Dimension reduction for mixtures of exponential families

Abstract

Dimension reduction for a set of distribution parameters has been important in various applications of datamining. The exponential family PCA has been proposed for that purpose, but it cannot be directly applied to mixture models that do not belong to an exponential family. This paper proposes a method to apply the exponential family PCA to mixture models. A key idea is to embed mixtures into a space of an exponential family. The problem is that the embedding is not unique, and the dimensionality of parameter space is not constant when the numbers of mixture components are different. The proposed method finds a sub-optimal solution by linear programming formulation. © Springer-Verlag Berlin Heidelberg 2008.