On Convergence Properties of the EM Algorithm for Gaussian Mixtures
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.
Cite
Text
Xu and Jordan. "On Convergence Properties of the EM Algorithm for Gaussian Mixtures." Neural Computation, 1996. doi:10.1162/NECO.1996.8.1.129Markdown
[Xu and Jordan. "On Convergence Properties of the EM Algorithm for Gaussian Mixtures." Neural Computation, 1996.](https://mlanthology.org/neco/1996/xu1996neco-convergence/) doi:10.1162/NECO.1996.8.1.129BibTeX
@article{xu1996neco-convergence,
title = {{On Convergence Properties of the EM Algorithm for Gaussian Mixtures}},
author = {Xu, Lei and Jordan, Michael I.},
journal = {Neural Computation},
year = {1996},
pages = {129-151},
doi = {10.1162/NECO.1996.8.1.129},
volume = {8},
url = {https://mlanthology.org/neco/1996/xu1996neco-convergence/}
}