MATLAB Implementation of the K-Medoids Clustering Algorithm

In this article, we introduce a clustering algorithm: the K-Medoids method. Unlike traditional centroid-based approaches, this algorithm selects actual data points called medoids to represent clusters. Here are the detailed algorithmic steps with implementation insights: For initial implementation, you can randomly select K data points as initial medoids (O1, O2, …, Oi, …, Ok) using MATLAB's randperm or datasample functions. The algorithm then enters an iterative loop: First, assign remaining objects to their closest medoid based on distance metrics (typically Euclidean distance using pdist2 function in MATLAB). Each object joins the cluster whose medoid minimizes the distance. For each cluster (Oi), sequentially evaluate potential replacements (Or) from within the cluster. Calculate the cost function E(Or) representing the total distance sum when replacing Oi with Or. In MATLAB implementation, this involves computing sum(min(pdist2(data, [medoids(1:i-1), Or, medoids(i+1:end)], 'euclidean'))). Select the replacement Or that minimizes E(Or) and update the medoid. This modifies all K medoids, and the process returns to the assignment step. The loop continues until medoids stabilize (convergence criteria met), typically when no medoid changes occur or cost reduction falls below a threshold. This algorithm demonstrates robustness to noisy data and outliers since medoids are actual data points. However, computational complexity is higher than K-Means, making it suitable primarily for small to medium datasets. Our provided MATLAB source code includes efficient distance matrix computation and convergence checking mechanisms. Practical implementation can be optimized through parameter adjustments: improving initial medoid selection via K-Means++ initialization, customizing distance metrics, or modifying the cost function. The article provides working MATLAB code with comments explaining key functions like medoid swapping and cluster reassignment. We hope this implementation guide assists in your clustering projects!