Fast learning by the α-ECME algorithm

Abstract

The /spl alpha/-EM (expectation maximization) algorithm is a super-class of the traditional log-EM algorithm. The case of /spl alpha/=-1 corresponds to the. log-EM algorithm. For the stable region of /spl alpha/>-1, the /spl alpha/-EM algorithm outperforms the traditional method in terms of the learning speed measured by iterations and CPU time. Both the /spl alpha/-EM algorithm and the log-EM algorithm try to maximize the conditional expectation on the tentative complete data. On the other hand, there is an extension of the traditional EM algorithm which includes direct maximization on the incomplete-data likelihood-which is the true performance measure. This is the ECME (expectation and conditional maximization or either) algorithm. Thus, this paper describes the /spl alpha/-version of the ECME first. Then, a speed evaluation is made on this /spl alpha/-ECME algorithm using the extended Fisher information matrix. Examples of unsupervised and supervised learning are given. The /spl alpha/-ECME algorithm is more meritorious than the plain /spl alpha/-EM or /spl alpha/-ECM (expectation and conditional maximization) algorithms in terms of the iteration count. If the CPU time is of ultimate importance, the plain /spl alpha/-EM algorithm and the /spl alpha/-ECME algorithm are comparable.