n",
       "      <td>-1.310638</td>\n",
       "      <td>-0.713468</td>\n",
       "      <td>0.339789</td>\n",
       "      <td>-1.196697</td>\n",
       "      <td>-1.222571</td>\n",
       "      <td>-1.391936</td>\n",
       "      <td>-1.174870</td>\n",
       "      <td>-0.679034</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.77705</td>\n",
       "      <td>-0.543510</td>\n",
       "      <td>-0.388426</td>\n",
       "      <td>1.068950</td>\n",
       "      <td>-0.836572</td>\n",
       "      <td>1.778524</td>\n",
       "      <td>0.276552</td>\n",
       "      <td>-1.539736</td>\n",
       "      <td>0.893714</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.08937</td>\n",
       "      <td>0.607182</td>\n",
       "      <td>1.236787</td>\n",
       "      <td>0.704370</td>\n",
       "      <td>-0.476446</td>\n",
       "      <td>-0.097160</td>\n",
       "      <td>0.276552</td>\n",
       "      <td>-1.174870</td>\n",
       "      <td>-1.072221</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.08937</td>\n",
       "      <td>-1.310638</td>\n",
       "      <td>-0.388426</td>\n",
       "      <td>0.704370</td>\n",
       "      <td>-1.196697</td>\n",
       "      <td>1.778524</td>\n",
       "      <td>1.945040</td>\n",
       "      <td>-1.539736</td>\n",
       "      <td>-1.072221</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   perform    leader    latest       fun   serious   bargain     value  \\\n",
       "0 -0.77705 -0.159946  0.586702  0.704370 -0.836572  1.778524  1.110796   \n",
       "1 -1.08937 -1.310638 -0.713468  0.339789 -1.196697 -1.222571 -1.391936   \n",
       "2 -0.77705 -0.543510 -0.388426  1.068950 -0.836572  1.778524  0.276552   \n",
       "3 -1.08937  0.607182  1.236787  0.704370 -0.476446 -0.097160  0.276552   \n",
       "4 -1.08937 -1.310638 -0.388426  0.704370 -1.196697  1.778524  1.945040   \n",
       "\n",
       "     trendy     rebuy brand  \n",
       "0 -0.445137  0.893714     a  \n",
       "1 -1.174870 -0.679034     a  \n",
       "2 -1.539736  0.893714     a  \n",
       "3 -1.174870 -1.072221     a  \n",
       "4 -1.539736 -1.072221     a  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_survey_norm = df_survey.copy()\n",
    "\n",
    "df_survey_norm.ix[:,:9] = skp.scale(df_survey_norm.ix[:,:9].astype(np.float))\n",
    "# df_survey_norm = df_survey_norm.drop(columns = 'brand')\n",
    "df_survey_norm.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After rescaling (normalization), the means of all columns are all technically 0, and standard deviation 1.0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Bivariate Analysis\n",
    "For initial inspection of bivariate relationships among the variables, let us create a correlation plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q3. Create a clustermap. What do you see?</font>\n",
    "- Can you identify the clusters of variables from the plot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x1c1e12ae80>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.clustermap(df_survey_norm.corr(),cmap=plt.cm.OrRd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can notice that after normalizaation, rebuy, bargin, and value are clustered, and highly related with each other. Also, latest, trendy are clustered together. So it supports the need that we should use PCA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## By-Brand Analysis\n",
    "We are going combine all products from one manufacturer into a row (based on the mean score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "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>perform</th>\n",
       "      <th>leader</th>\n",
       "      <th>latest</th>\n",
       "      <th>fun</th>\n",
       "      <th>serious</th>\n",
       "      <th>bargain</th>\n",
       "      <th>value</th>\n",
       "      <th>trendy</th>\n",
       "      <th>rebuy</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>brand</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>a</th>\n",
       "      <td>-0.886362</td>\n",
       "      <td>-0.528168</td>\n",
       "      <td>0.411179</td>\n",
       "      <td>0.656974</td>\n",
       "      <td>-0.919400</td>\n",
       "      <td>0.214203</td>\n",
       "      <td>0.184785</td>\n",
       "      <td>-0.525407</td>\n",
       "      <td>-0.596465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.931336</td>\n",
       "      <td>1.071294</td>\n",
       "      <td>0.726470</td>\n",
       "      <td>-0.972701</td>\n",
       "      <td>1.183733</td>\n",
       "      <td>0.041640</td>\n",
       "      <td>0.151415</td>\n",
       "      <td>0.740679</td>\n",
       "      <td>0.237092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>0.650249</td>\n",
       "      <td>1.163350</td>\n",
       "      <td>-0.102388</td>\n",
       "      <td>-0.845098</td>\n",
       "      <td>1.223346</td>\n",
       "      <td>-0.607347</td>\n",
       "      <td>-0.440898</td>\n",
       "      <td>0.025541</td>\n",
       "      <td>-0.132504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>-0.680231</td>\n",
       "      <td>-0.593373</td>\n",
       "      <td>0.352671</td>\n",
       "      <td>0.186665</td>\n",
       "      <td>-0.692521</td>\n",
