Learning GMM Using Elliptically Contoured Distributions

Model order selection and parameter estimation for Gaussian mixture model (GMM) are important issues for clustering analysis and density estimation. Most methods for model selection usually add a penalty term in the objective function that can penalize the models and choose an optimal one from a set of candidate models. This paper presents a simple and novel approach to determine the number of components and simultaneously estimate the parameters for GMM. By introducing the degenerating model, the proposed approach overcomes the drawback of likelihood estimate that is a non-decreasing function and can not be used to select the number of components. The degenerating model is a more general form of mixture component density and it can degenerate into the component density or a crater-like density when its parameter K varies from 1 to a bigger value. The likelihood of the crater-like density evaluated for the training data approximates to zero. This characteristic of the degenerating model forms the foundation of the proposed approach. The experimental results show robust and evident performance improvement of the approach.