On Convergence Properties of the EM Algorithm for Gaussian Mixtures.

Abstract

Expectation-Maximization(EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Jan 17, 1995
Accession Number
ADA295637

Entities

People

  • Lei Xu
  • Michael I. Jordan

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Artificial Intelligence Software
  • Cognitive Science
  • Computational Science
  • Convergence
  • Hidden Markov Models
  • Information Processing
  • Information Science
  • Information Systems
  • Learning
  • Markov Models
  • Models
  • Neural Networks
  • Probabilistic Models
  • Probability
  • Signal Processing

Fields of Study

  • Computer science

Readers

  • Operations Research
  • Statistical inference.

Technology Areas

  • Space