       "      <td>-0.881197</td>\n",
       "      <td>-0.933102</td>\n",
       "      <td>0.737030</td>\n",
       "      <td>-0.494236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e</th>\n",
       "      <td>-0.564673</td>\n",
       "      <td>0.192933</td>\n",
       "      <td>0.456685</td>\n",
       "      <td>0.296039</td>\n",
       "      <td>0.042135</td>\n",
       "      <td>0.551826</td>\n",
       "      <td>0.418373</td>\n",
       "      <td>0.138649</td>\n",
       "      <td>0.036566</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        perform    leader    latest       fun   serious   bargain     value  \\\n",
       "brand                                                                         \n",
       "a     -0.886362 -0.528168  0.411179  0.656974 -0.919400  0.214203  0.184785   \n",
       "b      0.931336  1.071294  0.726470 -0.972701  1.183733  0.041640  0.151415   \n",
       "c      0.650249  1.163350 -0.102388 -0.845098  1.223346 -0.607347 -0.440898   \n",
       "d     -0.680231 -0.593373  0.352671  0.186665 -0.692521 -0.881197 -0.933102   \n",
       "e     -0.564673  0.192933  0.456685  0.296039  0.042135  0.551826  0.418373   \n",
       "\n",
       "         trendy     rebuy  \n",
       "brand                      \n",
       "a     -0.525407 -0.596465  \n",
       "b      0.740679  0.237092  \n",
       "c      0.025541 -0.132504  \n",
       "d      0.737030 -0.494236  \n",
       "e      0.138649  0.036566  "
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_bybrand = df_survey_norm.groupby('brand').mean()\n",
    "df_bybrand.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the correlations of the values across columns for `bargain/value/rebuy`, which is consistent with the correlation matrix visualization above. But it is better to formalize such kind of insights, and the remainder of this lab introduces how to do so."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Principal Component Analysis\n",
    "\n",
    "We have demonstrated how to use principal component analysis (PCA) to do dimensionality reduction for visualization in the previous lab. Now let us look at PCA in greater details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q4_a. Create a PCA model</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a PCA model, call it pca_model\n",
    "pca_model = skd.PCA().fit(df_survey_norm.ix[:,:9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 9)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm that there are 9 components extracted from the data; each component is\n",
    "# a 9-dimensional vector.\n",
    "pca_model.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24339028112106417"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_model.explained_variance_[8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q4_b. Look at the variances explained by each component.  Interpret your results</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.98227784, 2.09865033, 1.08033521, 0.72793893, 0.6381841 ,\n",
       "       0.53537861, 0.39049493, 0.31235878, 0.24339028])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# These values equal to the eigenvalues of the correlation matrix.\n",
    "\n",
    "pca_model.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the value eigenvalues, first 3 are the most biggst ones, meaning they explain most of the variance. From 4th, there is not much differencce betweeen eigenvalues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way of determining the number of principal components to retain is to look at the explained variance as shown above, and drop those principal components whose explained variance is smaller than 1.\n",
    "\n",
    "Another way is to create a __Scree Plot__ as below, and find the \"elbow\" point on the plotted curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q5. Generate a scree plot</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1eafcf28>]"
      ]
     },
     "execution_count": 82,
     "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": [
    "# A \"scree\" plot.\n",
    "plt.plot(range(1,10),pca_model.explained_variance_,'b-o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9822778396485554"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_model.explained_variance_[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How many components do you think we should keep?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the scree plot, first 3 PCAs seem to explain most variance. After incresing more than 4 PCAs,  there will be not much increase for explaination of variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q6: Using the biplot code from the previous section, create a __biplot__, for this model.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatterplot of disaggregated data\n",
    "X = pca_model.transform(df_survey_norm.ix[:,:9])\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.title('PCA biplot')\n",
    "plt.ylim(-4, 10)\n",
    "\n",
    "# Add variable unit vector projections\n",
    "V = pca_model.transform(np.identity(X.shape[1]))\n",
    "for i, v in enumerate(V):\n",
    "    plt.annotate(df_survey_norm.columns[i], \n",
    "                 xy=(0,0), xytext=v[:2]*10, \n",
