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Model-based clustering. (English) Zbl 1364.62155
Summary: The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] AITKEN, A.C. (1926), “A Series Formula for the Roots of Algebraic and Transcendental Equations”, Proceedings of the Royal Society of Edinburgh, 45, 14-22. · JFM 51.0096.03
[2] AITKIN, M., and WILSON, G.T. (1980), “Mixture Models, Outliers, and the EM Algorithm”, Technometrics, 22(3), 325-331. · Zbl 0466.62034
[3] ANDERLUCCI, L., and VIROLI, C. (2015), “Covariance Pattern Mixture Models for Multivariate Longitudinal Data”, The Annals of Applied Statistics, 9(2), 777-800. · Zbl 1397.62214
[4] ANDREWS, J.L., and MCNICHOLAS, P.D. (2011a), “Extending Mixtures of Multivariate t-Factor Analyzers”, Statistics and Computing, 21(3), 361-373. · Zbl 1255.62171
[5] ANDREWS, J.L., and MCNICHOLAS, P.D. (2011b), “Mixtures of Modified t-Factor Analyzers for Model-Based Clustering, Classification, and Discriminant Analysis”, Journal of Statistical Planning and Inference, 141(4), 1479-1486. · Zbl 1204.62098
[6] ANDREWS, J.L., and MCNICHOLAS, P.D. (2012), “Model-Based Clustering, Classification, and Discriminant Analysis Via Mixtures of Multivariate \(t\)-Distributions: The \(t\)EIGEN Family”, Statistics and Computing, 22(5), 1021-1029. · Zbl 1252.62062
[7] ANDREWS, J.L., and MCNICHOLAS, P.D. (2013), vscc: Variable Selection for Clustering and Classification, R Package Version 0.2.
[8] ANDREWS, J.L., and MCNICHOLAS, P.D. (2014), “Variable Selection for Clustering and Classification”, Journal of Classification, 31(2), 136-153. · Zbl 1360.62310
[9] ANDREWS, J.L., MCNICHOLAS, P.D., and SUBEDI, S. (2011), “Model-Based Classification Via Mixtures of Multivariate t-Distributions”, Computational Statistics and Data Analysis, 55(1), 520-529. · Zbl 1247.62151
[10] ANDREWS, J.L.,WICKINS, J.R., BOERS, N.M., and MCNICHOLAS, P.D. (2015), teigen: Model-Based Clustering and Classification with the Multivariate t Distribution, R Package Version 2.1.0.
[11] ATTIAS, H. (2000), “A Variational Bayesian Framework for Graphical Models”, in Advances in Neural Information Processing Systems, Volume 12, MIT Press, pp. 209-215.
[12] AZZALINI, A., BROWNE, R.P., GENTON, M.G., and MCNICHOLAS, P.D. (2016), “On Nomenclature for, and the Relative Merits of, Two Formulations of Skew Distributions”, Statistics and Probability Letters, 110, 201-206. · Zbl 1376.60024
[13] AZZALINI, A., and CAPITANIO, A. (1999), “Statistical Applications of the Multivariate Skew Normal Distribution”, Journal of the Royal Statistical Society: Series B, 61(3), 579-602. · Zbl 0924.62050
[14] AZZALINI, A., and CAPITANIO, A. (2003), “Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skew \(t\) Distribution”, Journal of the Royal Statistical Society: Series B, 65(2), 367-389. · Zbl 1065.62094
[15] AZZALINI, A. (2014), The Skew-Normal and Related Families, with the collaboration of A. Capitanio, IMS monographs, Cambridge: Cambridge University Press. · Zbl 1338.62007
[16] AZZALINI, A., and VALLE, A.D. (1996), “The Multivariate Skew-Normal Distribution”, Biometrika / 83, 715-726. · Zbl 0885.62062
[17] BAEK, J., and MCLACHLAN, G.J. (2008), “Mixtures of Factor Analyzers with Common Factor Loadings for the Clustering and Visualisation of High-Dimensional Data”, Technical Report NI08018-SCH, Preprint Series of the Isaac Newton Institute for Mathematical Sciences, Cambridge.
[18] BAEK, J., and MCLACHLAN, G.J. (2011), “Mixtures of Common t-Factor Analyzers for Clustering High-Dimensional Microarray Data”, Bioinformatics, 27, 1269-1276.
[19] BAEK, J., MCLACHLAN, G.J., and FLACK, L.K. (2010), “Mixtures of Factor Analyzers with Common Factor Loadings: Applications to the Clustering and Visualization of High-Dimensional Data”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 32, 1298-1309.
[20] BANFIELD, J.D., and RAFTERY, A.E. (1993), “Model-Based Gaussian and Non-Gaussian Clustering”, Biometrics, 49(3), 803-821. · Zbl 0794.62034
[21] BARNDORFF-NIELSEN,O.E. (1997), “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling”, Scandinavian Journal of Statistics, 24(1), 1-13. · Zbl 0934.62109
[22] BARTLETT,M.S. (1953), “Factor Analysis in Psychology as a Statistician Sees It”, in Uppsala Symposium on Psychological Factor Analysis, Number 3 in Nordisk Psykologi’s Monograph Series, Copenhagen: Ejnar Mundsgaards, pp. 23-34. · Zbl 0052.15004
[23] BAUDRY, J.-P. (2015), “Estimation and Model Selection for Model-Based Clustering with the Conditional Classification Likelihood”, Electronic Journal of Statistics, 9, 1041-1077. · Zbl 1325.62120
[24] BAUM, L.E., PETRIE, T., SOULES, G., and WEISS, N. (1970), “A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains”, Annals of Mathematical Statistics, 41, 164-171. · Zbl 0188.49603
[25] BDIRI, T., BOUGUILA, N., and ZIOU, D. (2016), “Variational Bayesian Inference for Infinite Generalized Inverted Dirichlet Mixtures with Feature Selection and Its Application to Clustering”, Applied Intelligence, 44(3), 507-525.
[26] BENSMAIL, H., CELEUX, G., RAFTERY, A.E., and ROBERT, C.P. (1997), “Inference in Model-Based Cluster Analysis”, Statistics and Computing, 7(1), 1-10.
[27] BHATTACHARYA, S., and MCNICHOLAS, P.D. (2014), “A LASSO-Penalized BIC for Mixture Model Selection”, Advances in Data Analysis and Classification, 8(1), 45-61.
