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

Computational Statistics and Data Analysis

Volumn 55, Issue 4, 2011, Pages 1715-1725

  Ingrassia, Salvatore ^a   Rocci, Roberto ^b  

^a UNIVERSITY OF CATANIA   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Degeneracy; Dynamic constraints; EM algorithm; Mixture models

Indexed keywords

CONSTRAINED PARAMETER SPACE; CONSTRAINT-BASED; COVARIANCE MATRICES; DEGENERACY; DEGENERATED SOLUTIONS; DYNAMIC CONSTRAINTS; EIGENVALUES; EM ALGORITHMS; GAUSSIAN MIXTURES; LIKELIHOOD FUNCTIONS; LOCAL MAXIMUM; MIXTURE MODELS; MULTIVARIATE NORMAL; NUMERICAL EXPERIMENTS; PRIORI INFORMATION; THEORETICAL RESULT;

ARRAY PROCESSING; COVARIANCE MATRIX; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MIXTURES;

ALGORITHMS;

EID: 78650837148     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.10.026     Document Type: Article

References (13)

1. Biernacki, C., 2004. An asymptotic upper bound of the likelihood to prevent Gaussian mixtures from degenerating, Technical report, Universit de Franche-Comt.
2. C. Biernacki, and S. Chretien Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with the EM Statistics & Probability Letters 61 2003 373 382
3. J. Chen, and X. Tan Inference for multivariate normal mixtures Journal of the Multivariate Analysis 100 2009 1367 1383
4. N.E. Day Estimating the components of a mixture of two normal distributions Biometrika 56 1969 463 474
5. A.P. Dempster, N.M. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm (with discussion) Journal of the Royal Statistical Society B 39 1977 1 38
6. Forina, M., Lear, R., Armanino, C., Lauter, S., 1988. PARVUS an extendible package for data exploration, classification and correlation. In: Institute of Pharmaceutical and Food Analysis and Technologies, Genoa, Italy.
7. R.J. Hathaway A constrained formulation of maximum-likelihood estimation for normal mixture distributions The Annals of Statistics 13 1985 795 800
8. L. Hubert, and P. Arabie Comparing partitions Journal of Classification 2 1985 193 218
9. S. Ingrassia A likelihood-based constrained algorithm for multivariate normal mixture models Statistical Methods & Applications 13 2004 151 166
10. S. Ingrassia, and R. Rocci A constrained monotone EM algorithm for finite mixture of multivariate Gaussians Computational Statistics & Data Analysis 51 2007 5339 5351
11. G.J. McLachlan, and T. Krishnan The EM Algorithm and Extensions 2nd ed. 2008 John Wiley & Sons New York
12. B. Seo, and B.G. Lindsay A computational strategy for doubly smoothed MLE exemplified in the normal mixture model Computational Statistics & Data Analysis 54 2010 1930 1941
13. C.F.J. Wu On the convergence properties of the EM algorithm Annals of Statistics 11 1983 95 103