Maximum likelihood estimation of mixtures of factor analyzers

Computational Statistics and Data Analysis

Volumn 55, Issue 9, 2011, Pages 2712-2723

  Montanari, Angela ^a   Viroli, Cinzia ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Information matrix; Maximum likelihood; Model based clustering

Indexed keywords

BAYESIAN FRAMEWORKS; COVARIANCE MATRICES; DIMENSION REDUCTION; ESTIMATION METHODS; ESTIMATION PROBLEM; FACTOR ANALYZERS; FACTOR MODEL; INFORMATION MATRIX; MODEL-BASED CLUSTERING; SIMULATION STUDIES;

COVARIANCE MATRIX; ESTIMATION; MIXTURES;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 79956083513     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2011.04.001     Document Type: Article

References (24)

1. O. Boldea, and J.R. Magnus Maximum likelihood estimation of the multivariate normal mixture model Journal of the American Statistical Association 104 2009 1539 1549
2. R.D. Cook, and S. Weisberg An Introduction to Regression Graphics 1994 Wiley New York
3. H. Cramr Mathematical Methods of Statistics 1946 Princeton University Press Princeton, New Jersey
4. N.E. Day Estimating the components of a mixture of two normal distributions Biometrika 56 1969 463 474
5. N.M. Dempster, A.P. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm (with discussion) Journal of the Royal Statistical Society. Series B 39 1977 1 38
6. E. Fokou, and D.M. Titterington Mixtures of factor analysers. Bayesian estimation and inference in stochastic simulation Machine Learning 50 2003 73 94
7. C. Fraley, and A.E. Raftery Model-based clustering, discriminant analysis, and density estimation Journal of the American Statistical Association 97 2002 611 631
8. Z. Ghahramani, and M.J. Beal Variational inference for Bayesian mixtures of factor analyzers S.A. Solla, T.K. Leen, K.-R. Miller, Neural Information Processing Systems vol. 12 2000 MIT Press MA 449 455
9. Ghahramani, Z., Hilton, G.E., 1997. The EM algorithm for mixture of factor analyzers. Techical Report CRG-TR-96-1. Department of Computer Science, University of Toronto, Canada.
10. T.A. Louis Finding the observed information matrix when using the EM algorithm Journal of the Royal Statistical Society. Series B 44 1982 226 233
11. G.J. McLachlan, and K.E. Basford Mixture Models: Inference and Application to Clustering 1988 Marcel Dekker New York
12. G.J. McLachlan, and D. Peel Finite Mixture Models 2000 John Wiley & Sons Inc. New York
13. G.J. McLachlan, and D. Peel Mixtures of factor analyzers P. Langley, Proceedings of the Seventeenth International Conference on Machine Learning 2000 Morgan Kaufmann San Francisco 599 606
14. G.J. McLachlan, D. Peel, and R.W. Bean Modelling high-dimensional data by mixtures of factor analyzers Computational Statistics and Data Analysis 41 2003 379 388 (Pubitemid 36065383)
15. X.L. Meng, and D.B. Rubin Using EM to obtain asymptotic variancecovariance matrices: the SEM algorithm Journal of the American Statistical Association 86 1991 899 909
16. X.L. Meng, and D. van Dyk The EM algorithman old folk song sung to a fast new tune (with discussion) Journal of the Royal Statistical Society. Series B (Methodological) 59 1997 511 567 (Pubitemid 127686967)
17. R Development Core Team 2008. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org.
18. A.E. Raftery, and N. Dean Variable selection for model-based clustering Journal of the American Statistical Association 101 2006 168 178 (Pubitemid 43500033)
19. R.A. Redner, and H.F. Walker Mixture densities, maximum likelihood and the EM algorithm SIAM Review 26 1984 195 239
20. M. Stephens Dealing with label-switching in mixture models Journal of the Royal Statistical Society, Series B 62 2000 795 809
21. A. Utsugi, and T. Kumagai Bayesian analysis of mixtures of factor analyzers Neural Computation 13 2001 993 1002 (Pubitemid 33595019)
22. J.H. Wolfe Pattern clustering by multivariate mixture analysis Multivariate Behavioral Research 5 1970 329 350
23. J.H. Zhao, and P.L.H. Yu Fast ML estimation for the mixture of factor analyzers via an ECM algorithm IEEE Transactions on Neural Networks 19 2008 1956 1961
24. X. Zhou, and X. Liu The EM algorithm for the extended finite mixture of the factor analyzers model Computational Statistics and Data Analysis 52 2008 3939 3953