[28] BIERNACKI, C., CELEUX, G., and GOVAERT, G. (2000), “Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(7), 719-725.
[29] BIERNACKI, C., CELEUX, G., and GOVAERT, G. (2003), “Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture Models”, Computational Statistics and Data Analysis, 41, 561-575. · Zbl 1429.62235
[30] BIERNACKI, C., CELEUX, G., and GOVAERT, G. (2010), “Exact and Monte Carlo Calculations of Integrated Likelihoods for the Latent Class Model”, Journal of Statistical Planning and Inference, 140(11), 2991-3002. · Zbl 1203.62027
[31] BIERNACKI, C., CELEUX, G., GOVAERT, G., and LANGROGNET, F. (2006), “Model-Based Cluster and Discriminant Analysis with the MIXMOD Software”, Computational Statistics and Data Analysis, 51(2), 587-600. · Zbl 1157.62431
[32] BOUVEYRON, C., and BRUNET-SAUMARD, C. (2014), “Model-Based Clustering of High-Dimensional Data: A Review”, Computational Statistics and Data Analysis, 71, 52-78. · Zbl 1306.65033
[33] BOUVEYRON, C., CELEUX, G., and Girard, S. (2011), “Intrinsic Dimension Estimation by Maximum Likelihood in Isotropic Probabilistic PCA”, Pattern Recognition Letters, 32(14), 1706-1713.
[34] BOUVEYRON, C., GIRARD, S., and SCHMID, C. (2007a), “High-Dimensional Data Clustering”, Computational Statistics and Data Analysis, 52(1), 502-519. · Zbl 1452.62433
[35] BOUVEYRON, C., GIRARD, S., and SCHMID, C. (2007b), “High Dimensional Discriminant Analysis”, Communications in Statistics - Theory and Methods, 36(14), 2607-2623. · Zbl 1128.62072
[36] BRANCO, M.D., and DEY, D.K. (2001), “A General Class of Multivariate Skew-Elliptical Distributions”, Journal of Multivariate Analysis, 79, 99-113. · Zbl 0992.62047
[37] BROWNE, R.P., and MCNICHOLAS, P.D. (2012), “Model-Based Clustering and Classification of Data with Mixed Type”, Journal of Statistical Planning and Inference, 142(11), 2976-2984. · Zbl 1335.62093
[38] BROWNE, R.P., and MCNICHOLAS, P.D. (2014a), “Estimating Common Principal Components in High Dimensions”, Advances in Data Analysis and Classification, 8(2), 217-226.
[39] BROWNE, R.P., and MCNICHOLAS, P.D. (2014b), mixture: Mixture Models for Clustering and Classification, R Package Version 1.1.
[40] BROWNE, R.P., and P. D. MCNICHOLAS, P.D. (2014c), “Orthogonal Stiefel Manifold Optimization for Eigen-Decomposed Covariance Parameter Estimation in Mixture Models”, Statistics and Computing, 24(2), 203-210. · Zbl 1325.62008
[41] BROWNE, R.P., and MCNICHOLAS, P.D. (2015), “A Mixture of Generalized Hyperbolic Distributions”, Canadian Journal of Statistics, 43(2), 176-198. · Zbl 1320.62144
[42] BROWNE, R.P., MCNICHOLAS, P.D., and SPARLING, M.D. (2012), “Model-Based Learning Using a Mixture of Mixtures of Gaussian and Uniform Distributions”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(4), 814-817.
[43] CAGNONE, S., and VIROLI, C. (2012), “A Factor Mixture AnalysisModel for Multivariate Binary Data”, Statistical Modelling, 12(3), 257-277.
[44] CAMPBELL, N.A. (1984), “Mixture Models and Atypical Values”, Mathematical Geology, 16(5), 465-477.
[45] CARVALHO, C., CHANG, J., LUCAS, J., NEVINS, J., WANG, Q., and WEST, M. (2008), “High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics”, Journal of the American Statistical Association, 103(484), 1438-1456. · Zbl 1286.62091
[46] CATELL, R.B. (1949), “‘R’ and Other Coefficients of Pattern Similarity”, Psychometrika, 14, 279-298.
[47] CELEUX, G., and GOVAERT, G. (1991), “Clustering Criteria for Discrete Data and Latent Class Models”, Journal of Classification, 8(2), 157-176. · Zbl 0775.62150
[48] CELEUX, G., and GOVAERT, G. (1995), “Gaussian Parsimonious Clustering Models”, Pattern Recognition, 28(5), 781-793.
[49] CORDUNEANU, A., and BISHOP, C.M. (2001), “Variational Bayesian Model Selection for Mixture Distributions”, in Artificial Intelligence and Statistics, Los Altos, CA: Morgan Kaufmann, pp. 27-34.
[50] CORETTO, P., and HENNIG, C. (2015), “Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison with Other Methods for Robust Gaussian Clustering”, arXiv preprint arXiv:1405.1299v3. · Zbl 1442.62138
[51] CORMACK, R.M. (1971), “A Review of Classification (With Discussion)”, Journal of the Royal Statistical Society: Series A, 34, 321-367.
[52] DANG, U.J., BROWNE, R.P., and MCNICHOLAS, P.D. (2015), “Mixtures of Multivariate Power Exponential Distributions”, Biometrics, 71(4), 1081-1089. · Zbl 1419.62330
[53] DASGUPTA, A., and RAFTERY, A.E. (1998), “Detecting Features in Spatial Point Processes with Clutter ViaModel-Based Clustering”, Journal of the American Statistical Association, 93, 294-302. · Zbl 0906.62105
[54] DAY, N.E. (1969), “Estimating the Components of a Mixture of Normal Distributions”, Biometrika, 56, 463-474. · Zbl 0183.48106
[55] DE LA CRUZ-MESÍA, R., QUINTANA, R.A., and MARSHALL, G. (2008), “Model-Based Clustering for Longitudinal data”, Computational Statistics and Data Analysis, 52(3), 1441-1457. · Zbl 1452.62454
[56] DE VEAUX, R.D., and KRIEGER, A.M. (1990), “Robust Estimation of a Normal Mixture”, Statistics and Probability Letters, 10(1), 1-7.
