hw2/src/P4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import datasets\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "sns.reset_defaults()\n",
    "sns.set_theme(rc={'figure.dpi': 72, 'savefig.dpi': 300,\n",
    "              'figure.autolayout': True})\n",
    "sns.set_style('ticks')\n",
    "sns.set_context('paper')\n",
    "\n",
    "ds = datasets.load_digits()\n",
    "X = ds.data\n",
    "y = ds.target\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 216x216 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Part a\n",
    "si = np.random.permutation(X.shape[0])\n",
    "X = X[si]\n",
    "y = y[si]\n",
    "X_sample = X[:16]\n",
    "y_sample = y[:16]\n",
    "\n",
    "fig, axes = plt.subplots(4, 4, figsize=(3, 3))\n",
    "for xi, yi, ax in zip(X_sample, y_sample, axes.flatten()):\n",
    "    image = xi.reshape(8, 8)\n",
    "    ax.imshow(image, cmap=matplotlib.cm.binary)\n",
    "    ax.set_title(f\"Label={yi}\")\n",
    "    ax.axis('off')\n",
    "fig.savefig('P4_a.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Part b\n",
    "def euclidean_distance(u, v):\n",
    "    return np.sqrt(np.sum(np.square(u - v)))\n",
    "\n",
    "\n",
    "def cosine_distance(u, v):\n",
    "    u_norm = np.sum(np.square(u))\n",
    "    v_norm = np.sum(np.square(v))\n",
    "    sim = np.dot(u, v) / (u_norm * v_norm)\n",
    "    return 1 - sim\n",
    "\n",
    "\n",
    "def KNN(X_train, y_train, X_test, k=3, dist=euclidean_distance):\n",
    "    y_pred = np.zeros(X_test.shape[0], dtype=int)\n",
    "    neighbors = np.zeros((X_test.shape[0], k), dtype=int)\n",
    "    for i in range(X_test.shape[0]):\n",
    "        d = np.zeros(X_train.shape[0])\n",
    "        for j in range(X_train.shape[0]):\n",
    "            d[j] = dist(X_test[i], X_train[j])\n",
    "        neighbors[i] = np.argsort(d)[:k]\n",
    "        y_pred[i] = np.bincount(y_train[neighbors[i]]).argmax()\n",
    "    return y_pred, neighbors\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Part c\n",
    "def split_data(X, y, test_size):\n",
    "    tslen = int(test_size * len(y))\n",
    "    X_test = X[:tslen]\n",
    "    X_train = X[tslen:]\n",
    "    y_test = y[:tslen]\n",
    "    y_train = y[tslen:]\n",
    "    return X_train, X_test, y_train, y_test\n",
    "\n",
    "\n",
    "X_train, X_test, y_train, y_test = split_data(X, y, 0.2)\n",
    "K = list(range(1, 41))\n",
    "\n",
    "er_eu = []\n",
    "er_co = []\n",
    "for k in K:\n",
    "    y_pred_eu, _ = KNN(X_train, y_train, X_test, k, euclidean_distance)\n",
    "    y_pred_co, _ = KNN(X_train, y_train, X_test, k, cosine_distance)\n",
    "    er_eu.append(np.mean(y_pred_eu != y_test))\n",
    "    er_co.append(np.mean(y_pred_co != y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best k for Euclidean distance: 4\n",
      "Best k for Cosine distance: 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optk_eu = np.argmin(er_eu) + 1\n",
    "optk_co = np.argmin(er_co) + 1\n",
    "\n",
    "print('Best k for Euclidean distance:', optk_eu)\n",
    "print('Best k for Cosine distance:', optk_co)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "sns.lineplot(x=K, y=er_eu, marker='o', label='Euclidean Distance', ax=ax)\n",
    "sns.lineplot(x=K, y=er_co, marker='o', label='Cosine Distance', ax=ax)\n",
