Most clustering methods have been developed for the situation where the groups to be identified are well separated "blobs" in p-space. I have been interested in the case where the groups are defined by their shape, may be clustered around lines or even thin nonlinear curves, and may even intersect. Examples are groups of boundary pixels in images, groups of earthquakes clustered along seismic faults, and stars grouped in galaxies.
For a review of model-based clustering, see Fraley and Raftery (2002). Free software to carry it out, MCLUST, is available for R.
Current research projects in this area include model-based clustering for social networks (Handcock, Raftery and Tantrum 2007, Krivitsky et al 2007), and variable selection for model-based clustering (Raftery and Dean 2006),
Raftery, A.E., Niu, X., Hoff, P.D. and Yeung, K.Y. (2012). Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood. Journal of Computational and Graphical Statistics, 21:909-919.
Baudry, J.-P., Raftery, A.E., Celeux, G., Lo, K. and Gottardo, R. (2010). Combining Mixture Components for Clustering. Journal of Computational and Graphical Statistics 19:332-353.
Murphy, T.B., Dean. N. and Raftery, A.E. (2010). Variable Selection and Updating In Model-Based Discriminant Analysis for High Dimensional Data with Food Authenticity Applications. Annals of Applied Statistics 4:396-421.
Dean, N. and Raftery, A.E. (2010). Latent Class Analysis Variable Selection. Annals of the Institute of Statistical Mathematics 62:11-35.
Steele, R.J., Wang, N. and Raftery, A.E. (2010). Inference from multiple imputation for missing data using mixtures of normals. Statistical Methodology 7:351-365.
Steele, R.J. and Raftery, A.E. (2010). Performance of Bayesian Model Selection Criteria for Gaussian Mixture Models. In Frontiers of Statistical Decision Making and Bayesian Analysis (edited by M.-H. Chen et al), pages 113-130, New York: Springer. Earlier version.
Krivitsky, P., Handcock, M.S., Raftery, A.E. and Hoff, P. (2009). Representing Degree Distributions, Clustering, and Homophily in Social Networks With Latent Cluster Random Ects Models. Social Networks 31:204-213.
Handcock, M.S., Raftery, A.E. and Tantrum, J. (2007). Model-based clustering for social networks (with Discussion). Journal of the Royal Statistical Society, Series A, 170, 301-354.
Oh, M.-S. and Raftery, A.E. (2007). Model-based Clustering with Dissimilarities: A Bayesian Approach. Journal of Computational and Graphical Statistics, 16, 559-585.
Fraley, C. and Raftery, A.E. (2007). Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering. Journal of Classification, 24, 155-181.
Fraley C. and Raftery A.E. (2007). Model-based methods of classification: Using the mclust software in chemometrics. Journal of Statistical Software, 18, paper i06.
Fraley, C. and Raftery, A.E. (2006). MCLUST Version 3 for R: Normal Mixture Modeling and Model-Based Clustering. Technical Report no. 504, Department of Statistics, University of Washington.
Raftery, A.E. and Dean, N. (2006). Variable Selection for Model-Based Clustering. Journal of the American Statistical Assocation, 101, 168-178.
Steele, R., Raftery, A.E. and Emond, M. (2006). Computing Normalizing Constants for Finite Mixture Models via Incremental Mixture Importance Sampling (IMIS). Journal of Computational and Graphical Statistics, 15, 712-734.
Forbes, F., Peyrard, N., Fraley, C., Georgian-Smith, D., Goldhaber, D.M., and Raftery, A.E. (2006). Model-Based Region-of-Interest Selection in Dynamic Breast MRI. Journal of Computer Assisted Tomography, 30, 675-687.
Fraley, C. and Raftery, A.E. (2006). Some applications of model-based clustering in chemistry. R News, 6, no. 3, 17-23.
Fraley, C. and Raftery, A.E. (2006). Model-based microarray image analysis. R News, 6, no. 5, 60-63.
