Linear Discriminant Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LDA - Linear Discriminant Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear Discriminant Analysis is a dimensionality reduction technique which reduces dimensions based on a supervised algorithm. The algorithm reduces number of features/variables based on predefined class/labels present in the dataset. It selects the derived features in such a manner that the classes present in data are easily distinguishable.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Theory: http://www.sci.utah.edu/~shireen/pdfs/tutorials/Elhabian_LDA09.pdf\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll be using iris dataset for this example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#reading the dataset\n",
    "\n",
    "import pandas as pd\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",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</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>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2    3            4\n",
       "0  5.1  3.5  1.4  0.2  Iris-setosa\n",
       "1  4.9  3.0  1.4  0.2  Iris-setosa\n",
       "2  4.7  3.2  1.3  0.2  Iris-setosa\n",
       "3  4.6  3.1  1.5  0.2  Iris-setosa\n",
       "4  5.0  3.6  1.4  0.2  Iris-setosa"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#creating feature names list\n",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 'sepal length in cm', 1: 'sepal width in cm', 2: 'petal length in cm', 3: 'petal width in cm'}\n"
     ]
    }
   ],
   "source": [
    "print(feature_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#changing column names\n",
    "df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']\n",
    "#removing nulls\n",
    "df.dropna(how=\"all\", inplace=True) # to drop the empty line at file-end\n",
    "#printing sample\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'], dtype=object)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking dataset for possible labels\n",
    "df['class label'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#changing labels into numeric from categorical. its easier to deal with numeric labels\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "\n",
    "X = df.iloc[:,0:4].values\n",
    "y = df['class label'].values\n",
    "\n",
    "enc = LabelEncoder()\n",
    "label_encoder = enc.fit(y)\n",
    "y = label_encoder.transform(y) + 1\n",
    "\n",
    "label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#performing eda - plotting histograms of label wrt 4 features\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "get_ipython().magic(u'matplotlib inline')\n",
    "\n",
    "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])) #floor of min value in column\n",
    "    max_b = math.ceil(np.max(X[:,cnt]))  #ceiling of max value in column\n",
    "    bins = np.linspace(min_b, max_b, 25) #bins = min, min + (max - min)/25 , min + 2*(max - min)/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": [
    "## Step wise LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 - Computing d-dimensional mean vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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_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": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 - Computing the scatter matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 Within class scatter matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 Between class scatter matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "between-class Scatter Matrix:\n",
      " [[ 63.2121 -19.534  165.1647  71.3631]\n",
      " [-19.534   10.9776 -56.0552 -22.4924]\n",
      " [165.1647 -56.0552 436.6437 186.9081]\n",
      " [ 71.3631 -22.4924 186.9081  80.6041]]\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):  #enumerate just adds a number from 0 to every value in object\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)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 - Solving the generalized eigenvalue problem for the matrix S−1WSB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvector 1: \n",
      "[[-0.2049]\n",
      " [-0.3871]\n",
      " [ 0.5465]\n",
      " [ 0.7138]]\n",
      "Eigenvalue 1: 3.23e+01\n",
      "\n",
      "Eigenvector 2: \n",
      "[[-0.009 ]\n",
      " [-0.589 ]\n",
      " [ 0.2543]\n",
      " [-0.767 ]]\n",
      "Eigenvalue 2: 2.78e-01\n",
      "\n",
      "Eigenvector 3: \n",
      "[[-0.8844]\n",
      " [ 0.2854]\n",
      " [ 0.258 ]\n",
      " [ 0.2643]]\n",
      "Eigenvalue 3: 3.42e-15\n",
      "\n",
      "Eigenvector 4: \n",
      "[[-0.2234]\n",
      " [-0.2523]\n",
      " [-0.326 ]\n",
      " [ 0.8833]]\n",
      "Eigenvalue 4: 1.15e-14\n"
     ]
    }
   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B)) #makes eigenvector from matrix\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": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ok\n"
     ]
    }
   ],
   "source": [
    "#Checking the eigenvector-eigenvalue calculation\n",
    "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": [
    "#### 4.1 Ordering eigenvectors by decreasing order of eigenvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "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))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "32.27195779972981\n",
      "0.27756686384003953\n",
      "1.1483362279322388e-14\n",
      "3.422458920849769e-15\n"
     ]
    }
   ],
   "source": [
    "# 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": 37,
   "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": [
    "#Representing values in %\n",
    "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": [
    "#### 4.2 Choosing k eigenvectors with the largest eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here only 2 are adding information, hence selecting only first 2. We can also exclude the second one as the value add is too low."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.2049 -0.009 ]\n",
      " [-0.3871 -0.589 ]\n",
      " [ 0.5465  0.2543]\n",
      " [ 0.7138 -0.767 ]]\n"
     ]
    }
   ],
   "source": [
    "W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1))) #cbind 2 arrays\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": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lda = X.dot(W)\n",
    "assert X_lda.shape == (150,2), \"The matrix is not 150x2 dimensional.\" #Error debugger. If condition is true, does nothing, \n",
    "#else gives error message"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": [
    "## Comparison with PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Samrat Vij\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\__init__.py:424: MatplotlibDeprecationWarning: \n",
      "Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warn_deprecated(\"2.2\", \"Passing one of 'on', 'true', 'off', 'false' as a \"\n"
     ]
    },
    {
     "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": [
    "from sklearn.decomposition import PCA as sklearnPCA\n",
    "\n",
    "sklearn_pca = sklearnPCA(n_components=2)\n",
    "X_pca = sklearn_pca.fit_transform(X)\n",
    "\n",
    "def plot_pca():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X_pca[:,0][y == label],\n",
    "                y=X_pca[:,1][y == label],\n",
    "                marker=marker,\n",
    "                color=color,\n",
    "                alpha=0.5,\n",
    "                label=label_dict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('PC1')\n",
    "    plt.ylabel('PC2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title('PCA: Iris projection onto the first 2 principal components')\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.tight_layout\n",
    "    plt.grid()\n",
    "\n",
    "    plt.show()\n",
    "plot_pca()\n",
    "plot_step_lda()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LDA Using scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": 44,
   "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": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Samrat Vij\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\__init__.py:424: MatplotlibDeprecationWarning: \n",
      "Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warn_deprecated(\"2.2\", \"Passing one of 'on', 'true', 'off', 'false' as a \"\n"
     ]
    },
    {
     "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}