    "ax.set(\n",
    "    title='Error Rate vs. K Value (Elbow Technique)',\n",
    "    xlabel='K',\n",
    "    ylabel='Error Rate',\n",
    "    xticks=K,\n",
    ")\n",
    "fig.savefig('P4_c.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 144x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 288x72 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 648x72 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Part e\n",
    "ri = np.random.randint(0, X_test.shape[0] + 1)\n",
    "y_pred_eu, nei_eu = KNN(X_train, y_train, X_test[ri:ri+1], optk_eu, euclidean_distance)\n",
    "y_pred_co, nei_co = KNN(X_train, y_train, X_test[ri:ri+1], optk_co, cosine_distance)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(2, 1))\n",
    "image = X_test[ri].reshape(8, 8)\n",
    "ax.imshow(image, cmap=matplotlib.cm.binary)\n",
    "ax.set_title(f\"True Label={y_test[ri]}\")\n",
    "ax.axis('off')\n",
    "fig.suptitle('Random Test Image')\n",
    "fig.savefig('P4_e_1.png')\n",
    "plt.show()\n",
    "\n",
    "fig, axes = plt.subplots(1, optk_eu, figsize=(optk_eu, 1))\n",
    "for ni, ax in zip(nei_eu[0], axes.flatten()):\n",
    "    image = X_train[ni].reshape(8, 8)\n",
    "    ax.imshow(image, cmap=matplotlib.cm.binary)\n",
    "    ax.set_title(f\"Label={y_train[ni]}\")\n",
    "    ax.axis('off')\n",
    "fig.suptitle(f'Euclidean Neighbors (Predicted label={y_pred_eu[0]})')\n",
    "fig.savefig('P4_e_2.png')\n",
    "plt.show()\n",
    "\n",
    "fig, axes = plt.subplots(1, optk_co, figsize=(optk_co, 1))\n",
    "for ni, ax in zip(nei_co[0], axes.flatten()):\n",
    "    image = X_train[ni].reshape(8, 8)\n",
    "    ax.imshow(image, cmap=matplotlib.cm.binary)\n",
    "    ax.set_title(f\"Label={y_train[ni]}\")\n",
    "    ax.axis('off')\n",
    "fig.suptitle(f'Cosine Neighbors (Predicted label={y_pred_co[0]})')\n",
    "fig.savefig('P4_e_3.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix for Euclidean Distance:\n",
      "[[35  0  0  0  0  0  0  0  0  0]\n",
      " [ 0 37  0  0  0  0  0  0  0  0]\n",
      " [ 0  0 43  0  0  0  0  0  0  0]\n",
      " [ 0  0  0 37  0  0  0  0  0  0]\n",
      " [ 0  0  0  0 35  0  0  0  0  0]\n",
      " [ 0  0  0  0  0 29  0  0  0  1]\n",
      " [ 0  0  0  0  0  0 43  0  0  0]\n",
      " [ 0  0  0  0  0  0  0 31  0  0]\n",
      " [ 0  2  0  0  0  0  0  0 30  0]\n",
      " [ 0  0  0  0  0  1  0  0  2 33]] \n",
      "\n",
      "\n",
      "Confusion Matrix for Cosine Distance:\n",
      "[[35  0  0  0  0  0  0  0  0  0]\n",
      " [ 0 36  0  0  0  0  0  0  1  0]\n",
      " [ 0  0 43  0  0  0  0  0  0  0]\n",
      " [ 1  0  0 36  0  0  0  0  0  0]\n",
      " [ 0  0  0  0 34  0  0  1  0  0]\n",
      " [ 0  0  0  0  0 29  0  0  0  1]\n",
      " [ 1  0  0  0  0  0 42  0  0  0]\n",
      " [ 0  0  0  0  0  0  0 31  0  0]\n",
      " [ 1  1  0  5  0  0  0  0 24  1]\n",
      " [ 1  0  0  0  0  2  0  1  1 31]]\n"
     ]
    }
   ],
   "source": [
    "# Part f\n",
    "def confusion_matrix(y_true, y_pred, labels):\n",
    "    \"\"\"Confusion Matrix for Multi-Class Classification\"\"\"\n",
    "    m = np.zeros((len(labels), len(labels)), dtype=int)\n",
    "    for i in range(m.shape[0]):\n",
    "        for j in range(m.shape[1]):\n",