[57] DEAN, N., RAFTERY, A.E., and SCRUCCA, L. (2012), clustvarsel: Variable Selection for Model-Based Clustering, R package version 2.0.
[58] DEMPSTER, A.P., LAIRD, N.M., and RUBIN, D.B. (1977), “Maximum Likelihood from Incomplete Data Via the EM Algorithm”, Journal of the Royal Statistical Society: Series B, 39(1), 1-38. · Zbl 0364.62022
[59] DI LASCIO, F.M.L., and GIANNERINI, S. (2012), “A Copula-Based Algorithm for Discovering Patterns of Dependent Observations”, Journal of Classification, 29(1), 50-75. · Zbl 1360.62250
[60] EDWARDS, A.W.F., and CAVALLI-SFORZA, L.L. (1965), “A Method for Cluster Analysis”, Biometrics, 21, 362-375.
[61] EVERITT, B.S., and HAND, D.J. (1981), Finite Mixture Distributions, Monographs on Applied Probability and Statistics, London: Chapman and Hall. · Zbl 0466.62018
[62] EVERITT, B.S., LANDAU, S., LEESE, M., and STAHL, D. (2011), Cluster Analysis (5th ed.), Chichester: John Wiley & Sons. · Zbl 1274.62003
[63] FABRIGAR, L.R., WEGENER, D.T., MACCALLUM, R.C., and STRAHAN, E.J. (1999), “Evaluating the Use of Exploratory Factor Analysis in Psychological Research”, Psychological Methods, 4(3), 272-299.
[64] FLURY, B. (1988), Common Principal Components and Related Multivariate Models, New York: Wiley. · Zbl 1081.62535
[65] FRALEY, C., and RAFTERY, A.E. (1998), “How Many Clusters? Which Clustering Methods? Answers Via Model-Based Cluster Analysis”, The Computer Journal, 41(8), 578-588. · Zbl 0920.68038
[66] FRALEY, C., and RAFTERY, A.E. (1999), “MCLUST: Software for Model-Based Cluster Analysis”, Journal of Classification, 16, 297-306. · Zbl 0951.91500
[67] FRALEY, C., and RAFTERY, A.E. (2002a), “MCLUST: Software for Model-Based Clustering, Density Estimation, and Discriminant Analysis”, Technical Report 415, University of Washington, Department of Statistics. · Zbl 1073.62545
[68] FRALEY, C., and RAFTERY, A.E. (2002b), “Model-Based Clustering, Discriminant Analysis, and Density Estimation”, Journal of the American Statistical Association, 97(458), 611-631. · Zbl 1073.62545
[69] FRANCZAK, B.C., BROWNE, R.P., and MCNICHOLAS, P.D. (2014), “Mixtures of Shifted Asymmetric Laplace Distributions”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(6), 1149-1157.
[70] FRIEDMAN, H.P., and RUBIN, J. (1967), “On Some Invariant Criteria for Grouping Data”, Journal of the American Statistical Association, 62, 1159-1178.
[71] FRITZ, H., GARCÍA-ESCUDERO, L.A., and MAYO-ISCAR, A. (2012), “tclust: An R Package for a Trimming Approach to Cluster Analysis”, Journal of Statistical Software, 47(12), 1-26.
[72] FRÜHWIRTH-SCHNATTER, S. (2006), Finite Mixture and Markov Switching Models, New York: Springer-Verlag. · Zbl 1108.62002
[73] GALIMBERTI, G., MONTANARI, A., and VIROLI, C. (2009), “Penalized Factor Mixture Analysis for Variable Selection in Clustered Data”, Computational Statistics and Data Analysis, 53, 4301-4310. · Zbl 1453.62094
[74] GARCÍA-ESCUDERO, L.A.,GORDALIZA,A., MATRN, C., andMAYO-ISCAR,A. (2008), “A General Trimming Approach to Robust Cluster Analysis”, The Annals of Statistics, 36(3), 1324-1345. · Zbl 1360.62328
[75] GERSHENFELD, N. (1997), “Nonlinear Inference and Cluster-Weighted Modeling”, Annals of the New York Academy of Sciences, 808(1), 18-24.
[76] GHAHRAMANI, Z., and HINTON, G.E. (1997), “The EM Algorithm for Factor Analyzers”, Technical Report CRG-TR-96-1, University of Toronto, Toronto, Canada.
[77] GOLLINI, I., and MURPHY, T.B. (2014), “Mixture of Latent Trait Analyzers for Model-Based Clustering of Categorical Data”, Statistics and Computing, 24(4), 569-588. · Zbl 1325.62122
[78] GÓMEZ, E., GÓMEZ-VIILEGAS, M.A., and MARIN, J.M. (1998), “A Multivariate Generalization of the Power Exponential Family of Distributions”, Communications in Statistics - Theory and Methods, 27(3), 589-600. · Zbl 0895.62053
[79] GÓMEZ-SÁ NCHEZ-MANZANO, E., GÓMEZ-VILLEGAS, M.A., and Marín, J.M. (2008), “Multivariate Exponential Power Distributions as Mixtures of Normal Distributions with Bayesian Applications”, Communications in Statistics - Theory and Methods, 37(6), 972-985. · Zbl 1135.62041
[80] GOODMAN, L. (1974), “Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models”, Biometrika, 61(2), 215-231. · Zbl 0281.62057
[81] GORDON, A.D. (1981), Classification, London: Chapman and Hall.
[82] GRESELIN, F., and INGRASSIA, S. (2010), “Constrained Monotone EM Algorithms for Mixtures of Multivariate t-Distributions”, Statistics and Computing, 20(1), 9-22.
[83] HATHAWAY, R.J. (1985), “A Constrained Formulation of Maximum Likelihood Estimation for Normal Mixture Distributions”, The Annals of Statistics, 13(2), 795-800. · Zbl 0576.62039
[84] HEISER, W.J. (1995), “Recent Advances in Descriptive Multivariate Analysis”, in Convergent Computation by Iterative Majorization: Theory and Applications in Multidimensional Data Analysis, ed. W.J. Krzanowski, Oxford: Oxford University Press, pp. 157-189.
