Clustering with Bregman Divergences

A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms unify centroid-based parametric clustering approaches, such as classical kmeans and information-theoretic clustering, which arise by special choices of the Bregman divergence. The algorithms maintain the simplicity and scalability of the classical kmeans algorithm, while generalizing the basic idea to a very large class of clustering loss functions. There are two main contributions in this…