1932

Abstract

Clustering is the task of automatically gathering observations into homogeneous groups, where the number of groups is unknown. Through its basis in a statistical modeling framework, model-based clustering provides a principled and reproducible approach to clustering. In contrast to heuristic approaches, model-based clustering allows for robust approaches to parameter estimation and objective inference on the number of clusters, while providing a clustering solution that accounts for uncertainty in cluster membership. The aim of this article is to provide a review of the theory underpinning model-based clustering, to outline associated inferential approaches, and to highlight recent methodological developments that facilitate the use of model-based clustering for a broad array of data types. Since its emergence six decades ago, the literature on model-based clustering has grown rapidly, and as such, this review provides only a selection of the bibliography in this dynamic and impactful field.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-statistics-033121-115326
2023-03-09
2024-06-21
Loading full text...

Full text loading...

/deliver/fulltext/statistics/10/1/annurev-statistics-033121-115326.html?itemId=/content/journals/10.1146/annurev-statistics-033121-115326&mimeType=html&fmt=ahah

Literature Cited

  1. Ahlquist JS, Breunig C. 2012. Model-based clustering and typologies in the social sciences. Political Anal. 20:92–112
    [Google Scholar]
  2. Airoldi EM, Blei DM, Fienberg SE, Xing EP. 2008. Mixed-membership stochastic blockmodels. J. Mach. Learn. Res. 9:651981–2014
    [Google Scholar]
  3. Aitkin M, Rubin DB. 1985. Estimation and hypothesis testing in finite mixture models. J. R. Stat. Soc. Ser. B 47:167–75
    [Google Scholar]
  4. Antonazzo F, Biernacki C, Keribin C 2021. A binned technique for scalable model-based clustering on huge datasets. Book of Short Papers of the 5th International Workshop on Models and Learning for Clustering and Classification (MBC2 2020), Catania, Italy S Ingrassia, A Punzo, R Rocci 11–16 Milan: Ledizioni
    [Google Scholar]
  5. Banfield JD, Raftery AE. 1989. Model-based Gaussian and non-Gaussian clustering. Tech. Rep. 186 Dep. Stat., Univ. Washington Seattle, WA:
    [Google Scholar]
  6. Banfield JD, Raftery AE. 1993. Model-based Gaussian and non-Gaussian clustering. Biometrics 49:3803–21
    [Google Scholar]
  7. Baudry JP, Raftery AE, Celeux G, Lo K, Gottardo R. 2010. Combining mixture components for clustering. J. Comput. Graph. Stat. 19:332–53
    [Google Scholar]
  8. Benaglia T, Chauveau D, Hunter DR, Young D 2009. mixtools: An R package for analyzing finite mixture models. J. Stat. Softw. 32:61–29
    [Google Scholar]
  9. Bensmail H, Celeux G, Raftery AE, Robert CP. 1997. Inference in model-based cluster analysis. Stat. Comput. 7:11–10
    [Google Scholar]
  10. Benter W 1994. Computer based horse race handicapping and wagering systems: a report. Efficiency of Racetrack Betting Markets WT Ziemba, VS Lo, DB Haush 183–98 Singapore: World Sci.