[85] HENNIG, C. (2000), “Identifiablity of Models for Clusterwise Linear Regression”, Journal of Classification, 17(2), 273-296. · Zbl 1017.62058
[86] HENNIG, C. (2004), “Breakdown Points for Maximum Likelihood Estimators of Location-Scale Mixtures”, The Annals of Statistics, 32(4), 1313-1340. · Zbl 1047.62063
[87] HENNIG, C. (2015), “What are the True Clusters?”, Pattern Recognition Letters, 64, 53-62.
[88] HORN, J.L. (1965), “A Rationale and Technique for Estimating the Number of Factors in Factor Analysis”, Psychometrika, 30, 179-185. · Zbl 1367.62186
[89] HU, W. (2005), Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk, Ph. D. thesis, The Florida State University, Tallahassee.
[90] HUBER, P.J. (1964), “Robust Estimation of a Location Parameter”, The Annals of Mathematical Statistics, 35, 73-101. · Zbl 0136.39805
[91] HUBER, P.J. (1981), Robust Statistics, New York: Wiley. · Zbl 0536.62025
[92] HUMBERT, S., SUBEDI, S., COHN, J., ZENG, B., BI, Y.-M., CHEN, X., ZHU, T., MCNICHOLAS, P.D., and ROTHSTEIN, S.J. (2013), “Genome-Wide Expression Profiling of Maize in Response to Individual and Combined Water and Nitrogen Stresses”, BMC Genetics, 14(3).
[93] HUMPHREYS, L.G., and ILGEN, D.R. (1969), “Note on a Criterion for the Number of Common Factors”, Educational and Psychological Measurements, 29, 571-578.
[94] HUMPHREYS, L.G., and MONTANELLI, R.G. JR. (1975), “An Investigation of the Parallel Analysis Criterion for Determining the Number of Common Factors”, Multivariate Behavioral Research, 10, 193-205.
[95] INGRASSIA, S., MINOTTI, S.C., and PUNZO, A. (2014), “Model-Based Clustering Via Linear Cluster-Weighted Models”, Computational Statistics and Data Analysis, 71, 159-182. · Zbl 06975380
[96] INGRASSIA, S., MINOTTI, S.C., PUNZO, A., and VITTADINI, G. (2015), “The Generalized Linear Mixed Cluster-Weighted Model”, Journal of Classification, 32(1), 85-113. · Zbl 1331.62310
[97] INGRASSIA, S., MINOTTI, S.C., and VITTADINI, G. (2012), “Local Statistical Modeling Via the Cluster-Weighted Approach with Elliptical Distributions”, Journal of Classification, 29(3), 363-401. · Zbl 1360.62335
[98] INGRASSIA, S., and PUNZO, A. (2015), “Decision Boundaries for Mixtures of Regressions”, Journal of the Korean Statistical Society, 44(2), 295-306. · Zbl 1341.62181
[99] JAAKKOLA, T.S., and JORDAN, M.I. (2000), “Bayesian Parameter Estimation Via Variational Methods”, Statistics and Computing, 10(1), 25-37.
[100] JAIN, S., and NEAL, R.M. (2004), “A Split-Merge Markov Chain Monte Carlo Procedure for the Dirichlet Process Mixture Model”, Journal of Computational and Graphical Statistics, 13(1), 158-182.
[101] JAJUGA, K., and PAPLA, D. (2006), “Copula Functions in Model Based Clustering”, in From Data and Information Analysis to Knowledge Engineering, Studies in Classification, Data Analysis, and Knowledge Organization, eds. M. Spiliopoulou, R. Kruse, C. Borgelt, A.N¨urnberger, and W. Gaul, Berlin, Heidelberg: Springer, pp. 603-613.
[102] JORDAN, M.I., ZGHAHRAMANI, Z., JAAKKOLA, T.S., and SAUL, L.K. (1999), “An Introduction to Variational Methods for Graphical Models”, Machine Learning, 37, 183-233. · Zbl 0945.68164
[103] JÖRESKOG, K.G. (1990), “New Developments in LISREL: Analysis of Ordinal Variables Using Polychoric Correlations and Weighted Least Squares”, Quality and Quantity, 24(4), 387-404.
[104] KARLIS, D., and SANTOURIAN, A. (2009), “Model-Based Clustering with Non-Elliptically Contoured Distributions”, Statistics and Computing, 19(1), 73-83.
[105] KASS, R.E., and RAFTERY, A.E. (1995), “Bayes Factors”, Journal of the American Statistical Association, 90(430), 773-795. · Zbl 0846.62028
[106] KERIBIN, C. (2000), “Consistent Estimation of the Order of Mixture Models”, Sankhyā. The Indian Journal of Statistics. Series A, 62(1), 49-66. · Zbl 1081.62516
[107] KHARIN, Y. (1996), Robustness in Statistical Pattern Recognition, Dordrecht: Kluwer. · Zbl 0879.62054
[108] KOSMIDIS, I., and KARLIS, D. (2015), “Model-Based Clustering Using Copulas with Applications”, arXiv preprint arXiv:1404.4077v5. · Zbl 06652996
[109] KOTZ, S., KOZUBOWSKI, T.J., and PODGORSKI, K. (2001), The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance (1st ed.), Boston: Burkhäuser. · Zbl 0977.62003
[110] LAWLEY, D.N., and MAXWELL, A.E. (1962), “Factor Analysis as a Statistical Method”, Journal of the Royal Statistical Society: Series D, 12(3), 209-229. · Zbl 0161.39901
[111] LEE, S., and MCLACHLAN, G.J. (2011), “On the Fitting of Mixtures of Multivariate Skew \(t\)-distributions Via the EM Algorithm”, arXiv:1109.4706.
[112] LEE, S., and MCLACHLAN, G.J.(2014), “Finite Mixtures of Multivariate Skew t-Distributions: Some Recent and New Results”, Statistics and Computing, 24, 181-202. · Zbl 1325.62107
[113] LEE, S.X., and MCLACHLAN, G.J. (2013a), “Model-Based Clustering and Classification with Non-Normal Mixture Distributions”, Statistical Methods and Applications, 22(4), 427-454. · Zbl 1332.62209
[114] LEE, S.X., and MCLACHLAN, G.J. (2013b), “On Mixtures of Skew Normal and Skew t-Distributions”, Advances in Data Analysis and Classification, 7(3), 241-266. · Zbl 1273.62115
[115] LEISCH, F. (2004), “Flexmix: A General Framework For Finite Mixture Models And Latent Class Regression in R”, Journal of Statistical Software, 11(8), 1-18.