    "                 fontsize=13, color='orange',\n",
    "                 arrowprops=dict(\n",
    "                    arrowstyle='<-', linewidth=2, color='orange'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Exploratory Factor Analysis\n",
    "\n",
    "Exploratory Factor Analysis (EFA) can produce similar results to PCA, but is conceptually different. Refer to the lecture and reading materials for more details.\n",
    "\n",
    "We will introduce very simple EFA examples below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Factor1</th>\n",
       "      <th>Factor2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>perform</th>\n",
       "      <td>0.756645</td>\n",
       "      <td>1.780510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>leader</th>\n",
       "      <td>0.622420</td>\n",
       "      <td>2.035885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>latest</th>\n",
       "      <td>-1.357721</td>\n",
       "      <td>0.314338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fun</th>\n",
       "      <td>-0.662353</td>\n",
       "      <td>-0.895932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>serious</th>\n",
       "      <td>0.393280</td>\n",
       "      <td>1.870919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bargain</th>\n",
       "      <td>2.079388</td>\n",
       "      <td>-0.520444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value</th>\n",
       "      <td>2.080387</td>\n",
       "      <td>-0.334322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trendy</th>\n",
       "      <td>-1.339608</td>\n",
       "      <td>0.636778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rebuy</th>\n",
       "      <td>1.610265</td>\n",
       "      <td>0.320085</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Factor1   Factor2\n",
       "perform  0.756645  1.780510\n",
       "leader   0.622420  2.035885\n",
       "latest  -1.357721  0.314338\n",
       "fun     -0.662353 -0.895932\n",
       "serious  0.393280  1.870919\n",
       "bargain  2.079388 -0.520444\n",
       "value    2.080387 -0.334322\n",
       "trendy  -1.339608  0.636778\n",
       "rebuy    1.610265  0.320085"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build a 2-factor model\n",
    "fa_model = skd.FactorAnalysis(n_components=2).fit(df_survey_norm.ix[:,:9])\n",
    "\n",
    "# Show the loadings\n",
    "pd.DataFrame(fa_model.components_[:2,:].T, \n",
    "             index=df_bybrand.columns,\n",
    "             columns=['Factor1', 'Factor2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the factors with the principal components. Can you find the similarity between the results?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>perform</th>\n",
       "      <td>0.353484</td>\n",
       "      <td>0.485277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>leader</th>\n",
       "      <td>0.230633</td>\n",
       "      <td>0.443208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>latest</th>\n",
       "      <td>-0.441729</td>\n",
       "      <td>0.308197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fun</th>\n",
       "      <td>-0.282064</td>\n",
       "      <td>-0.184138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>serious</th>\n",
       "      <td>0.201338</td>\n",
       "      <td>0.461414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bargain</th>\n",
       "      <td>0.337656</td>\n",
       "      <td>-0.230171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value</th>\n",
       "      <td>0.346846</td>\n",
       "      <td>-0.190990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trendy</th>\n",
       "      <td>-0.341415</td>\n",
       "      <td>0.368495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rebuy</th>\n",
       "      <td>0.394661</td>\n",
       "      <td>-0.032136</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              PC1       PC2\n",
       "perform  0.353484  0.485277\n",
       "leader   0.230633  0.443208\n",
       "latest  -0.441729  0.308197\n",
       "fun     -0.282064 -0.184138\n",
       "serious  0.201338  0.461414\n",
       "bargain  0.337656 -0.230171\n",
       "value    0.346846 -0.190990\n",
       "trendy  -0.341415  0.368495\n",
       "rebuy    0.394661 -0.032136"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build a PCA model to compare with the factor model above\n",
    "pca_model = skd.PCA(n_components=2).fit(df_survey_norm.ix[:,:9])\n",
    "\n",
    "# Show the principcal components\n",
    "pd.DataFrame(pca_model.components_[:2,:].T, \n",
    "             index=df_bybrand.columns,\n",
    "             columns=['PC1', 'PC2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Factor1</th>\n",
       "      <th>Factor2</th>\n",
       "      <th>Factor3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>perform</th>\n",
       "      <td>0.546114</td>\n",
       "      <td>-0.756948</td>\n",
       "      <td>1.732959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>leader</th>\n",
       "      <td>0.159982</td>\n",
       "      <td>-1.105950</td>\n",
       "      <td>1.819042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>latest</th>\n",
       "      <td>-2.643658</td>\n",
       "      <td>-1.158210</td>\n",