    [Google Scholar]
  11. Biernacki C, Celeux G, Govaert G. 2000. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans. Pattern Anal. 22:7719–25
    [Google Scholar]
  12. Biernacki C, Jacques J 2013. A generative model for rank data based on insertion sort algorithm. Comput. Stat. Data Anal. 58:162–76
    [Google Scholar]
  13. Binder DA. 1978. Bayesian cluster analysis. Biometrika 65:131–38
    [Google Scholar]
  14. Bouveyron C, Celeux G, Murphy TB, Raftery AE. 2019. Model-Based Clustering and Classification for Data Science: With Applications in R Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  15. Bouveyron C, Jacques J 2011. Model-based clustering of time series in group-specific functional subspaces. Adv. Data Anal. Classif. 5:4281–300
    [Google Scholar]
  16. Busse LM, Orbanz P, Buhmann JM. 2007. Cluster analysis of heterogeneous rank data. Proceedings of the 24th International Conference on Machine Learning, ICML '07113–20 New York: ACM
    [Google Scholar]
  17. Cagnone S, Viroli C. 2012. A factor mixture analysis model for multivariate binary data. Stat. Model. 12:3257–77
    [Google Scholar]
  18. Carpaneto G, Toth P. 1980. Algorithm 548: Solution of the assignment problem [H]. ACM Trans. Math. Softw. 6:1104–11
    [Google Scholar]
  19. Celeux G, Govaert G. 1995. Gaussian parsimonious clustering models. Pattern Recognit. 28:5781–93
    [Google Scholar]
  20. Celeux G, Hurn M, Robert CP. 2000. Computational and inferential difficulties with mixture posterior distributions. J. Am. Stat. Assoc. 95:451957–70
    [Google Scholar]
  21. Celeux G, Martin-Magniette ML, Maugis C, Raftery AE. 2011. Letter to the editor: “A framework for feature selection in clustering. .” J. Am. Stat. Assoc. 106:493383
    [Google Scholar]
  22. Celeux G, Martin-Magniette ML, Maugis-Rabusseau C, Raftery AE. 2014. Comparing model selection and regularization approaches to variable selection in model-based clustering. J. Soc. Fr. Stat. 155:257–71
    [Google Scholar]
  23. Czekanowski J. 1909. Zur differential-diagnose der Neadertalgruppe. Korresp. Bl. Dtsch. Ges. Anthropol. Ethnol. Urgesch. 40:44–47
    [Google Scholar]
  24. Day NE. 1969. Estimating the components of a mixture of two normal distributions. Biometrika 56:3463–74
    [Google Scholar]
  25. Dean N, Raftery AE. 2010. Latent class analysis variable selection. Ann. Inst. Stat. Math. 62:111–35
    [Google Scholar]
  26. Dempster AP, Laird NM, Rubin DB. 1977. Maximum likelihood from incomplete data via the EM algorithm. With discussion. J. R. Stat. Soc. Ser. B 39:11–38
    [Google Scholar]
  27. Diebolt J, Robert CP. 1994. Estimation of finite mixture distributions through Bayesian sampling. J. R. Stat. Soc. Ser. B 56:2363–75
    [Google Scholar]
  28. Erosheva EA, Matsueda RL, Telesca D. 2014. Breaking bad: two decades of life-course data analysis in criminology, developmental psychology, and beyond. Annu. Rev. Stat. Appl. 1:301–32
    [Google Scholar]
  29. Everitt B. 1984. An Introduction to Latent Variable Models London: Chapman and Hall
    [Google Scholar]
  30. Ferguson TS. 1973. A Bayesian analysis of some nonparametric problems. Ann. Stat. 1:209–30
    [Google Scholar]
  31. Fop M, Murphy TB. 2017. LCAvarsel: variable selection for latent class analysis. R Package version 1.1
    [Google Scholar]
  32. Fop M, Murphy TB. 2018. Variable selection methods for model-based clustering. Stat. Surv. 12:18–65
    [Google Scholar]
  33. Fop M, Murphy TB, Scrucca L. 2019. Model-based clustering with sparse covariance matrices. Stat. Comput. 29:4791–819
    [Google Scholar]
  34. Fop M, Smart K, Murphy TB. 2017. Variable selection for latent class analysis with application to low back pain diagnosis. Ann. Appl. Stat. 11:2085–115
    [Google Scholar]
  35. Fraley C, Raftery AE. 1998. How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput. J. 41:8578–88
    [Google Scholar]
  36. Fraley C, Raftery AE. 2002. Model-based clustering, discriminant analysis and density estimation. J. Am. Stat. Assoc. 97:458611–31
    [Google Scholar]
  37. Frühwirth-Schnatter S. 2006. Finite Mixture and Markov Switching Models. New York: Springer
    [Google Scholar]
  38. Frühwirth-Schnatter S 2011. Dealing with label switching under model uncertainty. Mixtures: Estimation and Application K Mengersen, CP Robert, DM Titterington 213–39 New York: Wiley
    [Google Scholar]
  39. Frühwirth-Schnatter S, Celeux G, Robert CP. 2019. Handbook of Mixture Analysis Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  40. Frühwirth-Schnatter S, Malsiner-Walli G. 2019. From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering. Adv. Data Anal. Classif. 13:133–64
    [Google Scholar]
  41. García-Escudero LA, Gordaliza A, Greselin F, Ingrassia S, Mayo-Iscar A. 2018. Eigenvalues and constraints in mixture modeling: geometric and computational issues. Adv. Data Anal. Classif. 12:2203–33
    [Google Scholar]
  42. García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A. 2008. A general trimming approach to robust cluster analysis. Ann. Stat. 36:31324–45
    [Google Scholar]
  43. Ghahramani Z, Hinton GE. 1996. The EM algorithm for mixtures of factor analyzers. Tech. Rep. CRG-TR-96-1 Dep. Comput. Sci., Univ. Toronto, Toronto Can:.