[116] LEROUX, B.G. (1992), “Consistent Estimation of a Mixing Distribution”, The Annals of Statistics, 20(3), 1350-1360. · Zbl 0763.62015
[117] LI, J. (2005), “Clustering Based on a Multi-Layer Mixture Model”, Journal of Computational and Graphical Statistics, 14(3), 547-568.
[118] LI, K.C. (1991), “Sliced Inverse Regression for Dimension Reduction (With Discussion)”, Journal of the American Statistical Association, 86, 316-342. · Zbl 0742.62044
[119] LI, K.C. (2000), “High Dimensional Data Analysis Via the SIR/PHD Approach”, Unpublished manuscript.
[120] LIN, T.-I. (2009), “Maximum Likelihood Estimation for Multivariate Skew Normal Mixture Models”, Journal of Multivariate Analysis, 100, 257-265. · Zbl 1152.62034
[121] LIN, T.-I. (2010), “Robust Mixture Modeling Using Multivariate Skew t Distributions”, Statistics and Computing, 20(3), 343-356.
[122] LIN, T.-I., MCLACHLAN, G.J., and LEE, S.X. (2016), “Extending Mixtures of Factor Models Using the Restricted Multivariate Skew-Normal Distribution”, Journal of Multivariate Analysis, 143, 398-413. · Zbl 1328.62378
[123] LIN, T.-I., MCNicholas, P.D., and HSIU, J.H. (2014), “Capturing Patterns Via Parsimonious t Mixture Models”, Statistics and Probability Letters, 88, 80-87. · Zbl 1369.62131
[124] LOPES, H.F., and WEST, M. (2004), “Bayesian Model Assessment in Factor Analysis”, Statistica Sinica, 14, 41-67. · Zbl 1035.62060
[125] MARBAC, M., BIERNACKI, C., and VANDEWALLE, V. (2014), “Finite Mixture Model of Conditional Dependencies Modes to Cluster Categorical Data”, arXiv preprint arXiv:1402.5103. · Zbl 1414.62253
[126] MARBAC, M., BIERNACKI, C., and VANDEWALLE, V. (2015), “Model-Based Clustering of Gaussian Copulas for Mixed Data”, arXiv preprint arXiv:1405.1299v3. · Zbl 1384.62198
[127] MARKATOU, M. (2000), “Mixture Models, Robustness, and the Weighted Likelihood Methodology”, Biometrics, 56(2), 483-486. · Zbl 1060.62511
[128] MAUGIS, C. (2009), “The Selvarclust Software”, www.math.univ-toulouse.fr/ maugis/SelvarClustHomepage.html.
[129] MAUGIS, C., CELEUX, G., and MARTIN-MAGNIETTE, M.-L. (2009a), “Variable Selection for Clustering with Gaussian Mixture Models”, Biometrics, 65(3), 701-709. · Zbl 1172.62021
[130] MAUGIS, C., CELEUX, G., and MARTIN-MAGNIETTE, M.-L. (2009b), “Variable Selection in Model-Based Clustering: A General Variable Role Modeling”, Computational Statistics and Data Analysis, 53(11), 3872-3882. · Zbl 1453.62154
[131] MCGRORY, C., and TITTERINGTON, D. (2007), “Variational Approximations in Bayesian Model Selection for Finite Mixture Distributions”, Computational Statistics and Data Analysis, 51(11), 5352-5367. · Zbl 1445.62050
[132] MCLACHLAN, G.J., and BASFORD, K.E. (1988), Mixture Models: Inference and Applications to Clustering, New York: Marcel Dekker Inc. · Zbl 0697.62050
[133] MCLACHLAN, G.J., BEAN, R.W., and JONES, L.B.-T. (2007), “Extension of the Mixture of Factor Analyzers Model to Incorporate the Multivariate t-Distribution”, Computational Statistics and Data Analysis, 51(11), 5327-5338. · Zbl 1445.62053
[134] MCLACHLAN, G.J., and KRISHNAN, T. (2008), The EM Algorithm and Extensions (2nd ed.), New York: Wiley. · Zbl 1165.62019
[135] MCLACHLAN, G.J., and PEEL, D. (1998), “Robust Cluster Analysis Via Mixtures of Multivariate t-Distributions”, in Lecture Notes in Computer Science, Volume 1451, Berlin: Springer-Verlag, pp. 658-666.
[136] MCLACHLAN, G.J., and PEEL, D. (2000a), Finite Mixture Models, New York: John Wiley & Sons. · Zbl 0963.62061
[137] MCLACHLAN, G.J., and PEEL, D. (2000b), “Mixtures of Factor Analyzers”, in Proceedings of the Seventh International Conference on Machine Learning, San Francisco, Morgan Kaufmann, pp. 599-606.
[138] MCNEIL, A.J., FREY, R., and EMBRECHTS, P. (2005), Quantitative Risk Management: Concepts, Techniques and Tools., Princeton: Princeton University Press. · Zbl 1089.91037
[139] MCNICHOLAS, P.D. (2013), “Model-Based Clustering and Classification Via Mixtures of Multivariate t-Distributions”, in Statistical Models for Data Analysis, Studies in Classification, Data Analysis, and Knowledge Organization, eds. P. Giudici, S. Ingrassia, and M. Vichi, Switzerland: Springer International Publishing.
[140] MCNICHOLAS, P.D. (2016), Mixture Model-Based Classification, Boca Raton FL: Chapman & Hall/CRC Press. · Zbl 1454.62005
[141] MCNICHOLAS, P.D., and BROWNE, R.P. (2013), “Discussion of ‘How to Find an Appropriate Clustering for Mixed-Type Variables with Application to Socio-Economic Stratification’ by Hennig and Liao”, Journal of the Royal Statistical Society: Series C, 62(3), 352-353.
[142] MCNICHOLAS, P.D., ELSHERBINY, A., MCDAID, A.F., and MURPHY, T.B. (2015), pgmm: Parsimonious Gaussian Mixture Models, R Package Version 1.2.
[143] MCNICHOLAS, P.D., JAMPANI, K.R., and SUBEDI, S. (2015), longclust: Model-Based Clustering and Classification for Longitudinal Data, R Package Version 1.2.
