LDA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#https://towardsdatascience.com/linear-discriminant-analysis-in-python-76b8b17817c2\n",
    "from sklearn.datasets import load_wine\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=4)\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "wine = load_wine()\n",
    "X = pd.DataFrame(wine.data, columns=wine.feature_names)\n",
    "y = pd.Categorical.from_codes(wine.target, wine.target_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</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_of_diluted_wines</th>\n",
       "      <th>proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</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",
       "      <td>mean</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",
       "      <td>std</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",
       "      <td>min</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",
       "      <td>25%</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",
       "      <td>50%</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",
       "      <td>75%</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",
       "      <td>max</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": [
       "          alcohol  malic_acid         ash  alcalinity_of_ash   magnesium  \\\n",
       "count  178.000000  178.000000  178.000000         178.000000  178.000000   \n",
       "mean    13.000618    2.336348    2.366517          19.494944   99.741573   \n",
       "std      0.811827    1.117146    0.274344           3.339564   14.282484   \n",
       "min     11.030000    0.740000    1.360000          10.600000   70.000000   \n",
       "25%     12.362500    1.602500    2.210000          17.200000   88.000000   \n",
       "50%     13.050000    1.865000    2.360000          19.500000   98.000000   \n",
       "75%     13.677500    3.082500    2.557500          21.500000  107.000000   \n",
       "max     14.830000    5.800000    3.230000          30.000000  162.000000   \n",
       "\n",
       "       total_phenols  flavanoids  nonflavanoid_phenols  proanthocyanins  \\\n",
       "count     178.000000  178.000000            178.000000       178.000000   \n",
       "mean        2.295112    2.029270              0.361854         1.590899   \n",
       "std         0.625851    0.998859              0.124453         0.572359   \n",
       "min         0.980000    0.340000              0.130000         0.410000   \n",
       "25%         1.742500    1.205000              0.270000         1.250000   \n",
       "50%         2.355000    2.135000              0.340000         1.555000   \n",
       "75%         2.800000    2.875000              0.437500         1.950000   \n",
       "max         3.880000    5.080000              0.660000         3.580000   \n",
       "\n",
       "       color_intensity         hue  od280/od315_of_diluted_wines      proline  \n",
       "count       178.000000  178.000000                    178.000000   178.000000  \n",
       "mean          5.058090    0.957449                      2.611685   746.893258  \n",
       "std           2.318286    0.228572                      0.709990   314.907474  \n",
       "min           1.280000    0.480000                      1.270000   278.000000  \n",
       "25%           3.220000    0.782500                      1.937500   500.500000  \n",
       "50%           4.690000    0.965000                      2.780000   673.500000  \n",
       "75%           6.200000    1.120000                      3.170000   985.000000  \n",
       "max          13.000000    1.710000                      4.000000  1680.000000  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <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_of_diluted_wines</th>\n",
       "      <th>proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127.0</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>1065.0</td>\n",
       "    </tr>\n",
       "    <tr>\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>100.0</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>1050.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101.0</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>1185.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113.0</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>1480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118.0</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>735.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   alcohol  malic_acid   ash  alcalinity_of_ash  magnesium  total_phenols  \\\n",
       "0    14.23        1.71  2.43               15.6      127.0           2.80   \n",
       "1    13.20        1.78  2.14               11.2      100.0           2.65   \n",
       "2    13.16        2.36  2.67               18.6      101.0           2.80   \n",
       "3    14.37        1.95  2.50               16.8      113.0           3.85   \n",
       "4    13.24        2.59  2.87               21.0      118.0           2.80   \n",
       "\n",
       "   flavanoids  nonflavanoid_phenols  proanthocyanins  color_intensity   hue  \\\n",
