k-means Clustering Algorithm with MATLAB Implementation

In the following text, we will explore how to implement the k-means clustering algorithm using MATLAB. Clustering is a data analysis technique that groups similar data objects into larger collections where objects share common characteristics. This technique finds applications in various fields such as market segmentation, medical diagnosis, and astronomy. The k-means clustering algorithm is a simple yet effective method designed to partition n observations into k clusters, where each observation belongs to the cluster with the nearest mean (cluster center). The algorithm implementation typically involves initializing cluster centroids, assigning points to nearest centroids using Euclidean distance calculation, and iteratively updating centroid positions until convergence. We will examine the algorithm's core principles and provide a detailed MATLAB implementation using built-in functions like kmeans() or custom code demonstrating centroid initialization and assignment steps. The MATLAB implementation includes parameter specification for cluster numbers, distance metric selection, and replication settings to avoid local minima. Additionally, we will discuss methods for determining the optimal number of clusters using evaluation metrics like the silhouette coefficient or elbow method, and techniques for assessing algorithm performance through within-cluster sum of squares and convergence criteria. This comprehensive approach will help you better understand cluster analysis and its practical applications in data mining and pattern recognition.