LDA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(178, 13) (178,)\n"
     ]
    },
    {
     "data": {
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       "<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",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\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",
       "      <td>class_0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\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",
       "      <td>class_0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\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",
       "      <td>class_0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\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",
       "      <td>class_0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\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",
       "      <td>class_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    class  \n",
       "0                          3.92   1065.0  class_0  \n",
       "1                          3.40   1050.0  class_0  \n",
       "2                          3.17   1185.0  class_0  \n",
       "3                          3.45   1480.0  class_0  \n",
       "4                          2.93    735.0  class_0  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = X.join(pd.Series(y, name='class'))\n",
    "print(X.shape, y.shape)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LDA\n",
    "\n",
    "1. Compute the within class and between class scatter matrices\n",
    "2. Compute the eigenvectors and corresponding eigenvalues for the scatter matrices\n",
    "3. Sort the eigenvalues and select the top k\n",
    "4. Create a new matrix containing eigenvectors that map to the k eigenvalues\n",
    "5. Obtain the new features (i.e. LDA components) by taking the cross product of the data and the matrix from step 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Compute the within class and between class scatter matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Within class matrix\n",
    "\n",
    "Scatter within each class.\n",
    "\n",
    "$ S_w = \\sum_{i=1}^{C} {S_i} $ , where `c`: is the total no of classes\n",
    "\n",
    "$ S_i = \\sum_{x=1}^{m} {(x-u_i)(x-u_i)'} $, $ S_i $ is the scatter for that class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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",
       "      <th>alcohol</th>\n",
       "      <td>13.744746</td>\n",
       "      <td>12.278732</td>\n",
       "      <td>13.153750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>malic_acid</th>\n",
       "      <td>2.010678</td>\n",
       "      <td>1.932676</td>\n",
       "      <td>3.333750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ash</th>\n",
       "      <td>2.455593</td>\n",
       "      <td>2.244789</td>\n",
       "      <td>2.437083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alcalinity_of_ash</th>\n",
       "      <td>17.037288</td>\n",
       "      <td>20.238028</td>\n",
       "      <td>21.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>magnesium</th>\n",
       "      <td>106.338983</td>\n",
       "      <td>94.549296</td>\n",
       "      <td>99.312500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_phenols</th>\n",
       "      <td>2.840169</td>\n",
       "      <td>2.258873</td>\n",
       "      <td>1.678750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flavanoids</th>\n",
       "      <td>2.982373</td>\n",
       "      <td>2.080845</td>\n",
       "      <td>0.781458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nonflavanoid_phenols</th>\n",
       "      <td>0.290000</td>\n",
       "      <td>0.363662</td>\n",
       "      <td>0.447500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proanthocyanins</th>\n",
       "      <td>1.899322</td>\n",
       "      <td>1.630282</td>\n",
       "      <td>1.153542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_intensity</th>\n",
       "      <td>5.528305</td>\n",
       "      <td>3.086620</td>\n",
       "      <td>7.396250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hue</th>\n",
       "      <td>1.062034</td>\n",
       "      <td>1.056282</td>\n",
       "      <td>0.682708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>od280/od315_of_diluted_wines</th>\n",
       "      <td>3.157797</td>\n",
       "      <td>2.785352</td>\n",
       "      <td>1.683542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proline</th>\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": 17,
