Classification.ipynb

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  "metadata": {
    "colab": {
      "name": "Classification.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "display_name": "Python 2",
      "language": "python",
      "name": "python2"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TUkyNNPWTBPJ",
        "colab_type": "text"
      },
      "source": [
        "# Parametric and Non-Parametric Classification\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yoISMLx4TBPL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RH3FTq9CTBPk",
        "colab_type": "text"
      },
      "source": [
        "points2d.dat dataset is used. The sample includes 6000 instances. Each instance is represented by a feature vector of 2 dimensions. The third column corresponds to the class (0/1/2) of the instance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W46-oiUTTBPl",
        "colab_type": "text"
      },
      "source": [
        "## A: Mixture of Gaussians. \n",
        "\n",
        "Steps:\n",
        "* Implement mixture of gaussians.\n",
        "* Divide data to training and validation and test sets.\n",
        "* At training:\n",
        "    - Divide all data to their respective classes.\n",
        "    - Run mixture of gaussians with k=1,2,3 using different initial points (the general practice is to use k-means to initialize the means, you can use sklearn implementation of k-means). \n",
        "* At validation, select best model:\n",
        "    - Using validation data, select best number of gaussians for each class using prediction error.\n",
        "* On test set, report (for the best model):\n",
        "    - the number of Gaussians for class 0, 1 and 2,\n",
        "    - the prediction error, and\n",
        "    - the confusion matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eAJoCMugTBPm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "file = open('points2d.dat', 'r')\n",
        "data = np.array([])\n",
        "labels = list()\n",
        "for line in file:\n",
        "  words = line.split()\n",
        "  data = np.concatenate((data, list(map(float, words[:2]))), axis = 0)\n",
        "  labels.append(int(words[2]))\n",
        "data = np.reshape(data, (len(data)/2, 2))\n",
        "x_train = data[:int(len(data)*0.5)]\n",
        "labels_train = labels[:int(len(labels)*0.5)]\n",
        "x_valid = data[int(len(data)*0.5):int(len(data)*0.75)]\n",
        "labels_valid = labels[int(len(labels)*0.5):int(len(labels)*0.75)]\n",
        "x_test = data[int(len(data)*0.75):]\n",
        "labels_test = labels[int(len(labels)*0.75):]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OwjPREcpF9bV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def NormalPDF(x, mean, cov, d):\n",
        "  import math\n",
        "  return 1/pow((2 * math.pi), -d/2) * pow(abs(np.linalg.det(cov)), -1/2) * np.exp(-1/2 * np.dot(np.dot((x - mean).T, np.linalg.inv(cov)), (x - mean)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-y-0gvllWS7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        " def EM(xx, k):\n",
        "    from sklearn.cluster import KMeans\n",
        "    kmeans = KMeans(n_clusters=k)\n",
        "    kmeans.fit(xx)\n",
        "    means = kmeans.cluster_centers_\n",
        "    labeled_data = []\n",
        "    mixing_coeffs = []\n",
        "    covs = []\n",
        "    for i in range(k):\n",
        "        labeled_data.append([xx[j] for j in range(len(xx)) if labels[j] == i])\n",
        "        mixing_coeffs.append(len(labeled_data[i]))\n",
        "        covs.append(np.cov(np.asarray(labeled_data[i]).T))\n",
        "    mixing_coeffs = np.asarray(mixing_coeffs) / float(len(xx))\n",
        "    old_loglikelihood = 0\n",
        "    count = 0\n",
        "    while True:\n",
        "        # expectation\n",
        "        r_ics = np.array([])\n",
        "        for x in xx:\n",
        "            list1 = []\n",
        "            sum_r = 0\n",
        "            for i in range(k):\n",
        "                r = float(mixing_coeffs[i]) * NormalPDF(x, means[i], covs[i], 2)\n",
