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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.

Suggested Citation

  • 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. 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.
    2. 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.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Biernacki, Christophe & Chrétien, Stéphane, 2003. "Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 373-382, February.
    5. Chen, Jiahua & Tan, Xianming, 2009. "Inference for multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1367-1383, August.
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    1. repec:eee:csdana:v:119:y:2018:i:c:p:19-38 is not listed on IDEAS
    2. repec:spr:advdac:v:12:y:2018:i:2:d:10.1007_s11634-017-0293-y is not listed on IDEAS
    3. repec:spr:advdac:v:12:y:2018:i:2:d:10.1007_s11634-016-0279-1 is not listed on IDEAS
    4. Nicosia, Aurélien & Duchesne, Thierry & Rivest, Louis-Paul & Fortin, Daniel, 2017. "A general hidden state random walk model for animal movement," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 76-95.
    5. Hien Nguyen & Geoffrey McLachlan, 2015. "Maximum likelihood estimation of Gaussian mixture models without matrix operations," 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 371-394, December.

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