MultiVar Gaussian.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bcdfa230",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "addc38f2",
   "metadata": {},
   "source": [
    "## The wine recognition data \n",
    "This (https://archive.ics.uci.edu/ml/datasets/wine) is a one of the classic datasets.\n",
    "\n",
    "Each row corresponds to a particular bottle of wine. Each wine is characterized by 13 numericcal attributes\n",
    " \n",
    "#### The attributes \n",
    "1. Class = type of wine, can be 1,2 or 3, In this notebook we ignore class.\n",
    "1. Alcohol\n",
    "2. Malic acid\n",
    "3. Ash\n",
    "4. Alcalinity of ash  \n",
    "5. Magnesium\n",
    "6. Total phenols\n",
    "7. Flavanoids\n",
    "8. Nonflavanoid phenols\n",
    "9. Proanthocyanins\n",
    "10. Color intensity\n",
    "11. Hue\n",
    "12. OD280/OD315 of diluted wines\n",
    "13. Proline            \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8c80184d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Icon?      wine.data  wine.names\r\n"
     ]
    }
   ],
   "source": [
    "!ls data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f25a81a5",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   class  Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  \\\n",
       "0      1    14.23        1.71  2.43               15.6        127   \n",
       "1      1    13.20        1.78  2.14               11.2        100   \n",
       "2      1    13.16        2.36  2.67               18.6        101   \n",
       "3      1    14.37        1.95  2.50               16.8        113   \n",
       "4      1    13.24        2.59  2.87               21.0        118   \n",
       "\n",
       "   Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "0           2.80        3.06                  0.28             2.29   \n",
       "1           2.65        2.76                  0.26             1.28   \n",
       "2           2.80        3.24                  0.30             2.81   \n",
       "3           3.85        3.49                  0.24             2.18   \n",
       "4           2.80        2.69                  0.39             1.82   \n",
       "\n",
       "   Color intensity   Hue  OD280/OD315  Proline  \n",
       "0             5.64  1.04         3.92     1065  \n",
       "1             4.38  1.05         3.40     1050  \n",
       "2             5.68  1.03         3.17     1185  \n",
       "3             7.80  0.86         3.45     1480  \n",
       "4             4.32  1.04         2.93      735  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=pd.read_csv('data/wine.data',header=None)\n",
    "\n",
    "df.columns=['class','Alcohol','Malic acid','Ash','Alcalinity of ash','Magnesium','Total phenols','Flavanoids',\\\n",
    "'Nonflavanoid phenols','Proanthocyanins','Color intensity','Hue','OD280/OD315','Proline']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15625961",
   "metadata": {},
   "source": [
    "The `df.describe()` method in pandas provides summary statistics for each column in the dataframe `df`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "89ea82d1",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.938202</td>\n",
       "      <td>13.000618</td>\n",
       "      <td>2.336348</td>\n",
       "      <td>2.366517</td>\n",
       "      <td>19.494944</td>\n",
       "      <td>99.741573</td>\n",
       "      <td>2.295112</td>\n",
       "      <td>2.029270</td>\n",
       "      <td>0.361854</td>\n",
       "      <td>1.590899</td>\n",
       "      <td>5.058090</td>\n",
       "      <td>0.957449</td>\n",
       "      <td>2.611685</td>\n",
       "      <td>746.893258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.775035</td>\n",
       "      <td>0.811827</td>\n",
       "      <td>1.117146</td>\n",
       "      <td>0.274344</td>\n",
       "      <td>3.339564</td>\n",
       "      <td>14.282484</td>\n",
       "      <td>0.625851</td>\n",
       "      <td>0.998859</td>\n",
       "      <td>0.124453</td>\n",
       "      <td>0.572359</td>\n",
       "      <td>2.318286</td>\n",
       "      <td>0.228572</td>\n",
       "      <td>0.709990</td>\n",
       "      <td>314.907474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>11.030000</td>\n",
       "      <td>0.740000</td>\n",
       "      <td>1.360000</td>\n",
       "      <td>10.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.340000</td>\n",
       "      <td>0.130000</td>\n",
       "      <td>0.410000</td>\n",
       "      <td>1.280000</td>\n",
       "      <td>0.480000</td>\n",
       "      <td>1.270000</td>\n",
       "      <td>278.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>12.362500</td>\n",
