Week_4/Day_1/LDA_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_dict = {i:label for i,label in zip(\n",
    "                range(4),\n",
    "                  ('sepal length in cm',\n",
    "                  'sepal width in cm',\n",
    "                  'petal length in cm',\n",
    "                  'petal width in cm', ))}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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>sepal length in cm</th>\n",
       "      <th>sepal width in cm</th>\n",
       "      <th>petal length in cm</th>\n",
       "      <th>petal width in cm</th>\n",
       "      <th>class label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length in cm  sepal width in cm  petal length in cm  \\\n",
       "145                 6.7                3.0                 5.2   \n",
       "146                 6.3                2.5                 5.0   \n",
       "147                 6.5                3.0                 5.2   \n",
       "148                 6.2                3.4                 5.4   \n",
       "149                 5.9                3.0                 5.1   \n",
       "\n",
       "     petal width in cm     class label  \n",
       "145                2.3  Iris-virginica  \n",
       "146                1.9  Iris-virginica  \n",
       "147                2.0  Iris-virginica  \n",
       "148                2.3  Iris-virginica  \n",
       "149                1.8  Iris-virginica  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.io.parsers.read_csv(\n",
    "    filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',\n",
    "    header=None,\n",
    "    sep=',',\n",
    "    )\n",
    "df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']\n",
    "df.dropna(how=\"all\", inplace=True) # to drop the empty line at file-end\n",
    "\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['sepal length in cm','sepal width in cm', 'petal length in cm', 'petal width in cm']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2],\n",
       "       [5.4, 3.9, 1.7, 0.4],\n",
       "       [4.6, 3.4, 1.4, 0.3],\n",
       "       [5. , 3.4, 1.5, 0.2],\n",
       "       [4.4, 2.9, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5.4, 3.7, 1.5, 0.2],\n",
       "       [4.8, 3.4, 1.6, 0.2],\n",
       "       [4.8, 3. , 1.4, 0.1],\n",
       "       [4.3, 3. , 1.1, 0.1],\n",
       "       [5.8, 4. , 1.2, 0.2],\n",
       "       [5.7, 4.4, 1.5, 0.4],\n",
       "       [5.4, 3.9, 1.3, 0.4],\n",
       "       [5.1, 3.5, 1.4, 0.3],\n",
       "       [5.7, 3.8, 1.7, 0.3],\n",
       "       [5.1, 3.8, 1.5, 0.3],\n",
       "       [5.4, 3.4, 1.7, 0.2],\n",
       "       [5.1, 3.7, 1.5, 0.4],\n",
       "       [4.6, 3.6, 1. , 0.2],\n",
       "       [5.1, 3.3, 1.7, 0.5],\n",
       "       [4.8, 3.4, 1.9, 0.2],\n",
       "       [5. , 3. , 1.6, 0.2],\n",
       "       [5. , 3.4, 1.6, 0.4],\n",
       "       [5.2, 3.5, 1.5, 0.2],\n",
       "       [5.2, 3.4, 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.6, 0.2],\n",
       "       [4.8, 3.1, 1.6, 0.2],\n",
       "       [5.4, 3.4, 1.5, 0.4],\n",
       "       [5.2, 4.1, 1.5, 0.1],\n",
       "       [5.5, 4.2, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5. , 3.2, 1.2, 0.2],\n",
       "       [5.5, 3.5, 1.3, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [4.4, 3. , 1.3, 0.2],\n",
       "       [5.1, 3.4, 1.5, 0.2],\n",
       "       [5. , 3.5, 1.3, 0.3],\n",
       "       [4.5, 2.3, 1.3, 0.3],\n",
       "       [4.4, 3.2, 1.3, 0.2],\n",
       "       [5. , 3.5, 1.6, 0.6],\n",
       "       [5.1, 3.8, 1.9, 0.4],\n",
       "       [4.8, 3. , 1.4, 0.3],\n",
       "       [5.1, 3.8, 1.6, 0.2],\n",
