Mixtures of modified t-factor analyzers for model-based clustering, classification, and discriminant analysis

Journal of Statistical Planning and Inference

Volumn 141, Issue 4, 2011, Pages 1479-1486

  Andrews, Jeffrey L ^a   McNicholas, Paul D ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

Classification; Clustering; Discriminant analysis; Mixture models; Model based; Modified factor analysis; Modified t factor analyzers; Modified t factors; T Factor analyzers; T Factors

Indexed keywords

EID: 78650198655     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2010.10.014     Document Type: Article

References (47)

1. Aitken A.C. On Bernoulli's numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh 1926, 46:289-305.
2. Anderson E. The irises of the Gaspe Peninsula. Bulletin of the American Iris Society 1935, 59:2-5.
3. Andrews, J.L., McNicholas, P.D., to appear. Extending mixtures of multivariate t-factor analyzers. Statistics and Computing, doi:. http://10.1007/s11222-010-9175-2.
4. Andrews J.L., McNicholas P.D., Subedi S. Model-based classification via mixtures of multivariate t-distributions. Computational Statistics and Data Analysis 2011, 55(1):520-529.
5. Banfield J.D., Raftery A.E. Model-based Gaussian and non-Gaussian clustering. Biometrics 1993, 49(3):803-821.
6. Besag J., Green P., Higdon D., Mengersen K. Bayesian computation and stochastic systems. Statistical Science 1995, 10(1):3-41.
7. Böhning D., Dietz E., Schaub R., Schlattmann P., Lindsay B. The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family. Annals of the Institute of Statistical Mathematics 1994, 46:373-388.
8. Bouveyron C., Girard S., Schmid C. High-dimensional data clustering. Computational Statistics and Data Analysis 2007, 52(1):502-519.
9. Celeux G., Govaert G. Gaussian parsimonious clustering models. Pattern Recognition 1995, 28:781-793.
10. Dasgupta A., Raftery A.E. Detecting features in spatial point processes with clutter via model-based clustering. Journal of the American Statistical Association 1998, 93:94-302.
11. Dean N., Murphy T.B., Downey G. Using unlabelled data to update classification rules with applications in food authenticity studies. Journal of the Royal Statistical Society Series C 2006, 55(1):1-14.
12. Dempster A.P., Laird N.M., Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society Series B 1977, 39(1):1-38.
13. Fisher R.A. The use of multiple measurements in taxonomic problems. Annals of Eugenics 1936, 7(2):179-188.
14. Forina M., Armanino C., Castino M., Ubigli M. Multivariate data analysis as a discriminating method of the origin of wines. Vitis 1986, 25:189-201.
15. Fraley C., Raftery A.E. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 2002, 97(458):611-631.
16. Fraley, C., Raftery, A.E., 2006. MCLUSTversion 3 for R: normal mixture modeling and model-based clustering, Technical Report 504, Department of Statistics, University of Washington. Minor revisions January 2007 and November 2007.
17. Ghahramani, Z., Hinton, G.E., 1997. The EM algorithm for factor analyzers, Technical Report CRG-TR-96-1, University Of Toronto, Toronto.
18. Hubert L., Arabie P. Comparing partitions. Journal of Classification 1985, 2:193-218.
19. Karlis D., Meligkotsidou L. Finite mixtures of multivariate Poisson distributions with application. Journal of Statistical Planning and Inference 2007, 137(6):1942-1960.
20. Karlis D., Santourian A. Model-based clustering with non-elliptically contoured distributions. Statistics and Computing 2009, 19:73-83.
21. Keribin C. Estimation consistante de l'ordre de modèles de mélange. Comptes Rendus de l'Académie des Sciences Série I Mathématique 1998, 326(2):243-248.
22. Keribin C. Consistent estimation of the order of mixture models. Sankhyā, The Indian Journal of Statistics Series A 2000, 62(1):49-66.
23. Lagrange J.L. Méchanique Analitique 1788, Chez le Veuve Desaint, Paris.
24. Leroux B.G. Consistent estimation of a mixing distribution. The Annals of Statistics 1992, 20:1350-1360.
25. Lindsay, B.G., 1995. Mixture models: theory, geometry and applications, in: 'NSF-CBMS Regional Conference Series in Probability and Statistics', vol. 5. Institute of Mathematical Statistics, Hayward, California.
26. McLachlan G.J. Discriminant Analysis and Statistical Pattern Recognition 1992, John Wiley & Sons, New Jersey.
27. McLachlan G.J., Bean R.W., Jones L.B.-T. Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution. Computational Statistics and Data Analysis 2007, 51(11):5327-5338.
28. McLachlan G.J., Krishnan T. The EM Algorithm and Extensions 1997, Wiley, New York.
29. McLachlan G.J., Peel D. Robust cluster analysis via mixtures of multivariate t-distributions. Lecture Notes in Computer Science 1998, vol. 1451:658-666. Springer-Verlag, Berlin.
30. McLachlan G.J., Peel D. Finite Mixture Models 2000, John Wiley & Sons, New York.
31. McLachlan, G.J., Peel, D., 2000b. Mixtures of factor analyzers. In: Proceedings of the Seventh International Conference on Machine Learning. Morgan Kaufmann, San Francisco, pp. 599-606.
32. McNicholas P.D. Model-based classification using latent Gaussian mixture models. Journal of Statistical Planning and Inference 2010, 140(5):1175-1181.
33. McNicholas P.D., Murphy T.B. Parsimonious Gaussian mixture models. Statistics and Computing 2008, 18:285-296.
34. McNicholas P.D., Murphy T.B. Model-based clustering of longitudinal data. The Canadian Journal of Statistics 2010, 38(1):153-168.
35. McNicholas, P.D., Murphy, T.B., 2010b. Model-based clustering of microarray expression data via latent Gaussian mixture models. Bioinformatics 26. (21), 2705-2712.
36. McNicholas P.D., Murphy T.B., McDaid A.F., Frost D. Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models. Computational Statistics and Data Analysis 2010, 54(3):711-723.
37. Meng X.-L., Rubin D.B. Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 1993, 80:267-278.
38. Meng X.-L., van Dyk D. The EM algorithm-an old folk song sung to a fast new tune (with discussion). Journal of the Royal Statistical Society Series B 1997, 59:511-567.
39. R Development Core Team 2010. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria URL: http://www.R-project.org.
40. Rand W.M. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 1971, 66:846-850.
41. Roeder K., Wasserman L. Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association 1997, 92:894-902.
42. Schwarz G. Estimating the dimension of a model. The Annals of Statistics 1978, 6:31-38.
43. Spearman C. The proof and measurement of association between two things. American Journal of Psychology 1904, 15:72-101.
44. Tipping T.E., Bishop C.M. Mixtures of probabilistic principal component analysers. Neural Computation 1999, 11(2):443-482.
45. Tipping T.E., Bishop C.M. Probabilistic principal component analysers. Journal of the Royal Statistical Society Series B 1999, 61:611-622.
46. Titterington D.M., Smith A.F.M., Makov U.E. Statistical Analysis of Finite Mixture Distributions 1985, John Wiley & Sons, Chichester.
47. Woodbury M.A. Inverting Modified Matrices, Statistical Research Group, Memographic Report no. 42 1950, Princeton University, Princeton, New Jersey.