Mixture modelling for cluster analysis

Statistical Methods in Medical Research

Volumn 13, Issue 5, 2004, Pages 347-361

  McLachlan, G J ^a   Chang, S U ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANALYSIS OF VARIANCE; ARTICLE; CANCER SURVIVAL; CLUSTER ANALYSIS; DATA ANALYSIS; FACTORIAL ANALYSIS; MATHEMATICAL MODEL; PROBABILITY; PROSTATE CANCER; STATISTICAL ANALYSIS;

AUSTRALIA; BIOMEDICAL RESEARCH; CLUSTER ANALYSIS; FACTOR ANALYSIS, STATISTICAL; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL;

EID: 6444220705     PISSN: 09622802     EISSN: None     Source Type: Journal    
DOI: 10.1191/0962280204sm372ra     Document Type: Article

References (36)

1. McLachlan GJ, Peel D. Finite mixture models. New York: Wiley, 2000.
2. McLachlan GJ, Basford, KE. Mixture models: inference and applications to clustering. New York: Marcel Dekker, 1988.
3. Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society B 1977; 39: 1-38.
4. McLachlan GJ, Krishnan T. The EM algorithm and extensions New York: Wiley, 1997.
5. Hawkins DM, Muller MW, ten Krooden JA. Cluster analysis. In Hawkins DM, ed. Topics in applied multivariate analysis. Cambridge: Cambridge University Press, 1982; 303-56.
6. Aitkin M, Anderson D, Hinde J. Statistical modelling of data on teaching styles (with discussion). Journal of the Royal Statistical Society B 1981; 144: 419-61.
7. Marriott FHC. The interpretation of multiple observations London: Academic Press, 1974.
8. Ng, SK, McLachlan, GJ. On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures. Statistics and Computing 2003; 13: 45-55.
9. Coleman D, Dong X, Hardin J, Rocke DM, Woodruff DL. Some computational issues in cluster analysis with no a priori metric. Computational Statistics and Data Analysis 1999; 31: 1-11.
10. Biernacki C, Celeux G, Govaert G. Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics and Data Analysis 2003; 41: 561-75.
11. McLachlan GJ, Peel D, Basford KE, Adams P. The EMMIX software for the fitting of mixtures of normal and t-components. Journal of Statistical Software 1999; 4 (No. 2).
12. Fraley C, Raftery AE. How many clusters? Which clustering method? Answers via model-based cluster analysis. Computer Journal 1998; 41: 578-88.
13. Hartley HO, Rao JNK. Classification and estimation in analysis of variance problems. International Statistical Review 1968; 36: 141-47.
14. John S. On identifying the population of origin of each observation in a mixture of observations from two normal populations. Technometrics 1970; 12: 553-63.
15. Scott AJ, Symons MJ. Clustering methods based on likelihood ratio criteria. Biometrics 1971; 27: 387-97.
16. McLachlan GJ. The classification and mixture maximum likelihood approaches to cluster analysis. In Krishnaiah PR, Kanal L, eds. Handbook of statistics. Volume 2. Amsterdam: North-Holland, 1982; 199-208.
17. Bryant PG. Large-sample results for optimization-based clustering. Journal of Classification 1991; 8: 31-44.
18. Edwards AWF, Cavalli-Sforza LL. A method for cluster analysis. Biometrics 1965; 21: 362-75.
19. Friedman HP, Rubin H. On some invariant criteria for grouping data. Journal of the American Statistical Association 1967; 62 1159-78.
20. McLachlan GJ. On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics 1987; 36: 318-24.
21. Schwarz G. Estimating the dimension of a model. Annals of Statistics 1978; 6: 461-64.
22. Biernacki C, Celeux G, Govaert G. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence 2000; 22 719-25.
23. McLachlan GJ, Peel D. Robust cluster analysis via mixtures of multivariate t-distributions. In Amin A, Dori D, Pudil P, Freeman H, eds. Lecture notes in computer science, Volume 1451. Berlin: Springer-Verlag, 1998; 658-66.
24. Peel D. and McLachlan. GJ. Robust mixture modelling using the t-distribution. Statistics and Computing 2000; 10: 335-44.
25. Hennig C. Breakdown points of maximum likelihood-estimators of location-scale mixtures. Annals of Statistics 2002; in press.
26. Banfield JD, Raftery AE. Model-based Gaussian and non-Gaussian clustering. Biometrics 1993; 49: 803-21.
27. Bensmail H, Celeux G, Raftery AE, Robert CP. Inference in model-based cluster analysis. Statistics and Computing 1997; 7 1-10.
28. McLachlan GJ, Peel, D. Mixtures of factor analyzers, In Langley P, ed. Proceedings of the Seventeenth International Conference on Machine Learning. San Francisco: Morgan Kaufmann, 2000; 599-606.
29. McLachlan GJ, Peel D, Bean RW. Modelling high-dimensional data by mixtures of factor analyzers. Computational Statistics and Data Analysis 2003; 41: 379-88.
30. Ghahramani Z, Hinton GE. The EM algorithm for factor analyzers. Technical Report No. CRG-TR-96-1, Toronto: The University of Toronto, 1997.
31. Tipping ME, Bishop CM. Mixtures of probabilistic principal component analysers. Neural Computation 1999; 11: 443-82.
32. Meng XL, van Dyk D. The EM algorithm - an old folk song sung to a fast new tune (with discussion). Journal of the Royal Statistical Society B 1997; 59: 511-67.
33. Titterington DM, Murray GD, Murray LS, Spiegelhalter DJ, Skene AM, Habbema JDF, Gelpke, GJ. Comparison of discrimination techniques applied to a complex data set of head injured patients (with discussion). Journal of the Royal Statistical Society A 1981; 144: 145-75.
34. Hand DJ, Yi K. Idiot's Bayes - not so stupid after all? International Statistical Review 2001; 69: 385-98.
35. Hunt LA, Jorgensen MA. Mixture model clustering: a brief introduction to the MULTIMIX program. Australian and New Zealand Journal of Statistics 1999; 40: 153-71.
36. Byar DP, Green SB. The choice of treatment for cancer patients based on covariate information: application to prostate cancer. Bulletin du Cancer (Paris) 1980; 67: 477-90.