       "       [4.6, 3.2, 1.4, 0.2],\n",
       "       [5.3, 3.7, 1.5, 0.2],\n",
       "       [5. , 3.3, 1.4, 0.2],\n",
       "       [7. , 3.2, 4.7, 1.4],\n",
       "       [6.4, 3.2, 4.5, 1.5],\n",
       "       [6.9, 3.1, 4.9, 1.5],\n",
       "       [5.5, 2.3, 4. , 1.3],\n",
       "       [6.5, 2.8, 4.6, 1.5],\n",
       "       [5.7, 2.8, 4.5, 1.3],\n",
       "       [6.3, 3.3, 4.7, 1.6],\n",
       "       [4.9, 2.4, 3.3, 1. ],\n",
       "       [6.6, 2.9, 4.6, 1.3],\n",
       "       [5.2, 2.7, 3.9, 1.4],\n",
       "       [5. , 2. , 3.5, 1. ],\n",
       "       [5.9, 3. , 4.2, 1.5],\n",
       "       [6. , 2.2, 4. , 1. ],\n",
       "       [6.1, 2.9, 4.7, 1.4],\n",
       "       [5.6, 2.9, 3.6, 1.3],\n",
       "       [6.7, 3.1, 4.4, 1.4],\n",
       "       [5.6, 3. , 4.5, 1.5],\n",
       "       [5.8, 2.7, 4.1, 1. ],\n",
       "       [6.2, 2.2, 4.5, 1.5],\n",
       "       [5.6, 2.5, 3.9, 1.1],\n",
       "       [5.9, 3.2, 4.8, 1.8],\n",
       "       [6.1, 2.8, 4. , 1.3],\n",
       "       [6.3, 2.5, 4.9, 1.5],\n",
       "       [6.1, 2.8, 4.7, 1.2],\n",
       "       [6.4, 2.9, 4.3, 1.3],\n",
       "       [6.6, 3. , 4.4, 1.4],\n",
       "       [6.8, 2.8, 4.8, 1.4],\n",
       "       [6.7, 3. , 5. , 1.7],\n",
       "       [6. , 2.9, 4.5, 1.5],\n",
       "       [5.7, 2.6, 3.5, 1. ],\n",
       "       [5.5, 2.4, 3.8, 1.1],\n",
       "       [5.5, 2.4, 3.7, 1. ],\n",
       "       [5.8, 2.7, 3.9, 1.2],\n",
       "       [6. , 2.7, 5.1, 1.6],\n",
       "       [5.4, 3. , 4.5, 1.5],\n",
       "       [6. , 3.4, 4.5, 1.6],\n",
       "       [6.7, 3.1, 4.7, 1.5],\n",
       "       [6.3, 2.3, 4.4, 1.3],\n",
       "       [5.6, 3. , 4.1, 1.3],\n",
       "       [5.5, 2.5, 4. , 1.3],\n",
       "       [5.5, 2.6, 4.4, 1.2],\n",
       "       [6.1, 3. , 4.6, 1.4],\n",
       "       [5.8, 2.6, 4. , 1.2],\n",
       "       [5. , 2.3, 3.3, 1. ],\n",
       "       [5.6, 2.7, 4.2, 1.3],\n",
       "       [5.7, 3. , 4.2, 1.2],\n",
       "       [5.7, 2.9, 4.2, 1.3],\n",
       "       [6.2, 2.9, 4.3, 1.3],\n",
       "       [5.1, 2.5, 3. , 1.1],\n",
       "       [5.7, 2.8, 4.1, 1.3],\n",
       "       [6.3, 3.3, 6. , 2.5],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [7.1, 3. , 5.9, 2.1],\n",
       "       [6.3, 2.9, 5.6, 1.8],\n",
       "       [6.5, 3. , 5.8, 2.2],\n",
       "       [7.6, 3. , 6.6, 2.1],\n",
       "       [4.9, 2.5, 4.5, 1.7],\n",
       "       [7.3, 2.9, 6.3, 1.8],\n",
       "       [6.7, 2.5, 5.8, 1.8],\n",
       "       [7.2, 3.6, 6.1, 2.5],\n",
       "       [6.5, 3.2, 5.1, 2. ],\n",
       "       [6.4, 2.7, 5.3, 1.9],\n",
       "       [6.8, 3. , 5.5, 2.1],\n",
       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df['class label'].values\n",
    "enc = LabelEncoder()\n",
    "label_encoder = enc.fit(y)\n",
    "\n",
    "y = label_encoder.transform(y) + 1\n",
    "label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AxesSubplot(0.125,0.536818;0.352273x0.343182) 0\n",
      "AxesSubplot(0.547727,0.536818;0.352273x0.343182) 1\n",
      "AxesSubplot(0.125,0.125;0.352273x0.343182) 2\n",
      "AxesSubplot(0.547727,0.125;0.352273x0.343182) 3\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(16,8))\n",
    "\n",
    "for ax,cnt in zip(axes.ravel(), range(4)):  \n",
    "    \n",
    "    # set bin sizes\n",
    "    min_b = math.floor(np.min(X[:,cnt]))\n",
    "    max_b = math.ceil(np.max(X[:,cnt]))\n",
    "    bins = np.linspace(min_b, max_b, 25)\n",
    "\n",
    "    # plottling the histograms\n",
    "    for lab,col in zip(range(1,4), ('blue', 'red', 'green')):\n",
    "        ax.hist(X[y==lab, cnt],\n",
