On Convergence Properties of the EM Algorithm for Gaussian Mixtures
- 1 January 1996
- journal article
- Published by MIT Press in Neural Computation
- Vol. 8 (1) , 129-151
- https://doi.org/10.1162/neco.1996.8.1.129
Abstract
We build up the mathematical connection between the “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.Keywords
This publication has 4 references indexed in Scilit:
- Hierarchical Mixtures of Experts and the EM AlgorithmNeural Computation, 1994
- Statistical Physics, Mixtures of Distributions, and the EM AlgorithmNeural Computation, 1994
- On the Convergence Properties of the EM AlgorithmThe Annals of Statistics, 1983
- Growth transformations for functions on manifoldsPacific Journal of Mathematics, 1968