       "      <td>-0.363975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fun</th>\n",
       "      <td>-0.739775</td>\n",
       "      <td>0.211200</td>\n",
       "      <td>-1.006275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>serious</th>\n",
       "      <td>0.076810</td>\n",
       "      <td>-0.819109</td>\n",
       "      <td>1.716528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bargain</th>\n",
       "      <td>1.525118</td>\n",
       "      <td>-1.425781</td>\n",
       "      <td>-0.831515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value</th>\n",
       "      <td>1.600268</td>\n",
       "      <td>-1.285703</td>\n",
       "      <td>-0.555443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trendy</th>\n",
       "      <td>-1.885201</td>\n",
       "      <td>-0.352493</td>\n",
       "      <td>0.336696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rebuy</th>\n",
       "      <td>1.455021</td>\n",
       "      <td>-0.755642</td>\n",
       "      <td>0.305808</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Factor1   Factor2   Factor3\n",
       "perform  0.546114 -0.756948  1.732959\n",
       "leader   0.159982 -1.105950  1.819042\n",
       "latest  -2.643658 -1.158210 -0.363975\n",
       "fun     -0.739775  0.211200 -1.006275\n",
       "serious  0.076810 -0.819109  1.716528\n",
       "bargain  1.525118 -1.425781 -0.831515\n",
       "value    1.600268 -1.285703 -0.555443\n",
       "trendy  -1.885201 -0.352493  0.336696\n",
       "rebuy    1.455021 -0.755642  0.305808"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a three-factor model\n",
    "fa_model = skd.FactorAnalysis(n_components=3) \\\n",
    "              .fit(df_survey_norm.ix[:,:9])\n",
    "\n",
    "# Show the loadings\n",
    "df_loadings = pd.DataFrame(fa_model.components_[:3,:].T, \n",
    "                   index=df_bybrand.columns,\n",
    "                   columns=['Factor1', 'Factor2', 'Factor3'])\n",
    "df_loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x1c250e2b70>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the factor loading matrix\n",
    "sns.clustermap(df_loadings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q7. Can you describe the factors?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(YOUR INTERPRETATION HERE)__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a number of important concepts within factor analysis that are not covered here, including:\n",
    "- _simple structure_ of factors\n",
    "  - [reference](http://www.ats.ucla.edu/stat/spss/output/factor1.htm)\n",
    "  - [reference](https://en.wikipedia.org/wiki/Factor_analysis#Rotation_methods)\n",
    "- rotation (varimax, promax, ...)\n",
    "  - [strategy for selecting a rotation](http://jalt.org/test/PDF/Brown31.pdf)\n",
    "- orthogonal and oblique factors\n",
    "- determining the number of components in EFA\n",
    "- confirmatory factor analysis (CFA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Manifold Learning\n",
    "\n",
    "So far the dimensionality reduction methods we have studied are linear in nature. If the actual data points are distributed on a low-dimensional non-linear manifold living in a high-dimensional space, then linear methods will most likely fail to reveal the most intuitive structures of the data. This means we will see \"a mess\" in our low-dimensional visualization while the actual data actually has a very simple and elegant non-linear (e.g., curved) structure. \n",
    "\n",
    "In such situations where linear models face troubles, we can use manifold learning to do non-linear dimensionality reduction. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Multidimensional Scaling (MDS)\n",
    "MDS seeks a low-dimensional representation of the data that preserves the distances in the high-dimensional space. It can take any kind of distance matrix as input.\n",
    "\n",
    "Note that each time you run MDS, you will get a different result, unless `random_state` is fixed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q8. Create a MDS representation</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "### YOUR CODE HERE ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Use MDS to visualize *brands*.\n",
    "# Recall that df_bybrand is the mean-metric-by-brand \n",
    "# we created above.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(YOUR INTERPRETATION HERE)__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2  t-distributed Stochastic Neighbor Embedding (t-SNE)\n",
    "t-SNE is not a new technique, but rather one that has recently come into\n",
    "fashion, partly as a result of access to more powerful computing resources.\n",
    "t-SNE is similar to MDS.  If you have time, repeat the work you did in exercise 4.1 using ```sklearn.manifold.TSNE``` instead of MDS.  Please see t-SNE documentation at http://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"magenta\">Q9. Create a t-SNE representation</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "### YOUR CODE HERE ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use t-SNE to visualize *brands*.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(YOUR INTERPRETATION HERE)__"
   ]
  }
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