    "                   color=col,\n",
    "                   label='class %s' %label_dict[lab],\n",
    "                   bins=bins,\n",
    "                   alpha=0.5,)\n",
    "    ylims = ax.get_ylim()\n",
    "\n",
    "    # plot annotation\n",
    "    leg = ax.legend(loc='upper right', fancybox=True, fontsize=8)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    ax.set_ylim([0, max(ylims)+2])\n",
    "    ax.set_xlabel(feature_dict[cnt])\n",
    "    ax.set_title('Iris histogram #%s' %str(cnt+1))\n",
    "\n",
    "    # hide axis ticks\n",
    "    ax.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "axes[0][0].set_ylabel('count')\n",
    "axes[1][0].set_ylabel('count')\n",
    "\n",
    "fig.tight_layout()       \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LDA (5 steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Computing the d-dimensional mean vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Vector class 1: [5.006 3.418 1.464 0.244]\n",
      "\n",
      "Mean Vector class 2: [5.936 2.77  4.26  1.326]\n",
      "\n",
      "Mean Vector class 3: [6.588 2.974 5.552 2.026]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "mean_vectors = []\n",
    "for cl in range(1,4):\n",
    "    mean_vectors.append(np.mean(X[y==cl], axis=0))\n",
    "    print('Mean Vector class %s: %s\\n' %(cl, mean_vectors[cl-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([5.006, 3.418, 1.464, 0.244]),\n",
       " array([5.936, 2.77 , 4.26 , 1.326]),\n",
       " array([6.588, 2.974, 5.552, 2.026])]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Computing the Scatter Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "within-class Scatter Matrix:\n",
      " [[38.9562 13.683  24.614   5.6556]\n",
      " [13.683  17.035   8.12    4.9132]\n",
      " [24.614   8.12   27.22    6.2536]\n",
      " [ 5.6556  4.9132  6.2536  6.1756]]\n"
     ]
    }
   ],
   "source": [
    "S_W = np.zeros((4,4))\n",
    "for cl,mv in zip(range(1,4), mean_vectors):\n",
    "    class_sc_mat = np.zeros((4,4))                  # scatter matrix for every class\n",
    "    for row in X[y == cl]:\n",
    "        row, mv = row.reshape(4,1), mv.reshape(4,1) # make column vectors\n",
    "        class_sc_mat += (row-mv).dot((row-mv).T)\n",
    "    S_W += class_sc_mat                             # sum class scatter matrices\n",
    "print('within-class Scatter Matrix:\\n', S_W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "between-class Scatter Matrix:\n",
      " [[ 63.21213333 -19.534      165.16466667  71.36306667]\n",
      " [-19.534       10.9776     -56.0552     -22.4924    ]\n",
      " [165.16466667 -56.0552     436.64373333 186.90813333]\n",
      " [ 71.36306667 -22.4924     186.90813333  80.60413333]]\n"
     ]
    }
   ],
   "source": [
    "overall_mean = np.mean(X, axis=0)\n",
    "\n",
    "S_B = np.zeros((4,4))\n",
    "for i,mean_vec in enumerate(mean_vectors):  \n",
    "    n = X[y==i+1,:].shape[0]\n",
    "    mean_vec = mean_vec.reshape(4,1) # make column vector\n",
    "    overall_mean = overall_mean.reshape(4,1) # make column vector\n",
    "    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)\n",
    "\n",
    "print('between-class Scatter Matrix:\\n', S_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Solving the generalized eigenvalue problem for the matrix S−1WSB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvector 1: \n",
      "[[ 0.20490976]\n",
      " [ 0.38714331]\n",
      " [-0.54648218]\n",
      " [-0.71378517]]\n",
      "Eigenvalue 1: 3.23e+01\n",
      "\n",
      "Eigenvector 2: \n",
      "[[-0.00898234]\n",
      " [-0.58899857]\n",
      " [ 0.25428655]\n",
