k-Means Clustering with Hölder Divergences

Abstract

We introduced two novel classes of Hölder divergences and Hölder pseudo-divergences that are both invariant to rescaling, and that both encapsulate the Cauchy-Schwarz divergence and the skew Bhattacharyya divergences. We review the elementary concepts of those parametric divergences, and perform a clustering analysis on two synthetic datasets. It is shown experimentally that the symmetrized Hölder divergences consistently outperform significantly the Cauchy-Schwarz divergence in clustering tasks.