Renyi entropy penalized learning algorithm for Gaussian mixture with automated model selection

Gaussian mixture is a powerful statistical tool for data modeling and analysis. However, its model selection, i.e., the selection of number of Gaussians in the mixture for a sample dataset, is still a difficult task. Recently, a Shannon entropy penalized learning algorithm was established for Gaussian mixture modeling with a good feature that model selection can be made automatically during the parameter learning. In this paper, a Renyi entropy penalized learning algorithm is further proposed for Gaussian mixture modeling with automated model selection. It is demonstrated by the simulation experiments that the Renyi entropy penalized learning algorithm converges much faster than the Shannon entropy penalized learning algorithm. Moreover, the Renyi entropy penalized learning algorithm is successfully applied to classification of the Iris data and unsupervised image segmentation.