      " [-0.76703217]]\n",
      "Eigenvalue 2: 2.78e-01\n",
      "\n",
      "Eigenvector 3: \n",
      "[[-0.83786868]\n",
      " [ 0.16963186]\n",
      " [ 0.12293803]\n",
      " [ 0.50407077]]\n",
      "Eigenvalue 3: -4.13e-15\n",
      "\n",
      "Eigenvector 4: \n",
      "[[ 0.20003692]\n",
      " [-0.39490682]\n",
      " [-0.45668159]\n",
      " [ 0.77167076]]\n",
      "Eigenvalue 4: 1.20e-14\n"
     ]
    }
   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))\n",
    "\n",
    "for i in range(len(eig_vals)):\n",
    "    eigvec_sc = eig_vecs[:,i].reshape(4,1)   \n",
    "    print('\\nEigenvector {}: \\n{}'.format(i+1, eigvec_sc.real))\n",
    "    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ok\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(eig_vals)):\n",
    "    eigv = eig_vecs[:,i].reshape(4,1)\n",
    "    np.testing.assert_array_almost_equal(np.linalg.inv(S_W).dot(S_B).dot(eigv),\n",
    "                                         eig_vals[i] * eigv,\n",
    "                                         decimal=6, err_msg='', verbose=True)\n",
    "print('ok')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Selecting linear discriminants for the new feature subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "32.27195779972981\n",
      "0.27756686384004264\n",
      "1.1953730364935478e-14\n",
      "4.1311796919088535e-15\n"
     ]
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "\n",
    "print('Eigenvalues in decreasing order:\\n')\n",
    "for i in eig_pairs:\n",
    "    print(i[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained:\n",
      "\n",
      "eigenvalue 1: 99.15%\n",
      "eigenvalue 2: 0.85%\n",
      "eigenvalue 3: 0.00%\n",
      "eigenvalue 4: 0.00%\n"
     ]
    }
   ],
   "source": [
    "print('Variance explained:\\n')\n",
    "eigv_sum = sum(eig_vals)\n",
    "for i,j in enumerate(eig_pairs):\n",
    "    print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[ 0.20490976 -0.00898234]\n",
      " [ 0.38714331 -0.58899857]\n",
      " [-0.54648218  0.25428655]\n",
      " [-0.71378517 -0.76703217]]\n"
     ]
    }
   ],
   "source": [
    "W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))\n",
    "print('Matrix W:\\n', W.real)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5: Transforming the samples onto the new subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lda = X.dot(W)\n",
    "assert X_lda.shape == (150,2), \"The matrix is not 150x2 dimensional.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_step_lda():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X_lda[:,0].real[y == label],\n",
    "                y=X_lda[:,1].real[y == label],\n",
    "                marker=marker,\n",
    "                color=color,\n",
    "                alpha=0.5,\n",
    "                label=label_dict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title('LDA: Iris projection onto the first 2 linear discriminants')\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()\n",
    "\n",
    "plot_step_lda()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scikit-learn method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2],\n",
       "       [5.4, 3.9, 1.7, 0.4],\n",
       "       [4.6, 3.4, 1.4, 0.3],\n",
       "       [5. , 3.4, 1.5, 0.2],\n",
       "       [4.4, 2.9, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5.4, 3.7, 1.5, 0.2],\n",
       "       [4.8, 3.4, 1.6, 0.2],\n",
       "       [4.8, 3. , 1.4, 0.1],\n",
       "       [4.3, 3. , 1.1, 0.1],\n",
       "       [5.8, 4. , 1.2, 0.2],\n",
       "       [5.7, 4.4, 1.5, 0.4],\n",
       "       [5.4, 3.9, 1.3, 0.4],\n",
       "       [5.1, 3.5, 1.4, 0.3],\n",
