Closed-form cauchy-schwarz PDF divergence for mixture of Gaussians

Abstract

This paper presents an efficient approach to calculate the difference between two probability density functions (pdfs), each of which is a mixture of Gaussians (MoG). Unlike Kullback-Leibler divergence (DKL), the authors propose that the Cauchy-Schwarz (CS) pdf divergence measure (DCS) can give an analytic, closed-form expression for MoG. This property of the DCS makes fast and efficient calculations possible, which is tremendously desired in real-world applications where the dimensionality of the data/features is very high. We show that DCS follows similar trends to DKL, but can be computed much faster, especially when the dimensionality is high. Moreover, the proposed method is shown to significantly outperform DKL in classifying real-world 2D and 3D objects, and static hand posture recognition based on distances alone.