Gauss mixtures have gained popularity in statistics and statistical signal processing applications for a variety of reasons, including their ability to well approximate a 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.
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