Linear_Discriminant_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear discriminant analysis from scratch\n",
    "\n",
    "#### This notebook walks through the steps involved in LDA and the basics behind each calculation.\n",
    "\n",
    "#### The notebook is built by follow the link: https://docs.google.com/document/d/1b-HoS9oQUtCOKpK_ZWPSr95suki-Ozo21N-Sj8X_Vps/edit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Iris dataset is used for this demonstration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load the libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load and read the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>class label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>145</td>\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",
       "      <td>146</td>\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",
       "      <td>147</td>\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",
       "      <td>148</td>\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",
       "      <td>149</td>\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": [
       "       0    1    2    3     class label\n",
       "145  6.7  3.0  5.2  2.3  Iris-virginica\n",
       "146  6.3  2.5  5.0  1.9  Iris-virginica\n",
       "147  6.5  3.0  5.2  2.0  Iris-virginica\n",
       "148  6.2  3.4  5.4  2.3  Iris-virginica\n",
       "149  5.9  3.0  5.1  1.8  Iris-virginica"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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', ))}\n",
    "\n",
    "\n",
    "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",
    "\n",
    "df.columns = [i for i,l in sorted(feature_dict.items())] + ['class label']\n",
    "\n",
    "df.dropna(how = 'all', inplace = True)\n",
    "\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transform class labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[[0,1,2,3]].values\n",
    "\n",
    "y =df['class label'].values\n",
    "\n",
    "enc = LabelEncoder()\n",
    "#label_encoder = enc.fit(y)\n",
    "y = enc.fit_transform(y) + 1\n",
    "\n",
    "label_dict = {1: \"Setosa\", 2: 'Versicolor', 3:'Virginica'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12,6))\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()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### From just looking at these simple graphical representations of the features, we can already tell that the petal lengths and widths are likely better suited as potential features two separate between the three flower classes. In practice, instead of reducing the dimensionality via a projection (here: LDA), a good alternative would be a feature selection technique. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### LDA assumes:\n",
    "#### 1 - Normally distributed data\n",
    "#### 2 - Features are statistically independent\n",
    "#### 3 - Identical covariance matrices for each class\n",
    "\n",
    "#### These assumptions are required only for LDA as classier. If LDA is used only for dimensionality reduction, the algorithm works reasonably well if the assumptions are violated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 1 - Calculate the mean feature vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "np.set_printoptions(precision=4)\n",
    "\n",
    "mean_vector = []\n",
    "for i in range(1,4):\n",
    "    mean_vector.append(np.mean(X[y==i], axis = 0))\n",
    "    print(\"Mean vector class %s %s\\n\" %(i, mean_vector[i-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 2 - Calculate scatter matrices (both within class and between class)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "# Within class scatter matrix\n",
    "S_W = np.zeros((4,4))\n",
    "\n",
    "for cl, mean_vec in zip(range(1,4), mean_vector):\n",
    "    class_sc_mat = np.zeros((4,4))   # Make scatter matrix for every class\n",
    "    for row in X[y==cl]:\n",
    "        row, mean_vec =row.reshape(4,1), mean_vec.reshape(4,1)   # Make column vectors\n",
    "        class_sc_mat += (row - mean_vec).dot((row -mean_vec).T)\n",
    "    S_W += class_sc_mat\n",
    "    \n",
    "print(\"Within class scatter matrix: \\n\", S_W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "between-class Scatter Matrix:\n",
      " [[ 35.0564 -15.2395  96.07    39.9687]\n",
      " [-15.2395   6.6248 -41.7629 -17.3749]\n",
      " [ 96.07   -41.7629 263.2748 109.5321]\n",
      " [ 39.9687 -17.3749 109.5321  45.5694]]\n"
     ]
    }
   ],
   "source": [
    "# Between class scatter matrix\n",
    "\n",
    "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 SW(-1)SB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvector 1: \n",
      "[[-0.9308]\n",
      " [-0.1509]\n",
      " [ 0.2074]\n",
      " [ 0.2604]]\n",
      "Eigenvalue 1: 0.00e+00\n",
      "\n",
      "Eigenvector 2: \n",
      "[[-0.206 ]\n",
      " [-0.4039]\n",
      " [ 0.5553]\n",
      " [ 0.6972]]\n",
      "Eigenvalue 2: 1.97e+01\n",
      "\n",
      "Eigenvector 3: \n",
      "[[0.1461]\n",
      " [0.9796]\n",
      " [0.0483]\n",
      " [0.1292]]\n",
      "Eigenvalue 3: 8.66e-16\n",
      "\n",
      "Eigenvector 4: \n",
      "[[ 0.1477]\n",
      " [-0.2495]\n",
      " [-0.4458]\n",
      " [ 0.8469]]\n",
      "Eigenvalue 4: -3.47e-15\n"
     ]
    }
   ],
   "source": [
    "# Calculate eignevalues and eigenvectors\n",
    "\n",
    "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": "markdown",
   "metadata": {},
   "source": [
    "#### Step 4 - Selecting linear discriminant for new feature subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "19.742424906926757\n",
      "3.465028175567194e-15\n",
      "8.658112840473277e-16\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# 1 - Sorting eigenvectors by decreasing eigenvalues\n",
    "\n",
    "# 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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained:\n",
      "\n",
      "eigenvalue 1: 100.00%\n",
      "eigenvalue 2: 0.00%\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": "markdown",
   "metadata": {},
   "source": [
    "#### The first eigenvector is by far the most informative. We won't lose any information if we form a 1D subspace feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.206   0.1477]\n",
      " [-0.4039 -0.2495]\n",
      " [ 0.5553 -0.4458]\n",
      " [ 0.6972  0.8469]]\n"
     ]
    }
   ],
   "source": [
    "# Choosing k eigenvectors with the largest eigenvalues\n",
    "# Let's create a 2 dimensional subspace feature (4 x 2) projection matrix\n",
    "\n",
    "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 dataset into the new subspace feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix shape: (150, 2)\n"
     ]
    }
   ],
   "source": [
    "#Y = X W\n",
    "\n",
    "X_lda = X.dot(W)\n",
    "print(\"Matrix shape:\", X_lda.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the dataset in the new feature space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "# LDA\n",
    "sklearn_lda = LDA(n_components=2)\n",
    "X_lda_sklearn = sklearn_lda.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": 27,
   "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": [
    "plot_step_lda()\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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}