Bayesian regularization for normal mixture estimation and model-based clustering

Journal of Classification

Volumn 24, Issue 2, 2007, Pages 155-181

  Fraley, Chris ^a   Raftery, Adrian E ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

BIC; Conjugate prior; EM algorithm; Mixture models; Model based clustering; Posterior mode

Indexed keywords

EID: 36849029089     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-007-0004-5     Document Type: Article

References (57)

1. BANFIELD, J.D. and RAFTERY, A.E. (1993), "Model-based Gaussian and Non-Gaussian Clustering", Biometrics 49, 803-821.
2. BECHTEL, Y.C., BONAÏTI-PELLIÉ, C., POISSON, N., MAGNETTE, J., and BECHTEL, P.R. (1993), "A Population and Family Study of n-acetyltransferase Using Caffeine Urinary Metabolites", Clinical Pharmacology and Therapeutics 54, 134-141.
3. BENSMAIL, H., and CELEUX, G. (1996), "Regularized. Gaussian Discriminant Analysis Through Eigenvalue Decomposition", Journal of the American Statistical Association 91, 1743-1748.
4. BENSMAIL, H., CELEUX, G., RAFTERY, A.E., and ROBERT, C.P. (1997), "Inference in Model-based Cluster Analysis", Statistics and Computing 7, 1-10.
5. BENSMAIL, H., GOLEK, J., MOODY, M.M., SEMMES, J.O., and HAOUDI, A. (2005), "A Novel Approach to Clustering Proteomics Data Using Bayesian Fast Fourier Transform", Bioinformatics 21, 2210-2224.
6. BENSMAIL, H., and MEULMAN, J.J. (2003), "Model-based Clustering with Noise: Bayesian Inference and Estimation", Journal of Classification 20, 49-76.
7. BRAND, M. (1999), "Structure Discovery in Conditional Probability Models via an Entropic Prior and Parameter Extinction", Neural Computation 11, 1155-1182.
8. CAMPBELL, J.G., FRALEY, C., MURTAGH, F., and RAFTERY, A.E. (1997), "Linear Flaw Detection in Woven Textiles Using Model-based Clustering", Pattern Recognition Letters 18, 1539-1548.
9. CAMPBELL, J.G., FRALEY, C., STANFORD, F. MURTAGH, and A. E. RAPTERY (1999), "Model-Based Methods for Real-Time Textile Pault Detection", International Journal of Imaging Systems and Technology 10, 339-346.
10. CELEUX, G., and GOVAERT, G. (1995), "Gaussian Parsimonious Clustering Models", Pattern Recognition 28, 781-793.
11. CELEUX, G., and ROBERT, C.P. (1993), "Une Histoire de Discrétisation (avec Commentaires)", La Revue de Modulad 11, 7-44.
12. CRAWFORD, S.L. (1994), "An Application of the Laplace Method, to Finite Mixture Distributions", Journal of the American Statistical Association 89, 259-267.
13. CRAWFORD, S.L., DEGROOT, M.H., KADANE, J.B., and SMALL, M.J. (1992), "Modeling Lake Chemistry Distributions: Approximate Bayesian Methods for Estimating a Finite Mixture Model", Technometrics 34, 441-453.
14. DASGUPTA, A., and RAFTERY, A.E. (1998), "Detecting Features in Spatial Point Processes with Clutter via Model-based Clustering", Journal of the American Statistical Association 93, 294-302.
15. DELLAPORTAS, P. (1998), "Bayesian Classification of Neolithic Tools", Applied Statistics 47, 279-297.
16. DEMPSTER, A.P., LAIRD, N.M., and RUBIN, D.B. (1977), "Maximum Likelihood for Incomplete Data via the EM Algorithm (with Discussion)", Journal of the Royal Statistical Society, Series B 39, 1-38.
17. DIEBOLT, J., and ROBERT, C. (1994), "Estimation of Finite Mixtures Through Bayesian Sampling", Journal of the Royal. Statistical Society, Series B 56, 363-375.
