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Improved initialisation of model-based clustering using Gaussian hierarchical partitions

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  • Luca Scrucca
  • Adrian Raftery

Abstract

Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among the several approaches available in the literature, model-based agglomerative hierarchical clustering is used to provide initial partitions in the popular mclust R package. This choice is computationally convenient and often yields good clustering partitions. However, in certain circumstances, poor initial partitions may cause the EM algorithm to converge to a local maximum of the likelihood function. We propose several simple and fast refinements based on data transformations and illustrate them through data examples. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Luca Scrucca & Adrian Raftery, 2015. "Improved initialisation of model-based clustering using Gaussian hierarchical partitions," 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. 9(4), pages 447-460, December.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:4:p:447-460
    DOI: 10.1007/s11634-015-0220-z
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    References listed on IDEAS

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    1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard & Langrognet, Florent, 2006. "Model-based cluster and discriminant analysis with the MIXMOD software," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 587-600, November.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    4. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    5. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
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    2. Michael Fop & Pierre-Alexandre Mattei & Charles Bouveyron & Thomas Brendan Murphy, 2022. "Unobserved classes and extra variables in high-dimensional discriminant analysis," 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(1), pages 55-92, March.
    3. Branislav Panić & Jernej Klemenc & Marko Nagode, 2020. "Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation," Mathematics, MDPI, vol. 8(7), pages 1-30, July.
    4. Marek Śmieja & Magdalena Wiercioch, 2017. "Constrained clustering with a complex cluster 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. 11(3), pages 493-518, September.
    5. Alessandro Casa & Luca Scrucca & Giovanna Menardi, 2021. "Better than the best? Answers via model ensemble in density-based clustering," 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. 15(3), pages 599-623, September.
    6. Sahin, Özge & Czado, Claudia, 2022. "Vine copula mixture models and clustering for non-Gaussian data," Econometrics and Statistics, Elsevier, vol. 22(C), pages 136-158.
    7. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.

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