fisher_lda.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8uiCBkM0lpgE"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from numpy.linalg import inv as inv\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm as norm\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cKAcuH1flpgK"
   },
   "outputs": [],
   "source": [
    "def plot_pdfs(mean1, mean2, std1, std2, threshold, dataset_name):\n",
    "    # change X limits for pdf plot to -3 to 3 if normalised W is used. Otherwise set it to -30 to 30 \n",
    "    X_axis = np.linspace(-3.0,3.0,100000)\n",
    "    plt.plot(X_axis, norm.pdf(X_axis, mean1, std1),'-', color='b',label='Class 1 (value 1)')    \n",
    "    plt.plot(X_axis, norm.pdf(X_axis, mean2, std2),'-', color='r',label='Class 2 (value 0)')\n",
    "    plt.plot([threshold], norm.pdf([threshold], mean1, std1), '.', color='g',label='Threshold')\n",
    "    plt.legend(loc = 'upper right')\n",
    "    plt.title('Normal distributions. Threshold = '+ str(threshold))\n",
    "    plt.savefig('plots/' + str(dataset_name) + '_FldaNormDistribution.png')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "KEEa1HDblpgO"
   },
   "outputs": [],
   "source": [
    "def plot_projections(projections, y_test, threshold, dataset_name):\n",
    "    proj_pred_data = pd.DataFrame(np.concatenate((projections, y_test), axis=1))\n",
    "    proj1_pred = proj_pred_data.loc[proj_pred_data[1] == 1][[0]]\n",
    "    proj2_pred = proj_pred_data.loc[proj_pred_data[1] == 0][[0]]    \n",
    "    plt.plot(proj1_pred, np.ones(proj1_pred.shape), '.', color='b', label='Class 1 (value 1)')\n",
    "    plt.plot(proj2_pred, np.ones(proj2_pred.shape), '.', color='r',label='Class 2 (value 0)')\n",
    "    plt.plot([threshold], [1], '.', color='g',label='Threshold')\n",
    "    plt.legend(loc = 'upper right')\n",
    "    plt.title('Projections onto W vector. Threshold = '+ str(threshold))\n",
    "    plt.savefig('plots/' + str(dataset_name) + '_FldaProjections.png')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "EyP2qDQQlpgR"
   },
   "outputs": [],
   "source": [
    "def solve_pdfs(pdf_mean_1, pdf_mean_2, pdf_std_1, pdf_std_2):\n",
    "    coeff1 = 1/(2*pdf_std_1**2) - 1/(2*pdf_std_2**2)\n",
    "    coeff2 = pdf_mean_2/(pdf_std_2**2) - pdf_mean_1/(pdf_std_1**2)\n",
    "    coeff3 = pdf_mean_1**2 /(2*pdf_std_1**2) - pdf_mean_2**2 / (2*pdf_std_2**2) - np.log(pdf_std_2/pdf_std_1)\n",
    "\n",
    "    coeffs = [coeff1, coeff2, coeff3]\n",
    "\n",
    "    roots_of_eq = np.roots(coeffs)\n",
    "    threshold = roots_of_eq[1]\n",
    "    return threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "DPA7YKHrlpgV"
   },
   "outputs": [],
   "source": [
    "def find_w_cordinates(X_train1, X_train2):\n",
    "    \n",
    "    # 1. Find M1, M2, Cov1, Cov2\n",
    "    Mean1 = np.mean(X_train1,axis=0)\n",
    "    Mean2 = np.mean(X_train2,axis=0)\n",
    "    Mean_difference = np.subtract(Mean1,Mean2)\n",
    "\n",
    "    Cov1 = np.cov(np.transpose(X_train1))\n",
    "    Cov2 = np.cov(np.transpose(X_train2))\n",
    "\n",
    "    # 2. Within class spread Sw = Cov1 + Cov2  \n",
    "    Sw_inv = np.linalg.inv(np.add(Cov1,Cov2))\n",
    "    \n",
    "    # 3. W = (Sw_inv).(M1-M2)\n",
    "    W = np.dot(Sw_inv,Mean_difference)\n",
    "    \n",
    "    # 4. Normalise W\n",
    "    W_norm = W / np.linalg.norm(W)\n",
    "    \n",
    "    # Note:\n",
    "    # change X limits for pdf plot to -30 to 30 if W is used\n",
    "    # change X limits for pdf plot to -3 to 3 if normalised W is used\n",
    "    \n",
    "    return W_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pexi6axPlpgc"
   },
   "outputs": [],
   "source": [
