Approximation Algorithms for 2-Means Clustering

Clustering is a global approach to information classification, with applications in data mining, pattern recognition, image processing, bioinformatics, city planning, and more. Clustering is the partition of data into meaningful groups. Since the concept of “meaningful groups” varies widely among applications, there is a wide variety of clustering techniques. Broadly, these techniques can be categorized as linkage-based clustering, spectral clustering, and clustering with respect to an objective function. In this report, we focus on a specific instance of the latter category. K-means clustering is probably the most commonly used clustering technique that aims to minimize an objective function. Its popularity is probably due to its simplicity and flexibility. The optimal k-means clustering does not place bounds on the number of points in a cluster, does not restrict the radii of clusters, and allows points in a cluster to center around a point that is not part of the input. Additionally, the Lloyd algorithm is a simple and fast heuristic for solving k-means, although it does not have any performance guarantees.