       "       [5.7, 3.8, 1.7, 0.3],\n",
       "       [5.1, 3.8, 1.5, 0.3],\n",
       "       [5.4, 3.4, 1.7, 0.2],\n",
       "       [5.1, 3.7, 1.5, 0.4],\n",
       "       [4.6, 3.6, 1. , 0.2],\n",
       "       [5.1, 3.3, 1.7, 0.5],\n",
       "       [4.8, 3.4, 1.9, 0.2],\n",
       "       [5. , 3. , 1.6, 0.2],\n",
       "       [5. , 3.4, 1.6, 0.4],\n",
       "       [5.2, 3.5, 1.5, 0.2],\n",
       "       [5.2, 3.4, 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.6, 0.2],\n",
       "       [4.8, 3.1, 1.6, 0.2],\n",
       "       [5.4, 3.4, 1.5, 0.4],\n",
       "       [5.2, 4.1, 1.5, 0.1],\n",
       "       [5.5, 4.2, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5. , 3.2, 1.2, 0.2],\n",
       "       [5.5, 3.5, 1.3, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [4.4, 3. , 1.3, 0.2],\n",
       "       [5.1, 3.4, 1.5, 0.2],\n",
       "       [5. , 3.5, 1.3, 0.3],\n",
       "       [4.5, 2.3, 1.3, 0.3],\n",
       "       [4.4, 3.2, 1.3, 0.2],\n",
       "       [5. , 3.5, 1.6, 0.6],\n",
       "       [5.1, 3.8, 1.9, 0.4],\n",
       "       [4.8, 3. , 1.4, 0.3],\n",
       "       [5.1, 3.8, 1.6, 0.2],\n",
       "       [4.6, 3.2, 1.4, 0.2],\n",
       "       [5.3, 3.7, 1.5, 0.2],\n",
       "       [5. , 3.3, 1.4, 0.2],\n",
       "       [7. , 3.2, 4.7, 1.4],\n",
       "       [6.4, 3.2, 4.5, 1.5],\n",
       "       [6.9, 3.1, 4.9, 1.5],\n",
       "       [5.5, 2.3, 4. , 1.3],\n",
       "       [6.5, 2.8, 4.6, 1.5],\n",
       "       [5.7, 2.8, 4.5, 1.3],\n",
       "       [6.3, 3.3, 4.7, 1.6],\n",
       "       [4.9, 2.4, 3.3, 1. ],\n",
       "       [6.6, 2.9, 4.6, 1.3],\n",
       "       [5.2, 2.7, 3.9, 1.4],\n",
       "       [5. , 2. , 3.5, 1. ],\n",
       "       [5.9, 3. , 4.2, 1.5],\n",
       "       [6. , 2.2, 4. , 1. ],\n",
       "       [6.1, 2.9, 4.7, 1.4],\n",
       "       [5.6, 2.9, 3.6, 1.3],\n",
       "       [6.7, 3.1, 4.4, 1.4],\n",
       "       [5.6, 3. , 4.5, 1.5],\n",
       "       [5.8, 2.7, 4.1, 1. ],\n",
       "       [6.2, 2.2, 4.5, 1.5],\n",
       "       [5.6, 2.5, 3.9, 1.1],\n",
       "       [5.9, 3.2, 4.8, 1.8],\n",
       "       [6.1, 2.8, 4. , 1.3],\n",
       "       [6.3, 2.5, 4.9, 1.5],\n",
       "       [6.1, 2.8, 4.7, 1.2],\n",
       "       [6.4, 2.9, 4.3, 1.3],\n",
       "       [6.6, 3. , 4.4, 1.4],\n",
       "       [6.8, 2.8, 4.8, 1.4],\n",
       "       [6.7, 3. , 5. , 1.7],\n",
       "       [6. , 2.9, 4.5, 1.5],\n",
       "       [5.7, 2.6, 3.5, 1. ],\n",
       "       [5.5, 2.4, 3.8, 1.1],\n",
       "       [5.5, 2.4, 3.7, 1. ],\n",
       "       [5.8, 2.7, 3.9, 1.2],\n",
       "       [6. , 2.7, 5.1, 1.6],\n",
       "       [5.4, 3. , 4.5, 1.5],\n",
       "       [6. , 3.4, 4.5, 1.6],\n",
       "       [6.7, 3.1, 4.7, 1.5],\n",
       "       [6.3, 2.3, 4.4, 1.3],\n",
       "       [5.6, 3. , 4.1, 1.3],\n",
       "       [5.5, 2.5, 4. , 1.3],\n",
       "       [5.5, 2.6, 4.4, 1.2],\n",
       "       [6.1, 3. , 4.6, 1.4],\n",
       "       [5.8, 2.6, 4. , 1.2],\n",
       "       [5. , 2.3, 3.3, 1. ],\n",
       "       [5.6, 2.7, 4.2, 1.3],\n",
       "       [5.7, 3. , 4.2, 1.2],\n",
       "       [5.7, 2.9, 4.2, 1.3],\n",
       "       [6.2, 2.9, 4.3, 1.3],\n",
       "       [5.1, 2.5, 3. , 1.1],\n",
       "       [5.7, 2.8, 4.1, 1.3],\n",
       "       [6.3, 3.3, 6. , 2.5],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [7.1, 3. , 5.9, 2.1],\n",
       "       [6.3, 2.9, 5.6, 1.8],\n",
       "       [6.5, 3. , 5.8, 2.2],\n",
       "       [7.6, 3. , 6.6, 2.1],\n",
       "       [4.9, 2.5, 4.5, 1.7],\n",
       "       [7.3, 2.9, 6.3, 1.8],\n",
