{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "

K-Means Clustering

\n", "

\n", "Nazar Khan\n", "
CVML Lab\n", "
University of The Punjab\n", "

" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "K-Means clustering is an unsupervised learning technique used to group data points into K clusters based on feature similarity. Here’s a simple PyTorch-based tutorial for implementing K-Means clustering.\n", "\n", "The K-Means algorithm:\n", "1. Randomly initializes K cluster centroids.\n", "2. Assigns each data point to the nearest centroid.\n", "3. Updates centroids as the mean of assigned points.\n", "4. Repeats steps 2–3 until convergence." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Converged after 1 iterations.\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.datasets import make_blobs\n", "\n", "# Generate 2D Data\n", "n_samples = 300\n", "n_features = 2\n", "n_clusters = 3\n", "data, labels = make_blobs(n_samples=n_samples, centers=n_clusters, n_features=n_features, random_state=42)\n", "data = torch.tensor(data, dtype=torch.float)\n", "\n", "# Plot the data\n", "plt.scatter(data[:, 0], data[:, 1], c='gray', s=10)\n", "plt.title(\"Input Data\")\n", "plt.show()\n", "\n", "# Initialize centroids randomly\n", "def initialize_centroids(data, k):\n", " indices = torch.randperm(data.size(0))[:k]\n", " return data[indices]\n", "\n", "# Assign each point to the nearest centroid\n", "def assign_clusters(data, centroids):\n", " distances = torch.cdist(data, centroids) # Compute pairwise distances\n", " return torch.argmin(distances, dim=1)\n", "\n", "# Update centroids as the mean of assigned points\n", "def update_centroids(data, clusters, k):\n", " new_centroids = []\n", " for i in range(k):\n", " cluster_points = data[clusters == i]\n", " if len(cluster_points) == 0:\n", " # Handle empty clusters by reinitializing the centroid\n", " new_centroid = data[torch.randint(0, data.size(0), (1,))]\n", " else:\n", " new_centroid = cluster_points.mean(dim=0)\n", " new_centroids.append(new_centroid)\n", " return torch.stack(new_centroids)\n", "\n", "# K-Means Algorithm\n", "def kmeans(data, k, max_iters=100, tol=1e-4):\n", " centroids = initialize_centroids(data, k)\n", " prev_centroids = centroids.clone()\n", " \n", " for iteration in range(max_iters):\n", " clusters = assign_clusters(data, centroids)\n", " centroids = update_centroids(data, clusters, k)\n", " \n", " # Convergence check\n", " if torch.all(torch.abs(centroids - prev_centroids) < tol):\n", " print(f\"Converged after {iteration} iterations.\")\n", " break\n", " prev_centroids = centroids.clone()\n", " \n", " return centroids, clusters\n", "\n", "# Run K-Means\n", "k = 3\n", "centroids, clusters = kmeans(data, k)\n", "\n", "# Visualize the results\n", "plt.scatter(data[:, 0], data[:, 1], c=clusters.numpy(), s=10, cmap='viridis')\n", "plt.scatter(centroids[:, 0], centroids[:, 1], c='red', marker='X', s=100, label='Centroids')\n", "plt.title(\"K-Means Clustering Results\")\n", "plt.legend()\n", "plt.show()\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Automatic Estimation of K" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "To estimate the number of clusters (\\(K\\)) automatically, you can use techniques like the **Elbow Method** or **Silhouette Score**. Here’s how these methods can be implemented:\n", "\n", "---\n", "\n", "#### Approach 1: Elbow Method\n", "\n", "The Elbow Method evaluates the clustering performance for different values of \\(K\\) by calculating the **inertia** (sum of squared distances between points and their centroids). The optimal \\(K\\) is at the \"elbow\" of the curve, where increasing \\(K\\) no longer significantly reduces the inertia.