    [Google Scholar]
  44. Gollini I 2019. lvm4net: Latent variable models for networks. R Package version 0.3
    [Google Scholar]
  45. Gollini I, Murphy TB. 2014. Mixture of latent trait analyzers for model-based clustering of categorical data. Stat. Comput. 24:4569–88
    [Google Scholar]
  46. Gormley IC, Frühwirth-Schnatter S 2019. Mixture of experts models. Handbook of Mixture Analysis S Frühwirth-Schnatter, G Celeux, CP Robert 271–307 Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  47. Gormley IC, Murphy TB. 2006. Analysis of Irish third-level college applications data. J. R. Stat. Soc. Ser. A 169:2361–79
    [Google Scholar]
  48. Gormley IC, Murphy TB. 2008. Exploring voting blocs within the Irish electorate: a mixture modeling approach. J. Am. Stat. Assoc. 103:4831014–27
    [Google Scholar]
  49. Gormley IC, Murphy TB. 2010. A mixture of experts latent position cluster model for social network data. Stat. Methodol. 7:3385–405
    [Google Scholar]
  50. Gormley IC, Murphy TB. 2019. MEclustnet: the mixture of experts latent position cluster model for network data. R Package version 1.2.2
    [Google Scholar]
  51. Grün B, Leisch F. 2007. Fitting finite mixtures of generalized linear regressions in R. Comput. Stat. Data Anal. 51:115247–52
    [Google Scholar]
  52. Grün B, Leisch F. 2008. FlexMix version 2: Finite mixtures with concomitant variables and varying and constant parameters. J. Stat. Softw. 28:41–35
    [Google Scholar]
  53. Handcock MS, Raftery AE, Tantrum JM. 2007. Model-based clustering for social networks. J. R. Stat. Soc. Ser. A 170:21–22
    [Google Scholar]
  54. Hejblum BP, Alkhassim C, Gottardo R, Caron F, Thiébaut R 2019. Sequential Dirichlet process mixtures of multivariate skew t-distributions for model-based clustering of flow cytometry data. Ann. Appl. Stat. 13:1638–60
    [Google Scholar]
  55. Hennig C. 2010. Methods for merging Gaussian mixture components. Adv. Data Anal. Classif. 4:13–34
    [Google Scholar]
  56. Hunt L, Jorgensen M. 1999. Theory & methods: mixture model clustering using the MULTIMIX program. Aust. N. Z. J. Stat. 41:2154–71
    [Google Scholar]
  57. Hunt L, Jorgensen M. 2003. Mixture model clustering for mixed data with missing information. Comput. Stat. Data Anal. 41:3–4429–40
    [Google Scholar]
  58. Ishwaran H, James LF. 2001. Gibbs sampling methods for stick-breaking priors. J. Am. Stat. Assoc. 96:453161–73
    [Google Scholar]
  59. Jacobs RA, Jordan MI, Nowlan SJ, Hinton GE. 1991. Adaptive mixtures of local experts. Neural Comput. 3:179–87
    [Google Scholar]
  60. Jacques J, Preda C. 2014. Model-based clustering for multivariate functional data. Comput. Stat. Data Anal. 71:92–106
    [Google Scholar]
  61. Jasra A, Holmes CC, Stephens DA. 2005. Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Stat. Sci. 20:150–67
    [Google Scholar]
  62. Jordan MI, Jacobs RA. 1994. Hierarchical mixtures of experts and the EM algorithm. Neural Comput. 6:2181–214
    [Google Scholar]
  63. Kalli M, Griffin JE, Walker SG. 2011. Slice sampling mixture models. Stat. Comput. 21:193–105
    [Google Scholar]
  64. Karlis D 2019. Mixture modelling of discrete data. Handbook of Mixture Analysis S Frühwirth-Schnatter, G Celeux, CP Robert 193–218 Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  65. Karlis D, Meligkotsidou L. 2007. Finite mixtures of multivariate Poisson distributions with application. J. Stat. Plan. Inference 137:61942–60
    [Google Scholar]
  66. Keribin C. 2000. Consistent estimation of the order of mixture models. Sankhya A 62:149–66
    [Google Scholar]
  67. Krivitsky PN, Handcock MS. 2008. Fitting latent cluster models for networks with latentnet. J. Stat. Softw. 24:51–23
    [Google Scholar]
