Efficient model selection for mixtures of probabilistic PCA via hierarchical BIC

IEEE Transactions on Cybernetics

Volumn 44, Issue 10, 2014, Pages 1871-1883

  Zhao, Jianhua ^a  

^a YUNNAN UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

BIC; clustering; expectation maximization; mixture model; model selection; principal component analysis

Indexed keywords

BIC; CLUSTERING; EXPECTATION - MAXIMIZATIONS; MIXTURE MODEL; MODEL SELECTION;

PRINCIPAL COMPONENT ANALYSIS;

EID: 84907203415     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2014.2298401     Document Type: Article

References (33)

1. I. T. Jolliffe, Principal Component Analysis, 2nd ed. New York, NY, USA: Springer, 2002
2. N. Kambhatla and T. K. Leen, "Dimension reduction by local principal component analysis," Neural Comput., vol. 9, no. 7, pp. 1493-1516, Jan. 1997
3. G. Hinton, P. Dayan, and M. Revow, "Modelling the manifolds of handwritten digits," IEEE Trans. Neural Netw., vol. 8, no. 1, pp. 65-74, Jan. 1997
4. G. Hinton, M. Revow, and P. Dayan, "Recognizing handwritten digits using mixtures of linear models," in Proc. Adv. Neural Inf. Process. Syst., 1995, pp. 1015-1022
5. M. E. Tipping and C. M. Bishop, "Mixtures of probabilistic principal component analysers," Neural Comput., vol. 11, no. 2, pp. 443-482, 1999
6. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data using the EM algorithm (with discussion)," J. Roy. Stat. Soc. Ser. B, Stat. Methodol., vol. 39, no. 1, pp. 1-38, 1977
7. P. D. McNicholas and T. B. Murphy, "Parsimonious Gaussian mixture models," Statist. Comput., vol. 18, no. 3, pp. 285-296, Sep. 2008
8. C. Archer and T. K. Leen, "Optimal dimension reduction and transform coding with mixture principal components," in Proc. IEEE Int. Joint Conf. Neural Netw., vol. 2, 1996, pp. 916-920
9. P. Meinicke and H. Ritter, "Resolution-based complexity control for Gaussian mixture," Neural Comput., vol. 13, no. 2, pp. 453-475, 2001
10. T. Su and J. G. Dy, "Automated hierarchical mixtures of probabilistic principal component analyzers," in Proc. 21th Int. Conf. Mach. Learn., 2004, pp. 775-782
11. M. E. M. Musa, D. de Ridder, R. P. W. Duin, and V. Atalay, "Almost autonomous training of mixtures of principal component analyzers," Pattern Recognit. Lett., vol. 25, no. 9, pp. 1085-1095, 2004
12. M. A. T. Figueiredo and A. K. Jain, "Unsupervised learning of finite mixture models," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 3, pp. 381-396, Mar. 2002
13. C. M. Bishop, Pattern Recognition and Machine Learning. New York, NY, USA: Springer, 2006
14. C. M. Bishop, J. M. Winn, and C. C. Nh, "Non-linear Bayesian image modelling," in Proc. 6th Eur. Conf. Comput. Vis, 2000, pp. 3-17
15. Z. Ghahramani and M. Beal, "Variational inference for Bayesian mixture of factor analysers," in Proc. Adv. Neural Inf. Process. Syst., 2000, pp. 449-455
16. X. Wei and Z. Yang, "The infinite student's t-factor mixture analyzer for robust clustering and classification," Pattern Recognit., vol. 45, no. 12, pp. 4346-4357, 2012
17. C. Constantinopoulos and A. Likas, "Unsupervised learning of Gaussian mixtures based on variational component splitting," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 745-755, May 2007
18. G. Schwarz, "Estimating the dimension of a model," Ann. Statist., vol. 6, no. 2, pp. 461-464, 1978
19. G. Mclachlan and D. Peel, Finite Mixture Models. New York, NY, USA: Wiley, 1997
20. C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," J. Amer. Statist. Assoc., vol. 97, no. 458, pp. 611-631, 2002
21. J. L. Andrews and P. D. McNicholas, "Extending mixtures of multivariate t-factor analyzers." Statist. Comput., vol. 21, no. 3, pp. 361-373, 2011
22. X. L. Hu and L. Xu, "A comparative investigation on subspace dimension determination," Neural Netw., vol. 17, nos. 8-9, pp. 1051-1059, 2004
23. S. Srivastava, M. R. Gupta, and B. A. Frigyik, "Bayesian quadratic discriminant analysis," J. Mach. Learn. Res., vol. 8, no. 6, pp. 1277-1305, 2007
24. J. H. Friedman, "Regularized discriminant analysis," J. Amer. Statist. Assoc., vol. 84, no. 405, pp. 165-175, 1989
25. C. Biernacki, G. Celeux, and G. Govaert, "Assessing a mixture model for clustering with the integrated completed likelihood," IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 7, pp. 719-725, Jul. 2000
26. K. Bache and M. Lichman. (2013). UCI Machine Learning Repository [Online]. Available: http://archive.ics.uci.edu/ml
27. L. Hubert and P. Arabie, "Comparing partitions," J. Classif., vol. 2, no. 1, pp. 193-218, 1985
28. J. Zhao and P. L. H. Yu, "A note on variational Bayesian factor analysis," Neural Netw., vol. 22, no. 7, pp. 988-997, 2009
29. G. J. McLachlan, D. Peel, and R. W. Bean, "Modelling high-dimensional data by mixtures of factor analyzers," Comput. Statist. Data Anal., vol. 41, nos. 3-4, pp. 379-388, 2003
30. J. Zhao and P. L. H. Yu, "Fast ML estimation for the mixture of factor analyzers via an ECM algorithm," IEEE Trans. Neural Netw., vol. 19, no. 11, pp. 1956-1961, Nov. 2008
31. J. Baek, G. J. McLachlan, and L. K. Flack, "Mixtures of factor analyzers with common factor loadings: Applications to the clustering and visualization of high-dimensional data," IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 7, pp. 1298-1309, Jul. 2010
32. B. Wang and D. M. Titterington, "Convergence and asymptotic normality of variational bayesian approximations for exponential family models with missing values," in Proc. Uncertain. Artif. Intell., 2004, pp. 577-584
33. H. Attias, "Inferring parameters and structure of latent variable models by variational Bayes," in Proc. 15th Uncertain. Artif. Intell., 1999, pp. 21-30.