[144] MCNICHOLAS, P.D., and MURPHY, T.B. (2005), “Parsimonious Gaussian Mixture Models”, Technical Report 05/11, Department of Statistics, Trinity College Dublin, Dublin, Ireland.
[145] MCNICHOLAS, P.D., and MURPHY, T.B. (2008), “Parsimonious Gaussian Mixture Models”, Statistics and Computing, 18(3), 285-296.
[146] MCNICHOLAS, P.D., and MURPHY, T.B. (2010a), “Model-Based Clustering of Longitudinal Data”, Canadian Journal of Statistics, 38(1), 153-168. · Zbl 1190.62120
[147] MCNICHOLAS, P.D., and MURPHY, T.B. (2010b), “Model-Based Clustering of Microarray Expression Data Via Latent Gaussian Mixture Models”, Bioinformatics, 26(21), 2705-2712.
[148] MCNICHOLAS, P.D., and SUBEDI, S. (2012), “Clustering Gene Expression Time Course Data Using Mixtures of Multivariate t-Distributions”, Journal of Statistical Planning and Inference, 142(5), 1114-1127. · Zbl 1236.62068
[149] MCNICHOLAS, S.M., MCNICHOLAS, P.D., and BROWNE, R.P. (2014), “Mixtures of Variance-Gamma Distributions”, arxiv preprint arXiv:1309.2695v2. · Zbl 1381.62187
[150] MCPARLAND, D., GORMLEY, I.C., MCCORMICK, T.H., CLARK, S.J., KABUDULA, C.W., and COLLINSON, M.A. (2014), “Clustering South African Households Based on Their Asset Status Using Latent Variable Models”, The Annals of Applied Statistics, 8(2), 747-776. · Zbl 1454.62503
[151] MCQUITTY, L.L. (1956), “Agreement Analysis: A Method of Classifying Subjects According to Their Patterns of Responses”, British Journal of Statistical Psychology, 9, 5-16.
[152] MELNYKOV, V. (2016), “Model-Based Biclustering of Clickstream Data”, Computational Statistics and Data Analysis, 93, 31-45. · Zbl 06918686
[153] MENG, X.-L., and RUBIN, D.B. (1993), “Maximum Likelihood Estimation Via the ECM Algorithm: A General Framework”, Biometrika, 80, 267-278. · Zbl 0778.62022
[154] MENG, X.-L., and VAN DYK, D. (1997), “The EM Algorithm—An Old Folk Song Sung to a Fast New Tune (With Discussion)”, Journal of the Royal Statistical Society: Series B, 59(3), 511-567. · Zbl 1090.62518
[155] MONTANARI, A., and VIROLI, C. (2010a), “Heteroscedastic Factor Mixture Analysis”, Statistical Modelling, 10(4), 441-460.
[156] MONTANARI, A., and VIROLI, C. (2010b), “A Skew-Normal Factor Model for the Analysis of Student Satisfaction Towards University Courses”, Journal of Applied Statistics, 43, 473-487.
[157] MONTANARI, A., and VIROLI, C. (2011), “Maximum Likelihood Estimation of Mixture of Factor Analyzers”, Computational Statistics and Data Analysis, 55, 2712-2723. · Zbl 06917726
[158] MONTANELLI, R.G., JR., and HUMPHREYS, L.G. (1976), “Latent Roots of Random Data Correlation Matrices with Squared Multiple Correlations on the Diagonal: A Monte Carlo Study”, Psychometrika, 41, 341-348. · Zbl 0336.62040
[159] MORRIS, K., and MCNICHOLAS, P.D. (2013), “Dimension Reduction for Model-Based Clustering ViaMixtures of Shifted Asymmetric Laplace Distributions”, Statistics and Probability Letters, 83(9), 2088-2093, Erratum 2014, 85,168. · Zbl 1282.62153
[160] MORRIS, K., and MCNICHOLAS, P.D. (2016), “Clustering, Classification, Discriminant Analysis, and Dimension Reduction Via Generalized Hyperbolic Mixtures”, Computational Statistics and Data Analysis, 97, 133-150. · Zbl 06918497
[161] MORRIS, K., MCNICHOLAS, P.D., and SCRUCCA, L. (2013), “Dimension Reduction for Model-Based Clustering Via Mixtures of Multivariate t-Distributions”, Advances in Data Analysis and Classification, 7(3), 321-338. · Zbl 1273.62141
[162] MURRAY, P.M., BROWNE, R.B., and MCNICHOLAS, P.D. (2014a), “Mixtures of Skew-t Factor Analyzers”, Computational Statistics and Data Analysis, 77, 326-335. · Zbl 06984029
[163] MURRAY, P.M., MCNICHOLAS, P.D., and BROWNE, R.B. (2014b), “A Mixture of Common Skew-\(t\) Factor Analyzers”, Stat, 3(1), 68-82.
[164] MUTHEN, B., and ASPAROUHOV, T. (2006), “Item Response Mixture Modeling: Application to Tobacco Dependence Criteria”, Addictive Behaviors, 31, 1050-1066.
[165] O’HAGAN, A., MURPHY, T.B., GORMLEY, I.C., MCNICHOLAS, P.D., and KARLIS, D. (2016), “Clustering with the Multivariate Normal Inverse Gaussian Distribution”, Computational Statistics and Data Analysis, 93, 18-30. · Zbl 06918685
[166] ORCHARD, T., and WOODBURY, M.A. (1972), “A Missing Information Principle: Theory and Applications”, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Theory of Statistics, eds. L.M. Le Cam, J. Neyman, and E.L. Scott, Berkeley: University of California Press, pp. 697-715. · Zbl 0263.62023
[167] PAN, J., and MACKENZIE, G. (2003), “On Modelling Mean-Covariance Structures in Longitudinal Studies”, Biometrika, 90(1), 239-244. · Zbl 1039.62068
[168] PEARSON, K. (1894), “Contributions to the Mathematical Theory of Evolution”, Philosophical Transactions of the Royal Society, Part A, 185, 71-110. · JFM 25.0347.02
[169] PEEL, D., and MCLACHLAN, G.J. (2000), “Robust Mixture Modelling Using the t Distribution”, Statistics and Computing, 10(4), 339-348.
