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On the distribution of posterior probabilities in finite mixture models with application in clustering

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  • Melnykov, Volodymyr

Abstract

The paper discusses an approach based on the multivariate Delta method for approximating the distribution of posterior probabilities in finite mixture models. It can be used for developing distributions of many other characteristics involving posterior probabilities such as the entropy of fuzzy classification or expected cluster sizes. An application of the proposed methodology to clustering through merging mixture components is proposed and discussed. The methodology is studied and illustrated on simulated and well-known classification datasets with good results.

Suggested Citation

  • Melnykov, Volodymyr, 2013. "On the distribution of posterior probabilities in finite mixture models with application in clustering," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 175-189.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:175-189
    DOI: 10.1016/j.jmva.2013.07.014
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    References listed on IDEAS

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    1. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
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    3. Melnykov, Volodymyr & Chen, Wei-Chen & Maitra, Ranjan, 2012. "MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i12).
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    6. ?uksza Marta & Kluge Bogus?aw & Ostrowski Jerzy & Karczmarski Jakub & Gambin Anna, 2009. "Two-Stage Model-Based Clustering for Liquid Chromatography Mass Spectrometry Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-36, February.
    7. Christian Hennig, 2010. "Methods for merging Gaussian mixture components," 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. 4(1), pages 3-34, April.
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    Cited by:

    1. Melnykov, Volodymyr, 2016. "Model-based biclustering of clickstream data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 31-45.
    2. Volodymyr Melnykov & Semhar Michael, 2020. "Clustering Large Datasets by Merging K-Means Solutions," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 97-123, April.
    3. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    4. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.

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