       "      <td>1.602500</td>\n",
       "      <td>2.210000</td>\n",
       "      <td>17.200000</td>\n",
       "      <td>88.000000</td>\n",
       "      <td>1.742500</td>\n",
       "      <td>1.205000</td>\n",
       "      <td>0.270000</td>\n",
       "      <td>1.250000</td>\n",
       "      <td>3.220000</td>\n",
       "      <td>0.782500</td>\n",
       "      <td>1.937500</td>\n",
       "      <td>500.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>13.050000</td>\n",
       "      <td>1.865000</td>\n",
       "      <td>2.360000</td>\n",
       "      <td>19.500000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>2.355000</td>\n",
       "      <td>2.135000</td>\n",
       "      <td>0.340000</td>\n",
       "      <td>1.555000</td>\n",
       "      <td>4.690000</td>\n",
       "      <td>0.965000</td>\n",
       "      <td>2.780000</td>\n",
       "      <td>673.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>13.677500</td>\n",
       "      <td>3.082500</td>\n",
       "      <td>2.557500</td>\n",
       "      <td>21.500000</td>\n",
       "      <td>107.000000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>2.875000</td>\n",
       "      <td>0.437500</td>\n",
       "      <td>1.950000</td>\n",
       "      <td>6.200000</td>\n",
       "      <td>1.120000</td>\n",
       "      <td>3.170000</td>\n",
       "      <td>985.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>14.830000</td>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.230000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>162.000000</td>\n",
       "      <td>3.880000</td>\n",
       "      <td>5.080000</td>\n",
       "      <td>0.660000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>1.710000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>1680.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            class     Alcohol  Malic acid         Ash  Alcalinity of ash  \\\n",
       "count  178.000000  178.000000  178.000000  178.000000         178.000000   \n",
       "mean     1.938202   13.000618    2.336348    2.366517          19.494944   \n",
       "std      0.775035    0.811827    1.117146    0.274344           3.339564   \n",
       "min      1.000000   11.030000    0.740000    1.360000          10.600000   \n",
       "25%      1.000000   12.362500    1.602500    2.210000          17.200000   \n",
       "50%      2.000000   13.050000    1.865000    2.360000          19.500000   \n",
       "75%      3.000000   13.677500    3.082500    2.557500          21.500000   \n",
       "max      3.000000   14.830000    5.800000    3.230000          30.000000   \n",
       "\n",
       "        Magnesium  Total phenols  Flavanoids  Nonflavanoid phenols  \\\n",
       "count  178.000000     178.000000  178.000000            178.000000   \n",
       "mean    99.741573       2.295112    2.029270              0.361854   \n",
       "std     14.282484       0.625851    0.998859              0.124453   \n",
       "min     70.000000       0.980000    0.340000              0.130000   \n",
       "25%     88.000000       1.742500    1.205000              0.270000   \n",
       "50%     98.000000       2.355000    2.135000              0.340000   \n",
       "75%    107.000000       2.800000    2.875000              0.437500   \n",
       "max    162.000000       3.880000    5.080000              0.660000   \n",
       "\n",
       "       Proanthocyanins  Color intensity         Hue  OD280/OD315      Proline  \n",
       "count       178.000000       178.000000  178.000000   178.000000   178.000000  \n",
       "mean          1.590899         5.058090    0.957449     2.611685   746.893258  \n",
       "std           0.572359         2.318286    0.228572     0.709990   314.907474  \n",
       "min           0.410000         1.280000    0.480000     1.270000   278.000000  \n",
       "25%           1.250000         3.220000    0.782500     1.937500   500.500000  \n",
       "50%           1.555000         4.690000    0.965000     2.780000   673.500000  \n",
       "75%           1.950000         6.200000    1.120000     3.170000   985.000000  \n",
       "max           3.580000        13.000000    1.710000     4.000000  1680.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "desc=df.describe()\n",
    "desc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "22072413",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_stat(Col,_title='',_range=[],height=20):\n",
    "    Col.hist(bins=20)\n",
    "    _mean=Col.mean()\n",
    "    _std=Col.std()\n",
    "    for x in [_mean,_mean-_std,_mean+_std]:\n",
    "        plot([x,x],[0,height])\n",
    "        if len(_range)==2:\n",
    "            xlim(_range)\n",