       "       [6.7, 2.5, 5.8, 1.8],\n",
       "       [7.2, 3.6, 6.1, 2.5],\n",
       "       [6.5, 3.2, 5.1, 2. ],\n",
       "       [6.4, 2.7, 5.3, 1.9],\n",
       "       [6.8, 3. , 5.5, 2.1],\n",
       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "sklearn_lda = LDA(n_components=2)\n",
    "X_lda_sklearn = sklearn_lda.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.0849532 ,  0.32845422],\n",
       "       [ 7.1471629 , -0.75547326],\n",
       "       [ 7.51137789, -0.23807832],\n",
       "       [ 6.83767561, -0.64288476],\n",
       "       [ 8.15781367,  0.54063935],\n",
       "       [ 7.72363087,  1.48232345],\n",
       "       [ 7.23514662,  0.3771537 ],\n",
       "       [ 7.62974497,  0.01667246],\n",
       "       [ 6.58274132, -0.98737424],\n",
       "       [ 7.36884116, -0.91362729],\n",
       "       [ 8.42181434,  0.67622968],\n",
       "       [ 7.24739721, -0.08292417],\n",
       "       [ 7.35062105, -1.0393597 ],\n",
       "       [ 7.59646896, -0.77671553],\n",
       "       [ 9.86936588,  1.61486093],\n",
       "       [ 9.18033614,  2.75558626],\n",
       "       [ 8.59760709,  1.85442217],\n",
       "       [ 7.7995682 ,  0.60905468],\n",
       "       [ 8.1000091 ,  0.99610981],\n",
       "       [ 8.04543611,  1.16244332],\n",
       "       [ 7.52046427, -0.156233  ],\n",
       "       [ 7.60526378,  1.22757267],\n",
       "       [ 8.70408249,  0.89959416],\n",
       "       [ 6.26374139,  0.46023935],\n",
       "       [ 6.59191505, -0.36199821],\n",
       "       [ 6.79210164, -0.93823664],\n",
       "       [ 6.84048091,  0.4848487 ],\n",
       "       [ 7.948386  ,  0.23871551],\n",
       "       [ 8.01209273,  0.11626909],\n",
       "       [ 6.85589572, -0.51715236],\n",
       "       [ 6.78303525, -0.72933749],\n",
       "       [ 7.38668238,  0.59101728],\n",
       "       [ 9.16249492,  1.25094169],\n",
       "       [ 9.49617185,  1.84989586],\n",
       "       [ 7.36884116, -0.91362729],\n",
       "       [ 7.9756525 , -0.13519572],\n",
       "       [ 8.63115466,  0.4346228 ],\n",
       "       [ 7.36884116, -0.91362729],\n",
       "       [ 6.95602269, -0.67887846],\n",
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       "       [ 6.42449823,  1.26152073],\n",
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       "       [ 8.11232705,  0.78881818],\n",
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       "       [ 8.33988749,  0.6729437 ],\n",
       "       [ 7.69345171, -0.10577397],\n",
       "       [-1.45772244,  0.04186554],\n",
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       "       [-2.55339693, -0.46282362],\n",
       "       [-2.41954768, -0.95728766],\n",
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       "       [-0.2160281 , -1.57096512],\n",
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       "       [-1.95838993, -0.35044011],\n",
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       "       [-0.99937   , -0.47902036],\n",
       "       [-3.83709476, -1.39488292],\n",
       "       [-2.24344339, -1.41079358],\n",
       "       [-1.25428429, -0.53276537],\n",
       "       [-1.43952232, -0.12314653],\n",
       "       [-2.45921948, -0.91961551],\n",
       "       [-3.52471481,  0.16379275],\n",
       "       [-2.58974981, -0.17075771],\n",
       "       [ 0.31197324, -1.29978446],\n",
       "       [-1.10232227, -1.7357722 ],\n",
       "       [-0.59844322, -1.92334798],\n",
       "       [-0.89605882, -0.89192518],\n",
       "       [-4.49567379, -0.87924754],\n",
       "       [-2.9265236 ,  0.02499754],\n",
       "       [-2.10119821,  1.18719828],\n",