18. FIGUEIREDO, M.A.T., and JAIN, A.K. (2002), "Unsupervised Learning of Finite Mixture Models", IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 381-396.
19. FLURY, B.W. (1988), Common Principal Components and Related Multivariate Models, New York: Wiley.
20. FRALEY, C. (1998), "Algorithms for Model-based Gaussian Hierarchical Clustering", SIAM Journal on Scientific Computing 20, 270-281.
21. FRALEY, C., and RAFTERY, A.E. (1998), "How Many Clusters? Which Clustering Method? - Answers via Model-based Cluster Analysis. The Computer Journal 41, 578-588.
22. FRALEY, C., and RAFTERY, A.E. (1999), "MCLUST: Software for Model-based Cluster Analysis", Journal of Classification 16, 297-306.
23. FRALEY, C., and RAFTERY, A.E. (2002), "Model-based Clustering, Discriminant Analysis and Density Estimation", Journal of the American Statistical Association 97, 611-631.
24. FRALEY, C., and RAFTERY, A.E. (2003), "Enhanced. Software for Model-based Clustering, Density Estimation, and Discriminant Analysis: MCLUST", Journal of Classification 20, 263-286.
25. FRALEY, C., and RAFTERY, A.E. (2005, August), "Bayesian Regularization for Normal Mixture Estimation and Model-based Clustering", Technical Report 486, University of Washington, Department of Statistics.
26. FRALEY, C., and RAFTERY, A.E. (2006, September), "MCLUST Version 3 for R: Normal Mixture Modeling and Model-based Clustering", Technical Report 504, University of Washington, Department of Statistics.
27. FRALEY, C., RAFTERY, A.E., and WEHRENS, R. (2005), "Incremental Model-based Clustering for Large Datasets with Small Clusters", Journal of Computational and Graphical Statistics 14, 1-18.
28. GELMAN, A., CARLIN, J.B., STERN, H.S., and RUBIN, D.B. (1995), "Bayesian Data Analysis", London: Chapman and Hall.
29. GHAHRAMANI, Z., and HINTON, G.E. (1997), "The EM Algorithm, for Mixtures of Factor Analyzers", Technical Report CRG-TR-96-1, Toronto: University of Toronto, Department of Computer Science (revised).
30. LAVINE, M., and WEST, M. (1992), "A Bayesian Method for Classification and Discrimination", Canadian Journal of Statistics 20, 451-461.
31. MACQQUEEN, J. (1967), "Some Methods for Classification and Analysis of Multivariate Observations", in Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Eds. L.M.L. Cam and. J. Neyman, University of California Press, Volume 1, pp. 281-297.
32. MCLACHLAN, G.J., and BASPORD, K.E. (1988), Mixture Models : Inference and Applications to Clustering, New York: Marcel Dekker.
33. MCLACHLAN, G.J., and KRISHNAN, T. (1997), The EM Algorithm and Extensions, New York: Wiley.
34. MCLACHLAN, G.J. and PEEL, D. (1998), "Robust Cluster Analysis via Mixtures of Multivariate t-distributions", in Lecture Notes in Computer Science, Eds. A. Amin, D. Dori, P. Pudil, and H. Freeman, Springer, Volume 1451, pp. 658-666.
35. MCLACHLAN, G. J. and D. PEEL (2000), Finite Mixture Models, New York: Wiley.
36. MCLACHLAN, G.J., PEEL, D., BASFORD, K.E., and ADAMS, P. (1999), "The EMMIX Software for the Fitting of Mixtures of Normal i-components", Journal of Statistical Software 4 (on-line publication www.jstatsoft.org).
