Centroid-Based Clustering with αβ-Divergences

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 [Formula: see text]-divergences, which is governed by two parameters, [Formula: see text] and [Formula: see text]. We propose a new iterative algorithm, [Formula: see text]-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 ([Formula: see text]). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ([Formula: see text]) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.