Distribution based classification using Gaussian Mixture Models

A central task in classification is a measure of similarity between a dataset and a class that is characterised by a probability density function. The Bhattacharyya distance and the Kullback-Liebler divergence measure have been successful in comparing two multivariate normal density functions but their use is impracticable when the data is modelled using complex distributions such as Gaussian Mixture Models. The similarity is computed by combining the Bhattacharyya distances between corresponding mixtures in the reference and the test data model. In this paper we compare the performance of the Likelihood Ratio Test to a novel technique that defines a similarity measure between data and reference models having Gaussian Mixture probability density functions. When fitting a Gaussian Mixture Model to the test dataset our procedure ensures a one to one correspondence between the mixtures of the dataset and those of the reference model. This procedure has been tested using experiments, with both synthetic data and a Speaker Verification evaluation database. The performance was assessed using Detection Error Trade-off curves and demonstrates that the new measure performs significantly better than Likelihood Ratio Test.