\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def calculate_inertia(data, centroids, clusters):\n", " inertia = 0\n", " for i, centroid in enumerate(centroids):\n", " cluster_points = data[clusters == i]\n", " inertia += ((cluster_points - centroid) ** 2).sum().item()\n", " return inertia\n", "\n", "def find_optimal_k(data, max_k=10):\n", " inertias = []\n", " for k in range(1, max_k + 1):\n", " centroids, clusters = kmeans(data, k)\n", " inertia = calculate_inertia(data, centroids, clusters)\n", " inertias.append(inertia)\n", " \n", " # Plot the inertia values to visualize the \"elbow\"\n", " plt.plot(range(1, max_k + 1), inertias, marker='o')\n", " plt.title(\"Elbow Method for Optimal K\")\n", " plt.xlabel(\"Number of Clusters (K)\")\n", " plt.ylabel(\"Inertia\")\n", " plt.show()\n", "\n", " # Calculate the second derivative (rate of change of the slope)\n", " first_derivative = torch.tensor(inertias[:-1]) - torch.tensor(inertias[1:])\n", " second_derivative = first_derivative[:-1] - first_derivative[1:]\n", "\n", " # Find the index of the maximum second derivative\n", " optimal_k = torch.argmax(second_derivative).item() + 2 # +2 because of indexing offset\n", " return optimal_k, inertias" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Approach 2: Silhouette Score\n", "\n", "The Silhouette Score measures how similar a point is to its cluster compared to other clusters. The score ranges from -1 to 1, where 1 indicates well-separated clusters.\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def silhouette_score(data, clusters):\n", " from sklearn.metrics import silhouette_score\n", " return silhouette_score(data.numpy(), clusters.numpy())\n", "\n", "def find_optimal_k_silhouette(data, max_k=10):\n", " scores = []\n", " for k in range(2, max_k + 1): # Silhouette score is undefined for k=1\n", " centroids, clusters = kmeans(data, k)\n", " score = silhouette_score(data, clusters)\n", " scores.append(score)\n", " \n", " # Plot the silhouette scores\n", " plt.plot(range(2, max_k + 1), scores, marker='o')\n", " plt.title(\"Silhouette Method for Optimal K\")\n", " plt.xlabel(\"Number of Clusters (K)\")\n", " plt.ylabel(\"Silhouette Score\")\n", " plt.show()\n", " \n", " optimal_k = 2 + scores.index(max(scores)) # Add 2 since the range starts at 2\n", " return optimal_k" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "---\n", "\n", "### Full Code with Automatic \\(K\\) Estimation\n", "\n", "Here’s how the methods integrate with the existing K-Means implementation:\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged after 1 iterations.\n", "Converged after 2 iterations.\n", "Converged after 2 iterations.\n", "Converged after 5 iterations.\n", "Converged after 9 iterations.\n", "Converged after 10 iterations.\n", "Converged after 5 iterations.\n", "Converged after 9 iterations.\n", "Converged after 13 iterations.\n", "Converged after 16 iterations.\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Converged after 3 iterations.\n", "Converged after 3 iterations.\n", "Converged after 7 iterations.\n", "Converged after 5 iterations.\n", "Converged after 7 iterations.\n", "Converged after 12 iterations.\n", "Converged after 8 iterations.\n", "Converged after 14 iterations.\n", "Converged after 7 iterations.\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Optimal K (Elbow): 3\n", "Optimal K (Silhouette): 3\n", "Converged after 2 iterations.\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Find optimal K using Elbow Method\n", "optimal_k_elbow, inertias = find_optimal_k(data, max_k=10)\n", "\n", "# Find optimal K using Silhouette Method\n", "optimal_k_silhouette = find_optimal_k_silhouette(data, max_k=10)\n", "\n", "print(f\"Optimal K (Elbow): {optimal_k_elbow}\")\n", "print(f\"Optimal K (Silhouette): {optimal_k_silhouette}\")\n", "\n", "# Run K-Means with the estimated K\n", "centroids, clusters = kmeans(data, optimal_k_silhouette)\n", "\n", "# Visualize the results\n", "plt.scatter(data[:, 0], data[:, 1], c=clusters.numpy(), s=10, cmap='viridis')\n", "plt.scatter(centroids[:, 0], centroids[:, 1], c='red', marker='X', s=100, label='Centroids')\n", "plt.title(\"K-Means Clustering Results\")\n", "plt.legend()\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "### Output:\n", "- **Elbow Plot**: A curve showing the inertia vs. \\(K\\). You can pick the \"elbow\" point manually or via 2nd-derivative.\n", "- **Silhouette Plot**: A curve showing the silhouette scores. The peak indicates the optimal \\(K\\).\n", "\n", "These methods provide a principled way to estimate \\(K\\) before running the K-Means algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "cvml", "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": "3.12.7" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }