  Recent progress in center-based clustering algorithms combats poor local
minima by implicit annealing, using a family of generalized means. These
methods are variations of Lloyd's celebrated $k$-means algorithm, and are most
appropriate for spherical clusters such as those arising from Gaussian data. In
this paper, we bridge these algorithmic advances to classical work on hard
clustering under Bregman divergences, which enjoy a bijection to exponential
family distributions and are thus well-suited for clustering objects arising
from a breadth of data generating mechanisms. The elegant properties of Bregman
divergences allow us to maintain closed form updates in a simple and
transparent algorithm, and moreover lead to new theoretical arguments for
establishing finite sample bounds that relax the bounded support assumption
made in the existing state of the art. Additionally, we consider thorough
empirical analyses on simulated experiments and a case study on rainfall data,
finding that the proposed method outperforms existing peer methods in a variety
of non-Gaussian data settings.