[170] POURAHMADI, M. (1999), “Joint Mean-Covariance Models with Applications to Longitudinal Data: Unconstrained Parameterisation”, Biometrika, 86(3), 677-690. · Zbl 0949.62066
[171] POURAHMADI, M. (2000), “Maximum Likelihood Estimation of Generalised Linear Models for Multivariate Normal Covariance Matrix”, Biometrika, 87(2), 425-435. · Zbl 0954.62091
[172] POURAHMADI, M., DANIELS, M., and PARK, T. (2007), “Simultaneous Modelling of the Cholesky Decomposition of Several Covariance Matrices”, Journal of Multivariate Analysis, 98, 568-587. · Zbl 1107.62043
[173] PUNZO, A. (2014), “Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model”, Statistical Modelling, 14(3), 257-291.
[174] PUNZO, A., and INGRASSIA, S. (2015a), “Clustering Bivariate Mixed-Type Data Via the Cluster-Weighted Model”, Computational Statistics. To appear. · Zbl 1347.65030
[175] PUNZO, A., and INGRASSIA, S. (2015b), “Parsimonious Generalized Linear Gaussian Cluster-Weighted Models”, in, Advances in Statistical Models for Data Analysis, Studies in Classification, Data Analysis and Knowledge Organization, Switzerland, eds. I. Morlini, T. Minerva, and M. Vichi, Springer International Publishing, pp. 201-209.
[176] PUNZO, A., and MCNICHOLAS, P.D. (2014a), “Robust Clustering in Regression Analysis Via the Contaminated Gaussian Cluster-Weighted Model”, arXiv preprint arXiv:1409.6019v1. · Zbl 1373.62316
[177] PUNZO, A., and MCNICHOLAS, P.D. (2014b), “Robust High-Dimensional Modeling with the Contaminated Gaussian Distribution”, arXiv preprint arXiv:1408.2128v1. · Zbl 1373.62316
[178] PUNZO, A., and MCNICHOLAS, P.D. (2016), “Parsimonious Mixtures of Multivariate Contaminated Normal Distributions”, Biometrical Journal. To appear. · Zbl 1353.62124
[179] R CORE TEAM (2015), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
[180] RAFTERY, A.E. (1995), “Bayesian Model Selection in Social Research (With Discussion)”, Sociological Methodology, 25, 111-193.
[181] RAFTERY, A.E., and DEAN, N. (2006), “Variable Selection for Model-Based Clustering”, Journal of the American Statistical Association, 101(473), 168-178. · Zbl 1118.62339
[182] RANALLI, M., and ROCCI, R. (2016),“Mixture Methods for Ordinal Data: A Pairwise Likelihood Approach”, Statistics and Computing, 26(1), 529-547. · Zbl 1342.62111
[183] RAO, C.R. (1952), Advanced Statistical Methods in Biometric Research, New York: John Wiley and Sons, Inc. · Zbl 0047.38601
[184] RAU, A., MAUGIS-RABUSSEAU, C., MARTIN-MAGNIETTE, M.-L, and CELEUX, G. (2015), “Co-expression Analysis of High-Throughput Transcriptome Sequencing Data with Poisson Mixture Models”, Bioinformatics, 31(9), 1420-1427.
[185] SAHU, K., DEY, D.K., and BRANCO, M.D. (2003), “A New Class of Multivariate Skew Distributions with Applications to Bayesian Regression Models”, Canadian Journal of Statistics, 31(2), 129-150. Corrigendum: Vol. 37 (2009), 301-302. · Zbl 1039.62047
[186] SCHÖNER, B. (2000), Probabilistic Characterization and Synthesis of Complex Data Driven Systems, Ph. D. thesis, Cambridge MA: MIT.
[187] SCHROETER, P., VESIN, J., LANGENBERGER, T., and MEULI, R. (1998), “Robust Parameter Estimation of Intensity Distributions for BrainMagnetic Resonance Images”, IEEE Transactions on Medical Imaging, 17(2), 172-186.
[188] SCHWARZ, G. (1978), “Estimating the Dimension of a Model”, The Annals of Statistics, 6(2), 461-464. · Zbl 0379.62005
[189] SCOTT, A.J., and SYMONS, M.J. (1971), “Clustering Methods Based on Likelihood Ratio Criteria”, Biometrics, 27, 387-397.
[190] SCRUCCA, L. (2010), “Dimension Reduction for Model-Based Clustering”, Statistics and Computing, 20(4), 471-484.
[191] SCRUCCA, L. (2014), “Graphical Tools for Model-Based Mixture Discriminant Analysis”, Advances in Data Analysis and Classification, 8(2), 147-165.
[192] SHIREMAN, E., STEINLEY, D., and BRUSCO, M.J. (2015), “Examining the Effect of Initialization Strategies on the Performance of Gaussian Mixture Modeling”, Behavior Research Methods.
[193] SPEARMAN, C. (1904), “The Proof and Measurement of Association Between Two Things”, American Journal of Psychology, 15, 72-101.
[194] SPEARMAN, C. (1927), The Abilities of Man: Their Nature and Measurement, London: MacMillan and Co., Limited. · JFM 53.0521.13
[195] STEANE, M.A., MCNICHOLAS, P.D., and YADA, R. (2012), “Model-Based Classification Via Mixtures of Multivariate t-Factor Analyzers”, Communications in Statistics - Simulation and Computation, 41(4), 510-523. · Zbl 1294.62142
[196] 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, Vol, 2, New York: Springer, pp. 113-130.
[197] STEPHENSEN, W. (1953), The Study of Behavior, Chicago: University of Chicago Press.
[198] SUBEDI, S., and MCNICHOLAS, P.D. (2014), “Variational Bayes Approximations for Clustering Via Mixtures of Normal Inverse Gaussian Distributions”, Advances in Data Analysis and Classification, 8(2), 167-193.
[199] SUBEDI, S., and MCNICHOLAS, P.D. (2016), “A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting”, arXiv preprint arXiv:1306.5368v2.