       "0        3.06                  0.28             2.29             5.64  1.04   \n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "\n",
       "   od280/od315_of_diluted_wines  proline  \n",
       "0                          3.92   1065.0  \n",
       "1                          3.40   1050.0  \n",
       "2                          3.17   1185.0  \n",
       "3                          3.45   1480.0  \n",
       "4                          2.93    735.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[class_0, class_1, class_2]\n",
       "Categories (3, object): [class_0, class_1, class_2]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = X.join(pd.Series(y, name='class'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LDA from scractch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class_0</th>\n",
       "      <th>class_1</th>\n",
       "      <th>class_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>alcohol</td>\n",
       "      <td>13.744746</td>\n",
       "      <td>12.278732</td>\n",
       "      <td>13.153750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>malic_acid</td>\n",
       "      <td>2.010678</td>\n",
       "      <td>1.932676</td>\n",
       "      <td>3.333750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>ash</td>\n",
       "      <td>2.455593</td>\n",
       "      <td>2.244789</td>\n",
       "      <td>2.437083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>alcalinity_of_ash</td>\n",
       "      <td>17.037288</td>\n",
       "      <td>20.238028</td>\n",
       "      <td>21.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>magnesium</td>\n",
       "      <td>106.338983</td>\n",
       "      <td>94.549296</td>\n",
       "      <td>99.312500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>total_phenols</td>\n",
       "      <td>2.840169</td>\n",
       "      <td>2.258873</td>\n",
       "      <td>1.678750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>flavanoids</td>\n",
       "      <td>2.982373</td>\n",
       "      <td>2.080845</td>\n",
       "      <td>0.781458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>nonflavanoid_phenols</td>\n",
       "      <td>0.290000</td>\n",
       "      <td>0.363662</td>\n",
       "      <td>0.447500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>proanthocyanins</td>\n",
       "      <td>1.899322</td>\n",
       "      <td>1.630282</td>\n",
       "      <td>1.153542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>color_intensity</td>\n",
       "      <td>5.528305</td>\n",
       "      <td>3.086620</td>\n",
       "      <td>7.396250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>hue</td>\n",
       "      <td>1.062034</td>\n",
       "      <td>1.056282</td>\n",
       "      <td>0.682708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>od280/od315_of_diluted_wines</td>\n",
       "      <td>3.157797</td>\n",
       "      <td>2.785352</td>\n",
       "      <td>1.683542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>proline</td>\n",
       "      <td>1115.711864</td>\n",
       "      <td>519.507042</td>\n",
       "      <td>629.895833</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  class_0     class_1     class_2\n",
       "alcohol                         13.744746   12.278732   13.153750\n",
       "malic_acid                       2.010678    1.932676    3.333750\n",
       "ash                              2.455593    2.244789    2.437083\n",
       "alcalinity_of_ash               17.037288   20.238028   21.416667\n",
       "magnesium                      106.338983   94.549296   99.312500\n",
       "total_phenols                    2.840169    2.258873    1.678750\n",
       "flavanoids                       2.982373    2.080845    0.781458\n",
       "nonflavanoid_phenols             0.290000    0.363662    0.447500\n",
       "proanthocyanins                  1.899322    1.630282    1.153542\n",
       "color_intensity                  5.528305    3.086620    7.396250\n",
       "hue                              1.062034    1.056282    0.682708\n",
       "od280/od315_of_diluted_wines     3.157797    2.785352    1.683542\n",
       "proline                       1115.711864  519.507042  629.895833"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class_feature_means = pd.DataFrame(columns=wine.target_names)\n",
    "for c, rows in df.groupby('class'):\n",
    "    class_feature_means[c] = rows.mean()\n",
    "class_feature_means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "within_class_scatter_matrix = np.zeros((13,13))\n",
    "\n",
    "for c, rows in df.groupby('class'):\n",
    "    rows = rows.drop(['class'], axis=1)\n",
    "    s = np.zeros((13,13))\n",
    "\n",
    "    for index, row in rows.iterrows():\n",
    "        x, mc = row.values.reshape(13,1),class_feature_means[c].values.reshape(13,1)\n",
    "        s += (x - mc).dot((x - mc).T)\n",
    "    within_class_scatter_matrix += s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_means = df.mean()\n",
    "between_class_scatter_matrix = np.zeros((13,13))\n",
    "for c in class_feature_means:    \n",
    "    n = len(df.loc[df['class'] == c].index)\n",
    "    \n",