    "    title(_title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "488ef2b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_normal(s):\n",
    "    count, bins, ignored = plt.hist(s, 30, density=True);\n",
    "    sigma=std(s); mu=mean(s)\n",
    "    plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n",
    "                   np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n",
    "             linewidth=2, color='r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f5eeff92",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "j=1\n",
    "_class=1\n",
    "rdf=df[df['class']==_class]\n",
    "for name in ['Alcohol','Flavanoids']:\n",
    "    plot_normal(rdf[name])\n",
    "    title('%s, class=%d'%(name,_class))\n",
    "    figure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "101475a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from   scipy.stats import multivariate_normal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "10d4d332",
   "metadata": {},
   "outputs": [],
   "source": [
    "def scatterAndGauss(rdf,Feat1,Feat2,_cov,_mean):\n",
    "    fig, ax = plt.subplots()\n",
    "    scatter = ax.scatter(rdf[Feat1],rdf[Feat2],c=rdf['class'])\n",
    "    xlabel(Feat1)\n",
    "    ylabel(Feat2)\n",
    "\n",
    "    plot(_mean[0],_mean[1],'X')\n",
    "    N    = 200\n",
    "    X    = np.linspace(12.5, 15, N)\n",
    "    Y    = np.linspace(2, 4, N)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    pos  = np.dstack((X, Y))\n",
    "    rv   = multivariate_normal(_mean, _cov)\n",
    "    Z    = rv.pdf(pos)\n",
    "\n",
    "    plt.contour(X, Y, Z,5)\n",
    "#    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "e9925d85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "Feat1='Alcohol'\n",
    "Feat2='Flavanoids'\n",
    "subset=rdf[[Feat1,Feat2]]\n",
    "_cov=np.array(subset.cov())\n",
    "_cov[1,0]=0\n",
    "_cov[0,1]=0\n",
    "_mean=np.array(subset.mean())\n",
    "scatterAndGauss(rdf,Feat1,Feat2,_cov,_mean)\n",
    "title('assuming zero covariance')\n",
    "_cov=np.array(subset.cov())\n",
    "scatterAndGauss(rdf,Feat1,Feat2,_cov,_mean)\n",
    "title('using actual covariance');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d9b21811",
   "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>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alcohol</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.040513</td>\n",
       "      <td>-0.148595</td>\n",
       "      <td>-0.318367</td>\n",
       "      <td>0.159361</td>\n",
       "      <td>0.420687</td>\n",
       "      <td>0.414904</td>\n",
       "      <td>0.015659</td>\n",
       "      <td>0.307571</td>\n",
       "      <td>0.408291</td>\n",
       "      <td>0.080020</td>\n",
       "      <td>0.069818</td>\n",
       "      <td>0.360646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Malic acid</th>\n",
       "      <td>-0.040513</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.026221</td>\n",
       "      <td>0.060031</td>\n",
       "      <td>0.079317</td>\n",
       "      <td>-0.083514</td>\n",
       "      <td>-0.191278</td>\n",
       "      <td>-0.089366</td>\n",
       "      <td>-0.080798</td>\n",
       "      <td>-0.257587</td>\n",
       "      <td>-0.419981</td>\n",
       "      <td>0.173244</td>\n",
       "      <td>-0.372629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ash</th>\n",
       "      <td>-0.148595</td>\n",
       "      <td>0.026221</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.549330</td>\n",
       "      <td>0.382549</td>\n",
       "      <td>0.004802</td>\n",
       "      <td>-0.070454</td>\n",
       "      <td>0.465901</td>\n",
       "      <td>-0.145471</td>\n",
       "      <td>-0.124220</td>\n",
       "      <td>0.239214</td>\n",
       "      <td>-0.081593</td>\n",
       "      <td>-0.029525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <td>-0.318367</td>\n",
       "      <td>0.060031</td>\n",
       "      <td>0.549330</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.238337</td>\n",
       "      <td>-0.222999</td>\n",
       "      <td>-0.287103</td>\n",
       "      <td>0.302262</td>\n",
       "      <td>-0.173628</td>\n",
       "      <td>-0.210951</td>\n",
       "      <td>0.092980</td>\n",
       "      <td>-0.117704</td>\n",
       "      <td>-0.122436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Magnesium</th>\n",
       "      <td>0.159361</td>\n",
       "      <td>0.079317</td>\n",
       "      <td>0.382549</td>\n",
       "      <td>0.238337</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307241</td>\n",
       "      <td>0.123332</td>\n",
       "      <td>0.237248</td>\n",
       "      <td>-0.059042</td>\n",
