A Theoretical and Experimental Comparison of the EM and SEM Algorithm

Johannes Blömer, Kathrin Bujna, Daniel Kuntze

Published 2013-10-18, updated 2014-07-02Version 2

In this paper we provide a new analysis of the SEM algorithm. Unlike previous work, we focus on the analysis of a single run of the algorithm. First, we discuss the algorithm for general mixture distributions. Second, we consider Gaussian mixture models and show that with high probability the update equations of the EM algorithm and its stochastic variant are almost the same, given that the input set is sufficiently large. Our experiments confirm that this still holds for a large number of successive update steps. In particular, for Gaussian mixture models, we show that the stochastic variant runs nearly twice as fast.