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, 529-546.
Murtagh, F., Raftery, A.E., and J.L. Starck (2005). Bayesian inference for multiband image segmentation via model-based cluster trees. Image and Vision Computing, 23, 587-596.
Dean, N. and Raftery, A.E. (2005). ``Normal uniform mixture differential gene expression detection for cDNA microarrays.'' BMC Bioinformatics, 6, 173. (doi:10.1186/1471-2105-6-173).
Li, Q., Fraley, C., Bumgarner, R.E., Yeung, K.Y. and Raftery, A.E. (2005). ``Donuts, Scratches and Blanks: Robust Model-Based Segmentation of Microarray Images.'' Bioinformatics, 21(12), 2875-2882 (doi:10.1093/bioinformatics/bti447).
Walsh, D.C.I. and Raftery, A.E. (2005). Classification of mixtures of spatial point processes via partial Bayes factors. Journal of Computational and Graphical Statistics, 14, 139-154.
Wehrens, R., Buydens, L.M.C., Fraley, C. and Raftery, A.E. (2004). Model-Based Clustering for Image Segmentation and Large Datasets Via Sampling. Journal of Classification, 21, 231-253.
Fraley, C. and Raftery, A.E. (2002). Model-Based Clustering, Discriminant Analysis, and Density Estimation. Journal of the American Statistical Association, 97, 611-631.
Chris Fraley and Adrian E. Raftery (2002). "MCLUST: Software for Model-Based Clustering, Density Estimation and Discriminant Analysis" Technical Report no. 415, Department of Statistics, University of Washington.
Fionn Murtagh, Adrian E. Raftery and Jean-Luc Starck (2001). "Bayesian Inference for Color Quantization via Model-Based Clustering Trees". Technical Report no. 402, Department of Statistics, University of Washington.
Yeung K.Y., Fraley C., Murua A, Raftery, A.E. and Ruzzo, W.L. (2001).
Model-based clustering and data transformations for gene expression data.
Bioinformatics, 17, 977-987.
This paper was identified by ISI Science Citation Index/Web of Science as one of the most highly-cited papers in Gene Expression Data. Here is a commentary on the paper by lead author Ka Yee Yeung, published by ISI in its publication Fast Moving Fronts.
Stanford, D.C. and Raftery, A.E. (2000). Principal curve clustering with noise. IEEE Transactions on Pattern Analysis and Machine Analysis, 22, 601-609.
Fraley, C. and Raftery, A.E. (1999). MCLUST: Software for Model-Based Cluster Analysis. Journal of Classification, 16, 297-306.
Campbell, J.G., Fraley, C., Stanford, D., Murtagh, F. and Raftery, A.E. (1999). Model-based methods for textile fault detection. International Journal of Imaging Science and Technology, 10, 339-346.
Mukherjee, S., Feigelson, E.D., Babu, G.J., Murtagh, F., Fraley, C. and Raftery, A.E. (1998). Three types of gamma ray bursts. Astrophysical Journal, 508, 314-327.
Fraley, C. and Raftery, A.E. (1998). How many clusters? Which clustering methods? Answers via model-based cluster analysis. Computer Journal, 41, 578-588.
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.
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.
Bensmail, H., Celeux, G., Raftery, A.E. and Robert, C. (1997). Inference in model-based cluster analysis. Statistics and Computing, 7, 1-10.
Banfield, J.D. and Raftery, A.E. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics, 49, 803-821.
Banfield, J.D. and Raftery, A.E. (1992). Ice floe identification in satellite images using mathematical morphology and clustering about principal curves. Journal of the American Statistical Association, 8, 7-16.
Murtagh, F. and Raftery, A.E. (1984). Fitting straight lines to point patterns. Pattern Recognition, 17, 479-483.
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Updated April 14, 2014.
Copyright 2005-2014 by Adrian E. Raftery; all rights reserved.