        "                list1.append(r)\n",
        "                sum_r += r\n",
        "            list1 = np.asarray(list1)\n",
        "            r_ics = np.concatenate((r_ics, list1 / float(sum_r)))\n",
        "        r_ics = np.reshape(r_ics, (int(len(r_ics) / k), k))\n",
        "\n",
        "        # maximization\n",
        "        mcs = np.sum(r_ics, axis=0)\n",
        "        mixing_coeffs = mcs / float(np.sum(mcs))\n",
        "\n",
        "        means = np.array([])\n",
        "        for c in range(k):\n",
        "            arr = np.sum(r_ics.T[c].reshape(len(xx), 1) * xx, axis=0) / float(np.sum(r_ics.T[c].reshape(len(xx), 1)))\n",
        "            arr = np.asarray(arr)\n",
        "            means = np.concatenate((means, arr), axis=0)\n",
        "        means = means.reshape(k, 2)\n",
        "\n",
        "        covs = []\n",
        "        for c in range(k):\n",
        "            dot_sum = np.array([[0, 0], [0, 0]])\n",
        "            for i in range(len(xx)):\n",
        "                dot = np.dot(np.asarray(xx[i] - means[c]).reshape(1, 2).T, np.asarray(xx[i] - means[c]).reshape(1, 2))\n",
        "                dot = r_ics[i][c] * dot\n",
        "                dot_sum = dot_sum + (dot / float(mcs[c]))\n",
        "            covs.append(dot_sum)\n",
        "\n",
        "        # likelihood\n",
        "        log_likelihood = 0\n",
        "        for x in xx:\n",
        "            temp = 0\n",
        "            for c in range(k):\n",
        "                r = mixing_coeffs[c] * NormalPDF(x, means[c], covs[c], 2)\n",
        "                temp += r\n",
        "            log_likelihood += np.log(temp)\n",
        "\n",
        "        if count != 0 and log_likelihood - old_loglikelihood < 0.01:\n",
        "            return mixing_coeffs, means, covs\n",
        "\n",
        "        old_loglikelihood = log_likelihood\n",
        "        count += 1\n",
        "       "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a5Mn5MSS39PU",
        "colab_type": "code",
        "outputId": "1ae297c9-dbe9-4db4-fc2b-3d11cf503492",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "# Train\n",
        "x_train_0 = np.asarray([x_train[i] for i in range(len(x_train)) if labels_train[i] == 0])\n",
        "x_train_1 = np.asarray([x_train[i] for i in range(len(x_train)) if labels_train[i] == 1])\n",
        "x_train_2 = np.asarray([x_train[i] for i in range(len(x_train)) if labels_train[i] == 2])\n",
        "\n",
        "class_0_models = [EM(x_train_0, 1), EM(x_train_0, 2), EM(x_train_0, 3)]\n",
        "class_1_models = [EM(x_train_1, 1), EM(x_train_1, 2), EM(x_train_1, 3)]\n",
        "class_2_models = [EM(x_train_2, 1), EM(x_train_2, 2), EM(x_train_2, 3)]\n",
        "\n",
        "print class_2_models[1]"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(array([0.57541102, 0.42458898]), array([[-1.92445195, -2.92808644],\n",
            "       [-5.96266218, -4.93996574]]), [array([[ 3.43609232, -1.50410238],\n",
            "       [-1.50410238,  4.25488207]]), array([[ 2.48472833, -0.90126106],\n",
            "       [-0.90126106,  5.19681356]])])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kkQSI9qckamy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Validation\n",
        "errors = []\n",
        "\n",
        "for i_0 in range(3):\n",
        "    for i_1 in range(3):\n",
        "        for i_2 in range(3):\n",
        "            cluster_labels = [0 for n in range(i_0+1)]\n",
        "            cluster_labels.extend([1 for n in range(i_1+1)])\n",
        "            cluster_labels.extend([2 for n in range(i_2+1)])\n",
        "            k = i_0 + i_1 + i_2 + 3\n",
        "            means = np.concatenate((class_0_models[i_0][1], (np.concatenate((class_1_models[i_1][1], class_2_models[i_2][1]), axis=0))), axis=0)\n",
        "            covs = np.concatenate((class_0_models[i_0][2], (np.concatenate((class_1_models[i_1][2], class_2_models[i_2][2]), axis=0))), axis=0)\n",
