Hierarchical Gaussian mixture model

Gaussian mixture models (GMMs) are a convenient and essential tool for the estimation of probability density functions. Although GMMs are used in many research domains from image processing to machine learning, this statistical mixture modeling is usually complex and further need to be simplified. In this paper, we present a GMM simplification method based on a hierarchical clustering algorithm. Our method allows one to first to quickly compute a compact version of the initial GMM, and second to automatically learn the optimal number of components of the simplified GMM. Using the framework of Bregman divergences, this simplification algorithm, although presented here for GMMs, is suitable for any mixture of exponential families. Index Terms — Gaussian mixture model, mixture model simplification, hierarchical clustering, Bregman divergence, exponential family 1.