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

Abstract

A new likelihood maximization algorithm called the /spl alpha/-EM algorithm (/spl alpha/-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 /spl alpha/. The log-EM algorithm is a special case corresponding to /spl alpha/=-1. The main idea behind the /spl alpha/-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 /spl alpha/-logarithm which is related to the convex divergence. The convergence speed of the /spl alpha/-EM algorithm is theoretically analyzed through /spl alpha/-dependent update matrices and illustrated by numerical simulations. Finally, general guidelines for using the /spl alpha/-logarithmic methods are given. The choice of alternative surrogate functions is also discussed.