Centroid-Based Clustering with ab-Divergences

Abstract

Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of ab-divergences, which is governed by two parameters, a and b. We propose a new iterative algorithm, ab-k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair (a, b). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the (a, b) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.