Simplification and hierarchical representations of mixtures of exponential families

A mixture model in statistics is a powerful framework commonly used to estimate the probability measure function of a random variable. Most algorithms handling mixture models were originally specifically designed for processing mixtures of Gaussians. However, other distributions such as Poisson, multinomial, Gamma/Beta have gained interest in signal processing in the past decades. These common distributions are unified in the framework of exponential families in statistics. In this paper, we present three generic clustering algorithms working on arbitrary mixtures of exponential families: the Bregman soft clustering, the Bregman hard clustering, and the Bregman hierarchical clustering. These algorithms allow one to estimate a mixture model from observations, to simplify such a mixture model, and to automatically learn the “optimal” number of components in a simplified mixture model according to a resolution parameter. In addition, we present jMEF, an open source JavaTM library allowing users to create, process and manage mixtures of exponential families. In particular, jMEF includes the three aforementioned Bregman clustering algorithms.