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Degeneracy of the EM algorithm for the MLE of multivariate Gaussian mixtures and dynamic constraints

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  • Ingrassia, Salvatore
  • Rocci, Roberto

Abstract

EM algorithms for multivariate normal mixture decomposition have been recently proposed in order to maximize the likelihood function in a constrained parameter space having no singularities and a reduced number of spurious local maxima. However, such approaches require some a priori information about the eigenvalues of the covariance matrices. The behavior of the EM algorithm near a degenerated solution is investigated. The obtained theoretical results would suggest a new kind of constraint based on the dissimilarity between two consecutive updates of the eigenvalues of each covariance matrix. The performances of such a "dynamic" constraint are evaluated on the grounds of some numerical experiments.

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  • Ingrassia, Salvatore & Rocci, Roberto, 2011. "Degeneracy of the EM algorithm for the MLE of multivariate Gaussian mixtures and dynamic constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1715-1725, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1715-1725
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    References listed on IDEAS

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    1. Seo, Byungtae & Lindsay, Bruce G., 2010. "A computational strategy for doubly smoothed MLE exemplified in the normal mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1930-1941, August.
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    6. Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
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    Cited by:

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    3. Andrews, Jeffrey L., 2018. "Addressing overfitting and underfitting in Gaussian model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 160-171.
    4. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," 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(2), pages 235-260, June.
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    7. Luis Angel García-Escudero & Alfonso Gordaliza & Francesca Greselin & Salvatore Ingrassia & Agustín Mayo-Iscar, 2018. "Eigenvalues and constraints in mixture modeling: geometric and computational issues," 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(2), pages 203-233, June.
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