        "            mixing_coeffs = np.concatenate((class_0_models[i_0][0], (np.concatenate((class_1_models[i_1][0], class_2_models[i_2][0]), axis=0))), axis=0)\n",
        "            error = 0\n",
        "            for v in range(len(x_valid)):\n",
        "                list1 = []\n",
        "                for i in range(k):\n",
        "                    r = float(mixing_coeffs[i]) * NormalPDF(x_valid[v], means[i], covs[i], 2)\n",
        "                    list1.append(r)\n",
        "                    \n",
        "                if labels_valid[v] != cluster_labels[list1.index(max(list1))]:\n",
        "                    error += 1\n",
        "            errors.append((error / float(len(x_valid)), i_0, i_1, i_2))\n",
        "            "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gw_GosIjsJwL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "err, ind_model_0, ind_model_1, ind_model_2 = min(errors)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LIQBDSGhtoBI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Test\n",
        "cluster_labels = [0 for n in range(ind_model_0 + 1)]\n",
        "cluster_labels.extend([1 for n in range(ind_model_1 + 1)])\n",
        "cluster_labels.extend([2 for n in range(ind_model_2 + 1)])\n",
        "k = ind_model_0 + ind_model_1 + ind_model_2 + 3\n",
        "means = np.concatenate(\n",
        "    (class_0_models[ind_model_0][1], (np.concatenate((class_1_models[ind_model_1][1], class_2_models[ind_model_2][1]), axis=0))), axis=0)\n",
        "covs = np.concatenate(\n",
        "    (class_0_models[ind_model_0][2], (np.concatenate((class_1_models[ind_model_1][2], class_2_models[ind_model_2][2]), axis=0))), axis=0)\n",
        "mixing_coeffs = np.concatenate(\n",
        "    (class_0_models[ind_model_0][0], (np.concatenate((class_1_models[ind_model_1][0], class_2_models[ind_model_2][0]), axis=0))), axis=0)\n",
        "error = 0\n",
        "gmm_labels = []\n",
        "for t in range(len(x_test)):\n",
        "    list1 = []\n",
        "    for i in range(k):\n",
        "        r = float(mixing_coeffs[i]) * NormalPDF(x_test[t], means[i], covs[i], 2)\n",
        "        list1.append(r)\n",
        "    temp_lbl = cluster_labels[list1.index(max(list1))]\n",
        "    gmm_labels.append(temp_lbl)\n",
        "    if labels_test[t] != temp_lbl:\n",
        "        error += 1\n",
        "        \n",
        "\n",
        "error = error / float(len(x_test))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4BrsFYklwkDv",
        "colab_type": "code",
        "outputId": "a0a6b98a-1108-4548-ab55-0904c1a8b6c5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 379
        }
      },
      "source": [
        "# Report\n",
        "print('Best Model:')\n",
        "print('\\t For Class 0, k = %d' % (ind_model_0 + 1))\n",
        "print('\\t For Class 1, k = %d' % (ind_model_1 + 1))\n",
        "print('\\t For Class 2, k = %d' % (ind_model_2 + 1))\n",
        "print('Prediction Error: %f' % error)\n",
        "\n",
        "conf_matrix = np.array([[0,0,0], [0,0,0], [0,0,0]])\n",
        "for i in range(len(labels_test)):\n",
        "  conf_matrix[labels_test[i]][gmm_labels[i]] += 1\n",
        "\n",
        "col = ['Class 0 Predicted', 'Class 1 Predicted', 'Class 2 Predicted']\n",
        "row = ['Class 0 Actual', 'Class 1 Actual', 'Class 2 Actual']\n",
        "\n",
        "fig = plt.figure()\n",
        "fig.suptitle('Confusion Matrix')\n",
        "\n",
        "axs = plt.subplot()\n",
        "plt.table(cellText=conf_matrix,\n",
        "                      rowLabels=row,\n",
        "                      colLabels=col,\n",
        "                      loc='best')\n",
        "axs.axis('off')\n",
        "plt.show()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Best Model:\n",
            "\t For Class 0, k = 2\n",
            "\t For Class 1, k = 2\n",
            "\t For Class 2, k = 2\n",
            "Prediction Error: 0.300000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ky8uTJGVkZCgnJ0cdO3bUCy+8oPz8fO3cuVOpqamVOofKCNXcVaU2bdro3Xff1aZNmyRJ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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ynoko7LDTBPo",