37. MCLACHLAN, G.J., PEEL, D., and BEAN, R.W. (2003), "Modelling High-dimensional Data by Mixtures of Factor Analyzers", Computational Statistics and Data Analysis 41, 379-388.
38. MERBOUHA, A., and MKHADRI, A. (2001), "Regularization of the Location Model in Discrimination with Mixed Discrete and Continuous Variables", Computational Statistics and Data Analysis 45, 563-576.
39. MKHADRI, A., CELEUX, G., and NASROALLAH, A. (1997), "Regularization in Discriminant Analysis: An Overview", Computational Statistics and Data Analysis 23, 403-423.
40. MUKHERJEE, S., FEIGELSON, E.D., BABU, G.J., MURTAGH, F., FRALEY, C., and RAFTERY, A.E. (1998), "Three Types of Gamma Ray Bursts", The Astrophysical Journal 508, 314-327.
41. QUACKENBUSH, J. (2001), "Computational Analysis of Microarray Data", Nature Reviews Genetics 2, 418-427.
42. RAFTERY, A.E., and DEAN, N. (2006), "Variable Selection for Model-based Clustering", Journal of the American Statistical Association 101, 168-178.
43. REDNER, R.A., and WALKER, H.F. (1984), "Mixture Densities, Maximum Likelihood and the EM Algorithm", SIAMReview 26, 195-239.
44. RICHARDSON, S., and GREEN, P.J. (1997), "On Bayesian Analysis of Mixtures with an Unknown Number of Components", Journal of the Royal Statistical Society, Series B 59, 731-758.
45. ROBERTS, S., HUSMEIER, D., REZEK, I., and PENNY, W. (1998), "Bayesian Approaches to Gaussian Mixture Modeling", IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 1133-1142.
46. ROEDER, K. (1990), "Density Estimation with Confidence Sets Exemplified by Superclusters and Voids in the Galaxies", Journal of the American Statistical Association 85, 617-624.
47. ROEDER, K., and WASSERMAN, L. (1997), "Practical Bayesian Density Estimation Using Mixtures of Normals", Journal of the American Statistical Association 92, 894-902.
48. RYAN, TA., JOINER, B.L., and RYAN, B.F. (1976), The MINLTAB Student Handbook, North Scituate, Massachusetts: Duxbury.
49. SCHAPER, J.L. (1997), Analysis of Incomplete Multivariate Data by Simulation, London: Chapman and Hall.
50. SCHWARZ, G. (1978), "Estimating the Dimension of a Model", The Annals of Statistics 6, 461-464.
51. TITTERINGTON, D.M., SMITH, A.F., and MAKOV, U.E. (1985), Statistical Analysis of Finite Mixture Distributions, New York: Wiley.
52. WANG, N., and RAFTERY, A.E. (2002), "Nearest Neighbor Variance Estimation (NNVE): Robust Covarince Estimation via Nearest Neighbor Cleaning (with Discussion)", Journal of the American Statistical Association 97, 994-1019.
53. WARD, J.H. (1963), "Hierarchical Groupings to Optimize an Objective Function", Journal of the American Statistical Association 58, 234-244.
54. WEHRENS, R., BUYDENS, L., FRALEY, C., and RAFTERY, A.E. (2004), "Model-based Clustering for Image Segmentation and Large Datasets via Sampling", Journal of Classification 21, 231-253.
55. WEHRENS, R., SIMONETTI, A., and BUYDENS, L. (2002), "Mixture- modeling of Medical Magnetic Resonance Data", Journal of Chemometrics 16, 1-10.
56. YEUNG, K.Y., FRALEY, C., MURUA, A., RAFTERY, A.E., and RUZZO, W.L. (2001), "Model-based Clustering and Data Transformation for Gene Expression Data", Bioinformatics 17, 977-987.
57. ZHANG, Z., CHAN, K.L., WU, Y., and CHEN, C. (2004), "Learning a Multivariate Gaussian Mixture Model with the Reversible Jump MCMC Algorithm", Statistics and Computing 14, 343-355.