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Another interpretation of the EM algorithm for mixture distributions

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  • Hathaway, Richard J.

Abstract

The EM algorithm for mixture problems can be interpreted as a method of coordinate descent on a particular objective function. This view of the iteration partially illuminates the relationship of EM to certain clustering techniques and explains global convergence properties of the algorithm without direct reference to an incomplete data framework.

Suggested Citation

  • Hathaway, Richard J., 1986. "Another interpretation of the EM algorithm for mixture distributions," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 53-56, March.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:2:p:53-56
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    Cited by:

    1. Bhatia, Parmeet Singh & Iovleff, Serge & Govaert, Gérard, 2017. "blockcluster: An R Package for Model-Based Co-Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i09).
    2. Paul Koster & Hans Koster, 2013. "Commuters' Preferences for Fast and Reliable Travel," Tinbergen Institute Discussion Papers 13-075/VIII, Tinbergen Institute, revised 30 Apr 2015.
    3. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    4. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    5. Rawya Zreik & Pierre Latouche & Charles Bouveyron, 2017. "The dynamic random subgraph model for the clustering of evolving networks," Computational Statistics, Springer, vol. 32(2), pages 501-533, June.
    6. Hunt, Lynette A. & Basford, Kaye E., 2016. "Comparing classical criteria for selecting intra-class correlated features in Multimix," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 350-366.
    7. Christophe Biernacki & Matthieu Marbac & Vincent Vandewalle, 2021. "Gaussian-Based Visualization of Gaussian and Non-Gaussian-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 129-157, April.
    8. Gérard Govaert & Mohamed Nadif, 2018. "Mutual information, phi-squared and model-based co-clustering for contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 455-488, September.
    9. Hu, Tianming & Sung, Sam Yuan, 2006. "A hybrid EM approach to spatial clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1188-1205, March.
    10. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2022. "Gaussian mixture model with an extended ultrametric covariance structure," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 399-427, June.
    11. Michael Salter-Townshend & Thomas Murphy, 2014. "Mixtures of biased sentiment analysers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 85-103, March.
    12. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 195-212, September.
    13. Koster, Paul R. & Koster, Hans R.A., 2015. "Commuters’ preferences for fast and reliable travel: A semi-parametric estimation approach," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 289-301.
    14. Ferraro, Maria Brigida, 2024. "Fuzzy k-Means: history and applications," Econometrics and Statistics, Elsevier, vol. 30(C), pages 110-123.
    15. Bergé, Laurent R. & Bouveyron, Charles & Corneli, Marco & Latouche, Pierre, 2019. "The latent topic block model for the co-clustering of textual interaction data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 247-270.
    16. Di Zio, Marco & Guarnera, Ugo & Rocci, Roberto, 2007. "A mixture of mixture models for a classification problem: The unity measure error," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2573-2585, February.
    17. Govaert, Gérard & Nadif, Mohamed, 2008. "Block clustering with Bernoulli mixture models: Comparison of different approaches," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3233-3245, February.

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