A Lie group based Gaussian Mixture Model distance measure for multimedia comparison

In this paper, we propose a novel method to measure the distance between two Gaussian Mixture Models. The proposed distance measure is based on the minimum cost that must paid to transform from one Gaussian Mixture Model into the other. We parameterize the components of a Gaussian Mixture Model which are Gaussian probability density functions (pdf) as positive definite lower triangular transformation matrices. Then we identify that Gaussian pdfs form a Lie group. Based on Lie group theory, the geodesic length can be used to measure the minimum cost that must paid to transform from one Gaussian pdf into the other. Combining geodesic length with the earth mover\u27s distance, we propose the Lie group earth mover\u27s distance for Gaussian Mixture Models. We test our distance measure in image retrieval. The experimental results indicate that our distance measure is more effective than other measures including the Kullback-Liebler divergence. Copyright 2009 ACM