       "      <td>0.184661</td>\n",
       "      <td>-0.111386</td>\n",
       "      <td>0.120651</td>\n",
       "      <td>-0.147912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Total phenols</th>\n",
       "      <td>0.420687</td>\n",
       "      <td>-0.083514</td>\n",
       "      <td>0.004802</td>\n",
       "      <td>-0.222999</td>\n",
       "      <td>0.307241</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.803784</td>\n",
       "      <td>-0.016992</td>\n",
       "      <td>0.373601</td>\n",
       "      <td>0.650086</td>\n",
       "      <td>-0.224330</td>\n",
       "      <td>0.053165</td>\n",
       "      <td>0.294994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Flavanoids</th>\n",
       "      <td>0.414904</td>\n",
       "      <td>-0.191278</td>\n",
       "      <td>-0.070454</td>\n",
       "      <td>-0.287103</td>\n",
       "      <td>0.123332</td>\n",
       "      <td>0.803784</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.089538</td>\n",
       "      <td>0.548624</td>\n",
       "      <td>0.741560</td>\n",
       "      <td>0.007863</td>\n",
       "      <td>-0.088529</td>\n",
       "      <td>0.380446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <td>0.015659</td>\n",
       "      <td>-0.089366</td>\n",
       "      <td>0.465901</td>\n",
       "      <td>0.302262</td>\n",
       "      <td>0.237248</td>\n",
       "      <td>-0.016992</td>\n",
       "      <td>-0.089538</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.144535</td>\n",
       "      <td>-0.152460</td>\n",
       "      <td>0.411831</td>\n",
       "      <td>-0.323488</td>\n",
       "      <td>-0.015333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <td>0.307571</td>\n",
       "      <td>-0.080798</td>\n",
       "      <td>-0.145471</td>\n",
       "      <td>-0.173628</td>\n",
       "      <td>-0.059042</td>\n",
       "      <td>0.373601</td>\n",
       "      <td>0.548624</td>\n",
       "      <td>-0.144535</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.424696</td>\n",
       "      <td>0.103937</td>\n",
       "      <td>0.003106</td>\n",
       "      <td>0.142166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Color intensity</th>\n",
       "      <td>0.408291</td>\n",
       "      <td>-0.257587</td>\n",
       "      <td>-0.124220</td>\n",
       "      <td>-0.210951</td>\n",
       "      <td>0.184661</td>\n",
       "      <td>0.650086</td>\n",
       "      <td>0.741560</td>\n",
       "      <td>-0.152460</td>\n",
       "      <td>0.424696</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.028228</td>\n",
       "      <td>-0.186899</td>\n",
       "      <td>0.588770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hue</th>\n",
       "      <td>0.080020</td>\n",
       "      <td>-0.419981</td>\n",
       "      <td>0.239214</td>\n",
       "      <td>0.092980</td>\n",
       "      <td>-0.111386</td>\n",
       "      <td>-0.224330</td>\n",
       "      <td>0.007863</td>\n",
       "      <td>0.411831</td>\n",
       "      <td>0.103937</td>\n",
       "      <td>0.028228</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.310659</td>\n",
       "      <td>0.353366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OD280/OD315</th>\n",
       "      <td>0.069818</td>\n",
       "      <td>0.173244</td>\n",
       "      <td>-0.081593</td>\n",
       "      <td>-0.117704</td>\n",
       "      <td>0.120651</td>\n",
       "      <td>0.053165</td>\n",
       "      <td>-0.088529</td>\n",
       "      <td>-0.323488</td>\n",
       "      <td>0.003106</td>\n",
       "      <td>-0.186899</td>\n",
       "      <td>-0.310659</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.348169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Proline</th>\n",
       "      <td>0.360646</td>\n",
       "      <td>-0.372629</td>\n",
       "      <td>-0.029525</td>\n",
       "      <td>-0.122436</td>\n",
       "      <td>-0.147912</td>\n",
       "      <td>0.294994</td>\n",
       "      <td>0.380446</td>\n",
       "      <td>-0.015333</td>\n",
       "      <td>0.142166</td>\n",
       "      <td>0.588770</td>\n",
       "      <td>0.353366</td>\n",
       "      <td>-0.348169</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Alcohol  Malic acid       Ash  Alcalinity of ash  \\\n",
       "Alcohol               1.000000   -0.040513 -0.148595          -0.318367   \n",
       "Malic acid           -0.040513    1.000000  0.026221           0.060031   \n",
       "Ash                  -0.148595    0.026221  1.000000           0.549330   \n",
       "Alcalinity of ash    -0.318367    0.060031  0.549330           1.000000   \n",
       "Magnesium             0.159361    0.079317  0.382549           0.238337   \n",