       "       [-2.14367532,  0.09713697],\n",
       "       [-2.48342912, -1.92190266],\n",
       "       [-1.31792367, -0.15753271],\n",
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       "       [-2.38909697, -1.5823776 ],\n",
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       "       [-1.26934019, -1.20042096],\n",
       "       [-0.28888857, -1.78315025],\n",
       "       [-2.00077969, -0.8969707 ],\n",
       "       [-1.16910587, -0.52787187],\n",
       "       [-1.6092782 , -0.46274252],\n",
       "       [-1.41813799, -0.53933732],\n",
       "       [ 0.47271009, -0.78924756],\n",
       "       [-1.54557146, -0.58518894],\n",
       "       [-7.85608083,  2.11161905],\n",
       "       [-5.5156825 , -0.04401811],\n",
       "       [-6.30499392,  0.46211638],\n",
       "       [-5.60355888, -0.34236987],\n",
       "       [-6.86344597,  0.81602566],\n",
       "       [-7.42481805, -0.1726265 ],\n",
       "       [-4.68086447, -0.50758694],\n",
       "       [-6.31374875, -0.96068288],\n",
       "       [-6.33198886, -1.37715975],\n",
       "       [-6.87287126,  2.69458147],\n",
       "       [-4.45364294,  1.33693971],\n",
       "       [-5.4611095 , -0.21035161],\n",
       "       [-5.67679825,  0.82435717],\n",
       "       [-5.97407494, -0.10462115],\n",
       "       [-6.78782019,  1.5744553 ],\n",
       "       [-5.82871291,  1.98940576],\n",
       "       [-5.0664238 , -0.02730214],\n",
       "       [-6.60847169,  1.7420041 ],\n",
       "       [-9.18829265, -0.74909806],\n",
       "       [-4.76573133, -2.14417884],\n",
       "       [-6.29305487,  1.63373692],\n",
       "       [-5.37314577,  0.63153087],\n",
       "       [-7.58557489, -0.97390788],\n",
       "       [-4.38367513, -0.12213933],\n",
       "       [-5.73135125,  1.28143515],\n",
       "       [-5.27583147, -0.0384815 ],\n",
       "       [-4.0923206 ,  0.18307048],\n",
       "       [-4.08316687,  0.51770204],\n",
       "       [-6.53257435,  0.28724638],\n",
       "       [-4.577648  , -0.84457527],\n",
       "       [-6.23500611, -0.70621819],\n",
       "       [-5.21836582,  1.46644917],\n",
       "       [-6.81795935,  0.56784684],\n",
       "       [-3.80972091, -0.93451896],\n",
       "       [-5.09023453, -2.11775698],\n",
       "       [-6.82119092,  0.85698379],\n",
       "       [-6.54193229,  2.41858841],\n",
       "       [-4.99356333,  0.18488299],\n",
       "       [-3.94659967,  0.60744074],\n",
       "       [-5.22159002,  1.13613893],\n",
       "       [-6.67858684,  1.785319  ],\n",
       "       [-5.13687786,  1.97641389],\n",
       "       [-5.5156825 , -0.04401811],\n",
       "       [-6.81196984,  1.44440158],\n",
       "       [-6.87289126,  2.40383699],\n",
       "       [-5.67401294,  1.66134615],\n",
       "       [-5.19712883, -0.36550576],\n",
       "       [-4.98171163,  0.81297282],\n",
       "       [-5.90148603,  2.32075134],\n",
       "       [-4.68400868,  0.32508073]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_lda_sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_scikit_lda(X, title):\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X[:,0][y == label],\n",
    "                    y=X[:,1][y == label] * -1, # flip the figure\n",
    "                    marker=marker,\n",
    "                    color=color,\n",
    "                    alpha=0.5,\n",
    "                    label=label_dict[label])\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title(title)\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_scikit_lda(X_lda_sklearn, title='Default LDA via scikit-learn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}