On EM Estimation for Mixture of Multivariate t-Distributions

This paper formulates a novel expectation maximization (EM) algorithm for the mixture of multivariate t -distributions. By introducing a new kind of “missing” data, we show that the empirically improved iterative algorithm, in literature, for the mixture of multivariate t -distributions is in fact a type of EM algorithm; thus a theoretical analysis is established, which guarantees the empirical algorithm converges to the maximization likelihood estimates of the mixture parameters. Simulated experiment and real experiments on classification and image segmentation confirm the effectiveness of the improved EM algorithm.