       "Total phenols         0.420687   -0.083514  0.004802          -0.222999   \n",
       "Flavanoids            0.414904   -0.191278 -0.070454          -0.287103   \n",
       "Nonflavanoid phenols  0.015659   -0.089366  0.465901           0.302262   \n",
       "Proanthocyanins       0.307571   -0.080798 -0.145471          -0.173628   \n",
       "Color intensity       0.408291   -0.257587 -0.124220          -0.210951   \n",
       "Hue                   0.080020   -0.419981  0.239214           0.092980   \n",
       "OD280/OD315           0.069818    0.173244 -0.081593          -0.117704   \n",
       "Proline               0.360646   -0.372629 -0.029525          -0.122436   \n",
       "\n",
       "                      Magnesium  Total phenols  Flavanoids  \\\n",
       "Alcohol                0.159361       0.420687    0.414904   \n",
       "Malic acid             0.079317      -0.083514   -0.191278   \n",
       "Ash                    0.382549       0.004802   -0.070454   \n",
       "Alcalinity of ash      0.238337      -0.222999   -0.287103   \n",
       "Magnesium              1.000000       0.307241    0.123332   \n",
       "Total phenols          0.307241       1.000000    0.803784   \n",
       "Flavanoids             0.123332       0.803784    1.000000   \n",
       "Nonflavanoid phenols   0.237248      -0.016992   -0.089538   \n",
       "Proanthocyanins       -0.059042       0.373601    0.548624   \n",
       "Color intensity        0.184661       0.650086    0.741560   \n",
       "Hue                   -0.111386      -0.224330    0.007863   \n",
       "OD280/OD315            0.120651       0.053165   -0.088529   \n",
       "Proline               -0.147912       0.294994    0.380446   \n",
       "\n",
       "                      Nonflavanoid phenols  Proanthocyanins  Color intensity  \\\n",
       "Alcohol                           0.015659         0.307571         0.408291   \n",
       "Malic acid                       -0.089366        -0.080798        -0.257587   \n",
       "Ash                               0.465901        -0.145471        -0.124220   \n",
       "Alcalinity of ash                 0.302262        -0.173628        -0.210951   \n",
       "Magnesium                         0.237248        -0.059042         0.184661   \n",
       "Total phenols                    -0.016992         0.373601         0.650086   \n",
       "Flavanoids                       -0.089538         0.548624         0.741560   \n",
       "Nonflavanoid phenols              1.000000        -0.144535        -0.152460   \n",
       "Proanthocyanins                  -0.144535         1.000000         0.424696   \n",
       "Color intensity                  -0.152460         0.424696         1.000000   \n",
       "Hue                               0.411831         0.103937         0.028228   \n",
       "OD280/OD315                      -0.323488         0.003106        -0.186899   \n",
       "Proline                          -0.015333         0.142166         0.588770   \n",
       "\n",
       "                           Hue  OD280/OD315   Proline  \n",
       "Alcohol               0.080020     0.069818  0.360646  \n",
       "Malic acid           -0.419981     0.173244 -0.372629  \n",
       "Ash                   0.239214    -0.081593 -0.029525  \n",
       "Alcalinity of ash     0.092980    -0.117704 -0.122436  \n",
       "Magnesium            -0.111386     0.120651 -0.147912  \n",
       "Total phenols        -0.224330     0.053165  0.294994  \n",
       "Flavanoids            0.007863    -0.088529  0.380446  \n",
       "Nonflavanoid phenols  0.411831    -0.323488 -0.015333  \n",
       "Proanthocyanins       0.103937     0.003106  0.142166  \n",
       "Color intensity       0.028228    -0.186899  0.588770  \n",
       "Hue                   1.000000    -0.310659  0.353366  \n",
       "OD280/OD315          -0.310659     1.000000 -0.348169  \n",
       "Proline               0.353366    -0.348169  1.000000  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rdf.iloc[:,1:].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e1bbc66",
   "metadata": {},
   "source": [
    "### HW\n",
    "* Find which pair of features (in `rdf`) is most correlated (excluding the correlation of a feature with itself which is always zero)\n",
    "* Find which pair of features is most anti-correlated\n",
    "* Find which pair of features are closest to uncorrelated.\n",
    "* Use `scatterAndGauss()` to generate scatter-figures and contours og the fitted Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3718428d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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