    "    mc, m = class_feature_means[c].values.reshape(13,1), feature_means.values.reshape(13,1)\n",
    "    \n",
    "    between_class_scatter_matrix += n * (mc - m).dot((mc - m).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigen_values, eigen_vectors = np.linalg.eig(np.linalg.inv(within_class_scatter_matrix).dot(between_class_scatter_matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.081739435042472\n",
      "4.128469045639484\n",
      "8.881784197001252e-16\n",
      "7.41949604398113e-16\n",
      "7.41949604398113e-16\n",
      "6.57104310784389e-16\n",
      "6.57104310784389e-16\n",
      "2.9039090283069212e-16\n",
      "2.9039090283069212e-16\n",
      "2.58525572226227e-16\n",
      "6.126103277916086e-17\n",
      "6.126103277916086e-17\n",
      "4.86945776983596e-17\n"
     ]
    }
   ],
   "source": [
    "pairs = [(np.abs(eigen_values[i]), eigen_vectors[:,i]) for i in range(len(eigen_values))]\n",
    "pairs = sorted(pairs, key=lambda x: x[0], reverse=True)\n",
    "for pair in pairs:\n",
    "    print(pair[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance\n",
      "Eigenvector 0: 0.6874788878860784\n",
      "Eigenvector 1: 0.31252111211392164\n",
      "Eigenvector 2: 6.723424698398662e-17\n",
      "Eigenvector 3: 5.616486715430028e-17\n",
      "Eigenvector 4: 5.616486715430028e-17\n",
      "Eigenvector 5: 4.9742160522698054e-17\n",
      "Eigenvector 6: 4.9742160522698054e-17\n",
      "Eigenvector 7: 2.1982310366664338e-17\n",
      "Eigenvector 8: 2.1982310366664338e-17\n",
      "Eigenvector 9: 1.957013567229342e-17\n",
      "Eigenvector 10: 4.637400906181487e-18\n",
      "Eigenvector 11: 4.637400906181487e-18\n",
      "Eigenvector 12: 3.686132415666904e-18\n"
     ]
    }
   ],
   "source": [
    "eigen_value_sums = sum(eigen_values)\n",
    "print('Explained Variance')\n",
    "for i, pair in enumerate(pairs):\n",
    "    print('Eigenvector {}: {}'.format(i, (pair[0]/eigen_value_sums).real))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_matrix = np.hstack((pairs[0][1].reshape(13,1), pairs[1][1].reshape(13,1))).real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lda = np.array(X.dot(w_matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "le = LabelEncoder()\n",
    "y = le.fit_transform(df['class'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2863b225208>"
      ]
     },
     "execution_count": 31,
     "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": [
    "plt.xlabel('LD1')\n",
    "plt.ylabel('LD2')\n",
    "plt.scatter(\n",
    "    X_lda[:,0],\n",
    "    X_lda[:,1],\n",
    "    c=y,\n",
    "    cmap='rainbow',\n",
    "    alpha=0.7,\n",
    "    edgecolors='b'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LDA OutOfTheBox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "lda = LinearDiscriminantAnalysis()\n",
    "X_lda = lda.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6875, 0.3125])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2863a8b8608>"
      ]
     },
     "execution_count": 35,
     "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": [
    "plt.xlabel('LD1')\n",
    "plt.ylabel('LD2')\n",
    "plt.scatter(\n",
    "    X_lda[:,0],\n",
    "    X_lda[:,1],\n",
    "    c=y,\n",
    "    cmap='rainbow',\n",
    "    alpha=0.7,\n",
    "    edgecolors='b'\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LDA vs PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "X_pca = pca.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.9981, 0.0017])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6875, 0.3125])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PCA explains 0.9998271461166032 variance\n",
      "LDA explains 1.0 variance\n"
     ]
    }
   ],
   "source": [
    "print(f\"PCA explains {sum(pca.explained_variance_ratio_)} variance\")\n",
    "print(f\"LDA explains {sum(lda.explained_variance_ratio_)} variance\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2863b0d9688>"
      ]
     },
     "execution_count": 41,
     "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": [
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.scatter(\n",
    "    X_pca[:,0],\n",
    "    X_pca[:,1],\n",
    "    c=y,\n",
    "    cmap='rainbow',\n",
    "    alpha=0.7,\n",
    "    edgecolors='b'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X_lda, y, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18,  0,  0],\n",
       "       [ 0, 17,  0],\n",
       "       [ 0,  0, 10]], dtype=int64)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt = DecisionTreeClassifier()\n",
    "dt.fit(X_train, y_train)\n",
    "y_pred = dt.predict(X_test)\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (4,3) (3,2) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-20aba40ca292>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# a.shape = (4, 3)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# b.shape = (3, 2)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,3) (3,2) "
     ]
    }
   ],
   "source": [
    "a = np.random.randn(4, 3) # a.shape = (4, 3)\n",
    "b = np.random.randn(3, 2) # b.shape = (3, 2)\n",
    "c = a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}