Research on correct convergence of the EM algorithm for Gaussian mixtures

In this paper, we present a theoretical analysis on the correct convergence of expectation-maximization algorithm for Gaussian mixtures. We first introduce the expectation-maximization algorithm and its general convergence properties. We also give a variation of the expectation-maximization algorithm for Gaussian mixtures. We then prove that the expectation-maximization algorithm becomes a compact mapping in certain neighborhood of a consistent solution when a measure of the average overlap of Gaussian in the mixtures is small enough while the sample size is large enough. We further obtain and prove the condition of the correct convergence of it. And finally, we demonstrate the theoretical results by the simulation.