[200] SUBEDI, S., PUNZO, A., INGRASSIA, S., and MCNICHOLAS, P.D. (2013), “Clustering and Classification Via Cluster-Weighted Factor Analyzers”, Advances in Data Analysis and Classification, 7(1), 5-40. · Zbl 1271.62137
[201] SUBEDI, S., PUNZO, A., INGRASSIA, S., and MCNICHOLAS, P.D. (2015), “Cluster-Weighted t-Factor Analyzers for Robust Model-Based Clustering and Dimension Reduction”, Statistical Methods and Applications, 24(4), 623-649. · Zbl 1416.62362
[202] SUNDBERG, R. (1974), “Maximum Likelihood Theory for Incomplete Data from an Exponential Family”, Scandinavian Journal of Statistics, 1(2), 49-58. · Zbl 0284.62014
[203] TANG, Y., BROWNE, R.P., and MCNICHOLAS, P.D. (2015), “Model-Based Clustering of High-Dimensional Binary Data”, Computational Statistics and Data Analysis, 87, 84-101. · Zbl 06921468
[204] TESCHENDORFF, A., WANG, Y., BARBOSA-MORAIS, J., BRENTON, N., and CALDAS, C. (2005), “A Variational Bayesian Mixture Modelling Framework for Cluster Analysis of Gene-Expression Data”, Bioinformatics, 21(13), 3025-3033.
[205] TIEDEMAN, D.V. (1955), “On the Study of Types”, in Symposium on Pattern Analysis, ed. S.B. Sells, Randolph Field, Texas: Air University, U.S.A.F. School of Aviation Medicine, pp. 1-14.
[206] TIPPING, M.E. (1999), “Probabilistic Visualization of High-Dimensional Binary Data”, Advances in Neural Information Processing Systems (11), 592-598.
[207] TIPPING, M.E., and BISHOP, C.M. (1997), “Mixtures of Probabilistic Principal Component Analysers”, Technical Report NCRG/97/003, Aston University (Neural Computing Research Group), Birmingham, UK.
[208] TIPPING, M.E., and BISHOP, C.M. (1999), “Mixtures of Probabilistic Principal Component Analysers”, Neural Computation, 11(2), 443-482.
[209] TITTERINGTON, D.M., SMITH, A.F.M, and MAKOV, U.E. (1985), Statistical Analysis of Finite Mixture Distributions, Chichester: John Wiley & Sons. · Zbl 0646.62013
[210] TORTORA, C., MCNICHOLAS, P.D., and BROWNE, R.P. (2015), “A Mixture of Generalized Hyperbolic Factor Analyzers”, Advances in Data Analysis and Classification. To appear. · Zbl 1414.62278
[211] TRYON, R.C. (1939), Cluster Analysis, Ann Arbor: Edwards Brothers.
[212] TRYON, R.C. (1955), “Identification of Social Areas by Cluster Analysis”, in University of California Publications in Psychology, Volume 8, Berkeley: University of California Press.
[213] VERMUNT, J.K. (2003), “Multilevel Latent Class Models”, Sociological Methodology, 33(1), 213-239.
[214] VERMUNT, J.K. (2007), “Multilevel Mixture Item Response Theory Models: An Application in Education Testing”, in Proceedings of the 56th Session of the International Statistical Institute, Lisbon, Portugal, pp. 22-28.
[215] VIROLI, C. (2010), “Dimensionally Reduced Model-Based Clustering Through Mixtures of Factor Mixture Analyzers”, Journal of Classification, 27(3), 363-388. · Zbl 1337.62141
[216] VRAC, M., BILLARD, L., DIDAY, E., and CHEDIN, A. (2012), “Copula Analysis of Mixture Models”, Computational Statistics, 27(3), 427-457. · Zbl 1304.65087
[217] VRBIK, I., and MCNICHOLAS, P.D. (2012), “Analytic Calculations for the EM Algorithm for Multivariate Skew-t Mixture Models”, Statistics and Probability Letters, 82(6), 1169-1174. · Zbl 1244.65012
[218] VRBIK, I., and MCNICHOLAS, P.D. (2014), “Parsimonious Skew Mixture Models for Model-Based Clustering and Classification”, Computational Statistics and Data Analysis, 71, 196-210. · Zbl 06975382
[219] VRBIK, I., and MCNICHOLAS, P.D. (2015), “Fractionally-Supervised Classification”, Journal of Classification, 32(3), 359-381. · Zbl 1331.62319
[220] WANG, Q., CARVALHO, C., LUCAS, J., and WEST, M. (2007), “BFRM: Bayesian Factor Regression Modelling”, Bulletin of the International Society for Bayesian Analysis, 14(2), 4-5.
[221] WATERHOUSE, S., MACKAY, D., and ROBINSON, T. (1996), “Bayesian Methods for Mixture of Experts”, in Advances in Neural Information Processing Systems, Vol. 8. Cambridge, MA: MIT Press.
[222] WEI, Y., and MCNICHOLAS, P.D. (2015), “Mixture Model Averaging for Clustering”, Advances in Data Analysis and Classification, 9(2), 197-217. · Zbl 1414.62283
[223] WEST, M. (2003), “Bayesian Factor Regression Models in the ‘Large \(p\), Small \(n\)’ Paradigm”, in Bayesian Statistics, Volume 7, eds. J.M. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith, and M. West, Oxford: Oxford University Press, pp. 723-732.
[224] WOLFE, J.H. (1963), “Object Cluster Analysis of Social Areas”, Master’s thesis, University of California, Berkeley.
[225] WOLFE, J.H. (1965), “A Computer Program for the Maximum Likelihood Analysis of Types”, Technical Bulletin 65-15, U.S. Naval Personnel Research Activity.
[226] WOLFE, J.H. (1970), “Pattern Clustering by Multivariate Mixture Analysis”, Multivariate Behavioral Research, 5, 329-350.
[227] YOSHIDA, R., HIGUCHI, T., and IMOTO, S. (2004), “A Mixed Factors Model for Dimension Reduction and Extraction of a Group Structure in Gene Expression Data”, in Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference, pp. 161-172.
[228] YOSHIDA, R., HIGUCHI, T., IMOTO, S., and MIYANO, S. (2006), “ArrayCluster: An Analytic Tool for Clustering, Data Visualization and Module Finder on Gene Expression Profiles”, Bioinformatics, 22, 1538-1539.
[229] ZHOU, H., and LANGE, K.L. (2010), “On the Bumpy Road to the Dominant Mode”, Scandinavian Journal of Statistics, 37(4), 612-631. · Zbl 1226.62027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.