{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "47bd0cfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Q4A: K-Means clustering on Iris.csv; choose k with the elbow method.\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "82b6cace",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset shape: (150, 6)\n",
      "Features: ['SepalLengthCm', 'SepalWidthCm', 'PetalLengthCm', 'PetalWidthCm']\n"
     ]
    },
    {
     "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>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\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>2</td>\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>3</td>\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</td>\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</td>\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": [
       "   Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm      Species\n",
       "0   1            5.1           3.5            1.4           0.2  Iris-setosa\n",
       "1   2            4.9           3.0            1.4           0.2  Iris-setosa\n",
       "2   3            4.7           3.2            1.3           0.2  Iris-setosa\n",
       "3   4            4.6           3.1            1.5           0.2  Iris-setosa\n",
       "4   5            5.0           3.6            1.4           0.2  Iris-setosa"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the locally saved Iris dataset. Species is kept only for interpretation.\n",
    "iris = pd.read_csv(\"Iris.csv\")\n",
    "X = iris.drop(columns=[\"Id\", \"Species\"])\n",
    "X_scaled = StandardScaler().fit_transform(X)\n",
    "print(\"Dataset shape:\", iris.shape)\n",
    "print(\"Features:\", X.columns.tolist())\n",
    "iris.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "817a76a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " k    inertia\n",
      " 1 600.000000\n",
      " 2 223.732006\n",
      " 3 140.965817\n",
      " 4 114.617886\n",
      " 5  91.295445\n",
      " 6  81.756582\n",
      " 7  71.319821\n",
      " 8  62.651767\n",
      " 9  55.261841\n",
      "10  50.623169\n"
     ]
    }
   ],
   "source": [
    "# Fit K-Means for several k values and record within-cluster inertia.\n",
    "k_values = np.arange(1, 11)\n",
    "inertias = []\n",
    "for k in k_values:\n",
    "    model = KMeans(n_clusters=int(k), n_init=10, random_state=42)\n",
    "    model.fit(X_scaled)\n",
    "    inertias.append(model.inertia_)\n",
    "print(pd.DataFrame({\"k\": k_values, \"inertia\": inertias}).to_string(index=False))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6faa936e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected number of clusters: 3\n"
     ]
    }
   ],
   "source": [
    "# The elbow is the point farthest from the line joining the endpoints.\n",
    "# Inspect the plot too: this geometric rule is a guide, not a guarantee.\n",
    "scaled_inertia = (np.array(inertias) - min(inertias)) / (max(inertias) - min(inertias))\n",
    "scaled_k = (k_values - k_values[0]) / (k_values[-1] - k_values[0])\n",
    "distance_to_line = np.abs(scaled_inertia + scaled_k - 1) / np.sqrt(2)\n",
    "best_k = int(k_values[np.argmax(distance_to_line)])\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.plot(k_values, inertias, marker=\"o\")\n",
    "plt.axvline(best_k, color=\"crimson\", linestyle=\"--\", label=f\"Elbow: k={best_k}\")\n",
    "plt.xlabel(\"Number of clusters (k)\")\n",
    "plt.ylabel(\"Inertia\")\n",
    "plt.title(\"K-Means elbow method on Iris\")\n",
    "plt.legend()\n",
    "plt.grid(alpha=0.3)\n",
    "plt.show()\n",
    "print(\"Selected number of clusters:\", best_k)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8e5e0d7a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster sizes: {0: 53, 1: 50, 2: 47}\n",
      "Cluster           0   1   2\n",
      "Species                    \n",
      "Iris-setosa       0  50   0\n",
      "Iris-versicolor  39   0  11\n",
      "Iris-virginica   14   0  36\n"
     ]
    }
   ],
   "source": [
    "# Cluster using the selected k and inspect the result.\n",
    "final_model = KMeans(n_clusters=best_k, n_init=10, random_state=42)\n",
    "cluster_labels = final_model.fit_predict(X_scaled)\n",
    "print(\"Cluster sizes:\", pd.Series(cluster_labels).value_counts().sort_index().to_dict())\n",
    "print(pd.crosstab(iris[\"Species\"], cluster_labels, rownames=[\"Species\"], colnames=[\"Cluster\"]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7209f579",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PCA is used only for a two-dimensional visualization of the clusters.\n",
    "points_2d = PCA(n_components=2).fit_transform(X_scaled)\n",
    "plt.figure(figsize=(7, 5))\n",
    "plt.scatter(points_2d[:, 0], points_2d[:, 1], c=cluster_labels, cmap=\"viridis\", s=35)\n",
    "plt.xlabel(\"Principal component 1\")\n",
    "plt.ylabel(\"Principal component 2\")\n",
    "plt.title(f\"Iris K-Means clusters (k={best_k})\")\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
