Fast clustering of Gaussians and the virtue of representing Gaussians in exponential model format

Abstract

This paper aims to show the power and versatility of exponential models by focusing on exponential model representations of Gaussian Mixture Models (GMMs). In a recent series of papers by several authors, GMMs of varying structure and complexity have been considered. These GMMs can all be readily represented as exponential models and oftentimes favorably so. This paper shows how the exponential model representation can offer useful insight even in the case of diagonal and full co-variance GMMs! The power of the exponential model is illustrated by proving the concavity of the log det function and also by discovering how to speed up diagonal covariance Gaussian clustering.