    "            m[i, j] = np.sum((y_true == labels[i]) & (y_pred == labels[j]))\n",
    "    return m\n",
    "\n",
    "\n",
    "y_pred_eu, _ = KNN(X_train, y_train, X_test, optk_eu, euclidean_distance)\n",
    "y_pred_co, _ = KNN(X_train, y_train, X_test, optk_co, cosine_distance)\n",
    "\n",
    "labels = np.sort(np.unique(y_test))\n",
    "cm_eu = confusion_matrix(y_test, y_pred_eu, labels)\n",
    "cm_co = confusion_matrix(y_test, y_pred_co, labels)\n",
    "\n",
    "print('Confusion Matrix for Euclidean Distance:')\n",
    "print(cm_eu, '\\n\\n')\n",
    "\n",
    "print('Confusion Matrix for Cosine Distance:')\n",
    "print(cm_co)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euclidean Distance Performance for target 8:\n",
      "TP: 30\n",
      "TN: 329\n",
      "FP: 2\n",
      "FN: 2\n",
      "F1-score: 0.9375\n",
      "Precision: 0.9375\n",
      "TPR (Recall, Sensitivity): 0.9375\n",
      "TNR (Specificity): 0.994\n",
      "\n",
      "Euclidean Distance Performance for target 3:\n",
      "TP: 37\n",
      "TN: 322\n",
      "FP: 0\n",
      "FN: 0\n",
      "F1-score: 1.0\n",
      "Precision: 1.0\n",
      "TPR (Recall, Sensitivity): 1.0\n",
      "TNR (Specificity): 1.0\n"
     ]
    }
   ],
   "source": [
    "# Part g\n",
    "def performance_results(cm, labels, target_label):\n",
    "    i = list(labels).index(target_label)\n",
    "    TP = cm[i, i]\n",
    "    FN = cm[i, :i].sum() + cm[i, i+1:].sum()\n",
    "    FP = cm[:i, i].sum() + cm[i+1:, i].sum()\n",
    "\n",
    "    cm_ = cm.copy()\n",
    "    cm_[i, i] = 0\n",
    "    TN = cm_.flatten().sum()\n",
    "\n",
    "    TPR = TP / (TP + FN)\n",
    "    TNR = TN / (TN + FP)\n",
    "    precision = TP / (TP + FP)\n",
    "    F1 = 2 * precision * TPR / (precision + TPR)\n",
    "\n",
    "    print('TP:', TP)\n",
    "    print('TN:', TN)\n",
    "    print('FP:', FP)\n",
    "    print('FN:', FN)\n",
    "    print('F1-score:', round(F1, 4))\n",
    "    print('Precision:', round(precision, 4))\n",
    "    print('TPR (Recall, Sensitivity):', round(TPR, 4))\n",
    "    print('TNR (Specificity):', round(TNR, 4))\n",
    "\n",
    "\n",
    "print(f'Euclidean Distance Performance for target 8:')\n",
    "performance_results(cm_eu, labels, 8)\n",
    "print()\n",
    "\n",
    "print(f'Euclidean Distance Performance for target 3:')\n",
    "performance_results(cm_eu, labels, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine Distance Performance for target 6:\n",
      "TP: 42\n",
      "TN: 317\n",
      "FP: 0\n",
      "FN: 1\n",
      "F1-score: 0.9882\n",
      "Precision: 1.0\n",
      "TPR (Recall, Sensitivity): 0.9767\n",
      "TNR (Specificity): 1.0\n",
      "\n",
      "Cosine Distance Performance for target 4:\n",
      "TP: 34\n",
      "TN: 325\n",
      "FP: 0\n",
      "FN: 1\n",
      "F1-score: 0.9855\n",
      "Precision: 1.0\n",
      "TPR (Recall, Sensitivity): 0.9714\n",
      "TNR (Specificity): 1.0\n"
     ]
    }
   ],
   "source": [
    "# Part h\n",
    "print(f'Cosine Distance Performance for target 6:')\n",
    "performance_results(cm_co, labels, 6)\n",
    "print()\n",
    "\n",
    "print(f'Cosine Distance Performance for target 4:')\n",
    "performance_results(cm_co, labels, 4)"
   ]
  }
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