Gauss mixtures have gained popularity in statistics and statistical signal processing applications for a variety of reasons, including their ability to well approximatea large class of interesting densities and the availability of algorithms such as EM for constructing the models based on observed data. We here consider a different motivation and framework based on the information theoretic view of Gaussian sources as a "worst case" for compression developed by Sakrison and Lapidoth. This provides an approach for clustering Gauss mixture models using a minimum discrimination distortion measure and provides the intuitive support that good modeling is equivalent to good compression.
Robert M. Gray, John C. Young, Anuradha K. Aiyer