A comparison of distance metrics between mixture distributions

Many applications require measuring the distance between mixture distributions. For example in the content-based image retrieval (CBIR) systems and audio speech identification a distance measure between mixture models are often required. This is also an important element for multisensor tracking and fusion where different types of state representations employed by distributed agents need to be correlated. Various distance metrics have been developed to serve this purpose. The performance of these metrics can be evaluated by comparing probabilities of correct correlation verses false detection as a function of a pre-determined threshold on the calculated distance. In this paper, we compare several distance metrics for mixtures distributions. Specifically, we focus on three such distance measures, namely the Integral Square Error distance, the Bhattacharyya distance and the Kullback Leibler distance. To ensure that these techniques can be applied for general distributions, not just for Gaussian mixture model (GMM), we use these techniques in conjunction with a specific distance metric designed for mixture type, called general mixture distance (GMD). For evaluation purpose, we use GMM in the simulation as a test example of mixture models.