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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.
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Citations
Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
Cited by
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Ding, C. H. Q., Li, T., & Jordan, M. I. (2010) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.277 · Cited by 1,317
Self-citationEEG signal classification using wavelet feature extraction and a mixture of expert model.
SUBASI, A. (2007) · Expert Systems with Applications · doi:10.1016/j.eswa.2006.02.005 · Cited by 1,182
Distributed optimization in sensor networks
Rabbat, M., & Nowak, R. (2004) · Proceedings of the 3rd international symposium on Information processing in sensor networks · doi:10.1145/984622.984626 · Cited by 901
The EM Algorithm—an Old Folk-song Sung to a Fast New Tune
Meng, X.-L., & Van Dyk, D. (1997) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00082 · Cited by 802
Cry-based infant pathology classification using GMMs
Farsaie Alaie, H., Abou-Abbas, L., & Tadj, C. (2016) · Speech Communication · doi:10.1016/j.specom.2015.12.001 · Cited by 58
Metadata
- Authors
- Xu, L., & Jordan, M. I.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1996-01
- Volume
- 8
- Issue
- 1
- Pages
- 129-151
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2134199473
- Cited by
- 756
- References
- 1
- FWCI
- 12.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Xu, L., & Jordan, M. I. (1996). On Convergence Properties of the EM Algorithm for Gaussian Mixtures. Neural Computation. https://doi.org/10.1162/neco.1996.8.1.129
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