    "def find_threshold(X_train1, X_train2, W, dataset_name):\n",
    "    # Threshold = point of intersection of the pdfs (probability density functions)\n",
    "    \n",
    "    # 1. Find Projections\n",
    "    Proj1 = np.dot(W,X_train1.transpose())\n",
    "    Proj2 = np.dot(W,X_train2.transpose())\n",
    "    \n",
    "    # 2. Find Means of the projected data for class 1 and 2\n",
    "    proj_mean1 = np.mean(Proj1)\n",
    "    proj_mean2 = np.mean(Proj2)\n",
    "\n",
    "    # 3. Find Std deviations of the projected data for class 1 and 2\n",
    "    proj_std1 = np.std(Proj1)\n",
    "    proj_std2 = np.std(Proj2)\n",
    "\n",
    "    # 4. Solve the equations\n",
    "    threshold = solve_pdfs(proj_mean1, proj_mean2, proj_std1, proj_std2)\n",
    "    \n",
    "    # Plot the pdfs\n",
    "    plot_pdfs(proj_mean1, proj_mean2, proj_std1, proj_std2, threshold, dataset_name)\n",
    "    return threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ebnwkAodlpgf"
   },
   "outputs": [],
   "source": [
    "def find_predictions(X_test, W, threshold):\n",
    "    \n",
    "    # Project the Test data onto W\n",
    "    proj_testdata = np.dot(W, X_test.transpose()).reshape(X_test.shape[0],1)\n",
    "    \n",
    "    # Compare with threshold\n",
    "    predictions = (proj_testdata >= threshold).astype(int).reshape(X_test.shape[0],1)\n",
    "    \n",
    "    return proj_testdata, predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-rdB6rUrlpgn"
   },
   "outputs": [],
   "source": [
    "def accuracy(actual, predicted):\n",
    "    # Accuracy = (TP + TN)/(TP + TN + FP + FN)\n",
    "    \n",
    "    return np.mean((actual == predicted).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IAb_-UiSlpgv"
   },
   "outputs": [],
   "source": [
    "def precision(actual, predicted):\n",
    "    # Precision = (TP)/(TP + FP) = True pos out of the actual results\n",
    "    \n",
    "    TP = np.count_nonzero(np.logical_and((actual == 1) , (predicted == 1)).astype(int))\n",
    "    FP = np.count_nonzero(np.logical_and((actual == 0) , (predicted == 1)).astype(int))\n",
    "    return TP/(TP + FP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OTgZj8sAlpg0"
   },
   "outputs": [],
   "source": [
    "def recall(actual, predicted):\n",
    "    # Recall = (TP)/(TP + FN) = True pos out of the predicted results\n",
    "    \n",
    "    TP = np.count_nonzero(np.logical_and((actual == 1) , (predicted == 1)).astype(int))\n",
    "    FN = np.count_nonzero(np.logical_and((actual == 1) , (predicted == 0)).astype(int))\n",
    "    return TP/(TP + FN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zBewOvEOlpg5"
   },
   "outputs": [],
   "source": [
    "def f_score(actual , predicted):\n",
    "    # F_Score = 2PR/(P+R)\n",
    "    \n",
    "    P = precision(actual, predicted)\n",
    "    R = recall(actual, predicted)\n",
    "    return 2*P*R/(P + R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kvBW0HT-lphC",
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def fisher(X_train1, X_train2, X_test, y_test, dataset_name):\n",
    "    \n",
    "    # 1. Find Projection Line\n",
    "    W = find_w_cordinates(X_train1, X_train2)\n",
    "    \n",
    "    # 2. Find Threshold\n",
    "    threshold = find_threshold(X_train1, X_train2, W, dataset_name)\n",
    "    \n",
    "    # 3. Find Predictions for the Test Data by Projecting onto W and comparing to the threshold\n",
    "    projections, y_predicted = find_predictions(X_test, W, threshold)\n",
    "    \n",
    "    # Plot the projections\n",
    "    plot_projections(projections, y_test, threshold, dataset_name)\n",
    "    \n",
