The α-EM algorithm: Surrogate likelihood maximization using α-logarithmic information measures

A new likelihood maximization algorithm called the α-EM algorithm (α-Expectation-Maximization algorithm) is presented. This algorithm outperforms the traditional or logarithmic EM algorithm in terms of convergence speed for an appropriate range of the design parameter α. The log-EM algorithm is a special case corresponding to α = -1. The main idea behind the α-EM algorithm is to search for an effective surrogate function or a minorizer for the maximization of the observed data's likelihood ratio. The surrogate function adopted in this paper is based upon the α-logarithm which is related to the convex divergence. The convergence speed of the α-EM algorithm is theoretically analyzed through α-dependent update matrices and illustrated by numerical simulations. Finally, general guidelines for using the α-logarithmic methods are given. The choice of alternative surrogate functions is also discussed.