The EM Algorithm for Generalized Exponential Mixture Model

Gaussian mixture is an important distribution to describe mixture data, in which each part mixed must be assumed to be normal. But the normal distribution may not be able to model the data adequately for some cases, so that Gaussian mixture is invalid. The generalized exponential distribution is a flexible density model, which can describe uniform, Gaussian, Laplacian and other sub- and super-Gaussian unimodal densities. In this paper, the generalized exponential mixture model is studied, in which Gaussian mixture and Laplacian mixture are two special cases. Different distributions can also be mixed, such as mixing a Laplacian with a Gaussian. In 1-dimension real space, the EM algorithm is developed to address the solution to the mixture model. The EM algorithm can be conditionally popularized to n-dimension real space. Numerical simulations and image segmentation experiment demonstrate feasibility and effectiveness of the proposed approach.