    "    print('W',W)\n",
    "    print('Threshold:',threshold)\n",
    "    print('accuracy:',accuracy(y_test , y_predicted))\n",
    "    print('precision:',precision(y_test , y_predicted))\n",
    "    print('recall:',recall(y_test , y_predicted))\n",
    "    print('f_score:',f_score(y_test , y_predicted)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "q_iFzK5xlphJ"
   },
   "source": [
    "# DATASET - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aREBe9pelphK",
    "outputId": "bd851b1f-d7e5-4325-cdaf-0309de96fe33"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TESTCASE - 1\n"
     ]
    },
    {
     "data": {
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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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W [0.03304637 0.99945382]\n",
      "Threshold: -0.15207088287130205\n",
      "accuracy: 0.993\n",
      "precision: 0.9939879759519038\n",
      "recall: 0.992\n",
      "f_score: 0.9929929929929929\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('data/a1_d1.csv', header=None)\n",
    "\n",
    "\"\"\"\n",
    "N = total number of points in the given dataset\n",
    "\n",
    "X = [\n",
    "     [f1, f2, f3, ..] (1),\n",
    "     [f1, f2, f3, ..] (2),\n",
    "     [..............] (.),\n",
    "     [..............] (.),\n",
    "     [..............] (N)\n",
    "    ]\n",
    "    \n",
    "y = [label1, label2, label3, ....labelN]\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# X => Feature vectors of all the points in the given dataset\n",
    "# y => Corresponding labels\n",
    "\n",
    "X = data[[0,1]]\n",
    "y = data[[2]]\n",
    "\n",
    "# label = 1 -> Class 1\n",
    "# label = 0 -> Class 2\n",
    "\n",
    "# X_1 => Feature vectors of all the points in class1\n",
    "# X_2 => Feature vectors of all the points in class2\n",
    "\n",
    "X_1 = data.loc[data[2]==1][[0,1]]\n",
    "X_2 = data.loc[data[2]==0][[0,1]]\n",
    "\n",
    "print('TESTCASE - 1')\n",
    "\n",
    "fisher(X_1, X_2, X, y.values, \"a1_d1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QTWIeT9ilphP"
   },
   "source": [
    "# DATASET - 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JlW17kM0lphQ",
    "outputId": "633494a3-799c-40f0-8837-ad5d7b622ca1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TESTCASE - 2\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W [-0.00655686 -0.01823739  0.99981218]\n",
      "Threshold: -0.3893028020993765\n",
      "accuracy: 1.0\n",
      "precision: 1.0\n",
      "recall: 1.0\n",
      "f_score: 1.0\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('data/a1_d2.csv', header=None)\n",
    "\n",
    "\"\"\"\n",
    "N = total number of points in the given dataset\n",
    "\n",
    "X = [\n",
    "     [f1, f2, f3, ..] (1),\n",
    "     [f1, f2, f3, ..] (2),\n",
    "     [..............] (.),\n",
    "     [..............] (.),\n",
    "     [..............] (N)\n",
    "    ]\n",
    "    \n",
    "y = [label1, label2, label3, ....labelN]\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# X => Feature vectors of all the points in the given dataset\n",
    "# y => Corresponding labels\n",
    "\n",
    "X = data[[0,1,2]]\n",
    "y = data[[3]]\n",
    "\n",
    "# label = 1 -> Class 1\n",
    "# label = 0 -> Class 2\n",
    "\n",
    "# X_1 => Feature vectors of all the points in class1\n",
    "# X_2 => Feature vectors all the points in class2\n",
    "\n",
    "X_1 = data.loc[data[3]==1][[0,1,2]]\n",
    "X_2 = data.loc[data[3]==0][[0,1,2]]\n",
    "\n",
    "print('TESTCASE - 2')\n",
    "fisher(X_1, X_2, X, y.values, \"a1_d2\")"
   ]
  }
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