Experimenting with K-means Algorithm

The K-means algorithm is a classic unsupervised learning method primarily used for data clustering analysis. Its core principle involves iterative computation to partition datasets into K clusters, ensuring each data point belongs to the cluster with the nearest centroid.

Implementing K-means in MATLAB typically follows these key steps: 1. Initialize Centroids: Randomly select K data points as initial cluster centers using functions like `randperm` or `datasample` 2. Assign Data Points: Calculate distances between each point and all centroids using Euclidean distance (`pdist2`) and assign points to nearest clusters 3. Update Centroids: Recompute mean values for each cluster using `mean()` function to generate new centroids 4. Iterative Optimization: Repeat steps 2-3 until centroids stabilize (convergence) or maximum iterations are reached, implementing convergence checks using `while` loops or tolerance comparisons

MATLAB's built-in `kmeans` function provides direct clustering capabilities, eliminating manual iteration implementation. The function supports multiple distance metrics (e.g., 'sqeuclidean', 'cityblock') through its 'Distance' parameter, and allows optimization of centroid initialization via 'Replicates' and 'Start' parameters to improve convergence efficiency.

In practical applications, K-means performance is sensitive to initial centroid selection and may converge to local optima. Mitigation strategies include: - Multiple algorithm runs with different initializations using the 'Replicates' option - Implementing K-means++ initialization algorithm through the 'Start' parameter set to 'plus' - Combining with optimization techniques like silhouette analysis (`silhouette`) for cluster validation