        "colab_type": "text"
      },
      "source": [
        "## B: K-Nearest Neighbor\n",
        "Steps:\n",
        "* Implement k-nearest neighbor. \n",
        "* Run it with k=1,10,40. \n",
        "* Using test set, Report\n",
        "    - best k,\n",
        "    - prediction error for all k’s.\n",
        "    - confusion matrix for all k’s."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9fh-2niJTE_J",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def KNN(xx_train, train_labels, xx_test, k):\n",
        "  labels = []\n",
        "  for x in xx_test:\n",
        "    l = [(np.linalg.norm(x - xx_train[i]), train_labels[i]) for i in range(len(xx_train))]\n",
        "    l.sort(key=lambda x: x[0])\n",
        "    votes = [0, 0, 0]\n",
        "    for tuple in l[:k]:\n",
        "      votes[tuple[1]] += 1\n",
        "    most_voted = votes.index(max(votes))\n",
        "    labels.append(most_voted)\n",
        "  return labels\n",
        "\n",
        "knn_labels = [KNN(x_train, labels_train, x_test, 1)]\n",
        "knn_labels.append(KNN(x_train, labels_train, x_test, 10))\n",
        "knn_labels.append(KNN(x_train, labels_train, x_test, 40))\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TScOjEAJcZLZ",
        "colab_type": "code",
        "outputId": "8df706aa-d0cc-41d3-b8b0-01c85e1a4c70",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 379
        }
      },
      "source": [
        "err  = [0, 0, 0]\n",
        "conf_matrices = []\n",
        "for l in range(len(knn_labels)):\n",
        "  conf_matrix = np.array([[0,0,0], [0,0,0], [0,0,0]])\n",
        "  for i in range(len(labels_test)):\n",
        "    if knn_labels[l][i] != labels_test[i]:\n",
        "      err[l] += (1.0 / len(labels_test))\n",
        "    conf_matrix[labels_test[i]][knn_labels[l][i]] += 1\n",
        "  conf_matrices.append(conf_matrix)\n",
        "\n",
        "best_k = 0\n",
        "ind = err.index(min(err))\n",
        "if ind == 0:\n",
        "  best_k = '1'\n",
        "elif ind == 1:\n",
        "  best_k = '10'\n",
        "else:\n",
        "  best_k = '40'\n",
        "\n",
        "print('Best k: ' + best_k)\n",
        "print ('Prediction Errors:')\n",
        "print('\\tk = 1: ' + str(err[0]))\n",
        "print('\\tk = 10: ' + str(err[1]))\n",
        "print('\\tk = 40: ' + str(err[2]))\n",
        "\n",
        "cols = ['Class 0 Predicted', 'Class 1 Predicted', 'Class 2 Predicted']\n",
        "rows = ['Class 0 Actual', 'Class 1 Actual', 'Class 2 Actual']\n",
        "\n",
        "fig = plt.figure()\n",
        "fig.suptitle('Confusion Matrices')\n",
        "\n",
        "axs = plt.subplot(3,1,1)\n",
        "plt.table(cellText=conf_matrices[0],\n",
        "                      rowLabels=rows,\n",
        "                      colLabels=cols,\n",
        "                      loc='best')\n",
        "plt.title('k=1')\n",
        "axs.axis('off')\n",
        "\n",
        "axs2 = plt.subplot(3,1, 2)\n",
        "plt.table(cellText=conf_matrices[1],\n",
        "                      rowLabels=rows,\n",
        "                      colLabels=cols,\n",
        "                      loc='best')\n",
        "plt.title('k=10')\n",
        "axs2.axis('off')\n",
        "\n",
        "axs3 = plt.subplot(3,1,3)\n",
        "plt.table(cellText=conf_matrices[2],\n",
        "                      rowLabels=rows,\n",
        "                      colLabels=cols,\n",
        "                      loc='best')\n",
        "plt.title('k=40')\n",
        "axs3.axis('off')\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Best k: 10\n",
            "Prediction Errors:\n",
            "\tk = 1: 0.33\n",
            "\tk = 10: 0.26\n",
            "\tk = 40: 0.27\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NtWvXcvvtt5eYr7VAVVl++9vf0qNHjxLPDVQ1k7u7O+7u7ra9iUGDBtldIlHd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\nxAFIRESKxAFIRESKxAFIRESK9D8x8cMlObfY4gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}