     "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": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, n = X.shape\n",
    "within_class_matrix = np.zeros((n, n))\n",
    "\n",
    "for c, rows in df.groupby('class'):\n",
    "    rows = rows.drop(['class'], axis=1)\n",
    "    s = np.zeros((n, n))\n",
    "    for i, row in rows.iterrows():\n",
    "        mean = class_feature_means[c].values.reshape(-1, 1)\n",
    "        x = row.values.reshape(-1, 1)\n",
    "        s += (x-mean) @ ((x-mean).T)\n",
    "    within_class_matrix += s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Between Class Scatter Matrix\n",
    "\n",
    "\\begin{equation}\n",
    "S_B = \\sum_{i=1}^c {N_i * (m_i - m) * (m_i - m).T}\n",
    "\\end{equation}\n",
    "\n",
    "$ N_i $: No of samples in a class\n",
    "\n",
    "$ m_i $: class variance\n",
    "\n",
    "`m`: mean of all features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "between_class_matrix = np.zeros((n,n))\n",
    "features_mean = df.mean()\n",
    "\n",
    "for c in class_feature_means:\n",
    "    n_i = len(df[df['class'] == c])\n",
    "    m_i = class_feature_means[c].values.reshape(-1, 1)\n",
    "    m = features_mean.values.reshape(-1, 1)\n",
    "    between_class_matrix += n_i * (m_i - m) @ (m_i - m).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make linear discriminant by finding eigen values for this equation\n",
    "\n",
    "\\begin{equation}\n",
    "S_w^{-1} * S_B\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigen_values, eigen_vectors = np.linalg.eig(np.linalg.inv(within_class_matrix).dot(between_class_matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.08173943504247\n",
      "4.128469045639485\n",
      "8.757468096729126e-16\n",
      "6.997096258273158e-16\n",
      "6.567555883195076e-16\n",
      "6.567555883195076e-16\n",
      "2.9002924633706455e-16\n",
      "2.447634471068126e-16\n",
      "2.447634471068126e-16\n",
      "2.1950033409800432e-16\n",
      "4.134903483865132e-17\n",
      "3.950057054838905e-17\n",
      "0.0\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": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance\n",
      "Eigenvector 0: 0.6874788878860782\n",
      "Eigenvector 1: 0.3125211121139217\n",
      "Eigenvector 2: 6.629318613355477e-17\n",
      "Eigenvector 3: 5.2967341647222384e-17\n",
      "Eigenvector 4: 4.971576256952484e-17\n",
      "Eigenvector 5: 4.971576256952484e-17\n",
      "Eigenvector 6: 2.1954933320029802e-17\n",
      "Eigenvector 7: 1.8528356116767136e-17\n",
      "Eigenvector 8: 1.8528356116767136e-17\n",
      "Eigenvector 9: 1.6615962906186698e-17\n",
      "Eigenvector 10: 3.1300819286174307e-18\n",
      "Eigenvector 11: 2.9901549703892255e-18\n",
      "Eigenvector 12: 0.0\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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "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": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lda = np.array(X.dot(w_matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lda_df = pd.DataFrame(X_lda, columns=['lda1', 'lda2'])\n",
    "X_lda_df['class'] = df['class']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the Lda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f464868f7b8>"
      ]
     },
     "execution_count": 83,
     "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": [
    "sns.scatterplot(x='lda1', y='lda2', hue='class', data=X_lda_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_val = X.values\n",
    "mean, std = X_val.mean(axis=0), X_val.std(axis=0)\n",
    "X_val = (X_val - mean) / (2*std)\n",
    "cov_mat = X_val.T @ X_val\n",
    "U, S, V = np.linalg.svd(cov_mat)\n",
    "U_red = U[:, :2]\n",
    "Z = X_val @ U_red\n",
    "X_pca_df = pd.DataFrame(Z, columns=['pca1', 'pca2'])\n",
    "X_pca_df['class'] = df['class']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f464413eb00>"
      ]
     },
     "execution_count": 113,
     "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": [
    "sns.scatterplot(x='pca1', y='pca2', hue='class', data=X_pca_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see there is a clear difference here! LDA Separates the classes well whereas PCA doesnot. Well, PCA was never meant to do this.\n",
    "\n",
    "> PCA is reducing dimensions by minimising the projection error or maximising the scatter\n",
    "\n",
    "> whereas, LDA is reducing dimensions by minimizing `interclass variance`($S_W$) and maximizing `intraclass variance`($S_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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}