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

Yasuo Matsuyama

    Research output: Contribution to journalArticle

    37 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)692-706
    Number of pages15
    JournalIEEE Transactions on Information Theory
    Volume49
    Issue number3
    DOIs
    Publication statusPublished - 2003 Mar

    Keywords

    • α-EM algorithm
    • α-logarithm
    • Convergence speed
    • Convex divergence
    • Exponential family
    • Independent component analysis
    • Minorization-maximization
    • Supervised and unsupervised learning
    • Surrogate function
    • Vector quantization

    ASJC Scopus subject areas

    • Information Systems
    • Electrical and Electronic Engineering

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