  68. Krivitsky PN, Handcock MS. 2020. latentnet: Latent position and cluster models for statistical networks. R Package version 2.10.5
    [Google Scholar]
  69. Krivitsky PN, Handcock MS, Raftery AE, Hoff PD. 2009. Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Soc. Netw. 31:3204–13
    [Google Scholar]
  70. Latouche P, Birmelé E, Ambroise C. 2011. Overlapping stochastic block models with application to the French political blogosphere. Ann. Appl. Stat. 5:1309–36
    [Google Scholar]
  71. Lazarsfeld PF 1950a. The logical and mathematical foundations of latent structure analysis. Studies in Social Psychology in World War II. Vol. IV: Measurement and Prediction SA Stouffer, L Guttman, EA Suchman, PF Lazarsfeld 362–412 Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  72. Lazarsfeld PF 1950b. Some latent structures. Studies in Social Psychology in World War II. Vol. IV: Measurement and Prediction SA Stouffer, L Guttman, EA Suchman, PF Lazarsfeld 413–73 Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  73. Lebret R, Iovleff S, Langrognet F, Biernacki C, Celeux G, Govaert G. 2015. Rmixmod: the R package of the model-based unsupervised, supervised, and semi-supervised classification mixmod library. J. Stat. Softw. 67:61–29
    [Google Scholar]
  74. Lee SX, McLachlan GJ. 2013. Model-based clustering and classification with non-normal mixture distributions. Stat. Methods Appl. 22:4427–54
    [Google Scholar]
  75. Lee SX, McLachlan GJ. 2018. EMMIXcskew: an R package for the fitting of a mixture of canonical fundamental skew t-distributions. J. Stat. Softw. 83:31–32
    [Google Scholar]
  76. Lee SX, McLachlan GJ. 2022. An overview of skew distributions in model-based clustering. J. Multivar. Anal. 188:104853
    [Google Scholar]
  77. Leisch F. 2004. FlexMix: a general framework for finite mixture models and latent class regression in R. J. Stat. Softw. 11:81–18
    [Google Scholar]
  78. Linnaeus C. 1753. Species Plantarum Stockholm: Laurentii Salvii. , 1st ed..
    [Google Scholar]
  79. Linzer DA, Lewis JB. 2011. poLCA: An R package for polytomous variable latent class analysis. J. Stat. Softw. 42:101–29
    [Google Scholar]
  80. Liu Q, Crispino M, Scheel I, Vitelli V, Frigessi A. 2019. Model-based learning from preference data. Annu. Rev. Stat. Appl. 6:329–54
    [Google Scholar]
  81. Maier LM, Anderson DE, De Jager PL, Wicker LS, Hafler DA. 2007. Allelic variant in CTLA4 alters T cell phosphorylation patterns. PNAS 104:4718607–12
    [Google Scholar]
  82. Mallows CL. 1957. Non-null ranking models. Biometrika 44:1/2114–30
    [Google Scholar]
  83. Malsiner-Walli G, Frühwirth-Schnatter S, Grün B. 2016. Model-based clustering based on sparse finite Gaussian mixtures. Stat. Comput. 26:303–24
    [Google Scholar]
  84. Maugis C, Celeux G, Martin-Magniette ML. 2009a. Variable selection for clustering with Gaussian mixture models. Biometrics 65:3701–9
    [Google Scholar]
  85. Maugis C, Celeux G, Martin-Magniette ML. 2009b. Variable selection in model-based clustering: a general variable role modeling. Comput. Stat. Data Anal. 53:113872–82
    [Google Scholar]
  86. McLachlan G, Peel D. 1998. Robust cluster analysis via mixtures of multivariate t-distributions. Advances in Pattern Recognition A Amin, D Dori, P Pudil, H Freeman 658–66 Berlin: Springer-Verlag
    [Google Scholar]
  87. McLachlan G, Peel D. 2000. Finite Mixture Models. New York: Wiley-Interscience
    [Google Scholar]
  88. McLachlan GJ, Basford KE. 1988. Mixture Models: Inference and Applications to Clustering New York: Marcel Dekker
    [Google Scholar]
  89. McLachlan GJ, Bean RW, Peel D. 2002. A mixture model–based approach to the clustering of microarray expression data. Bioinformatics 18:3413–22
    [Google Scholar]
  90. McLachlan GJ, Krishnan T. 2008. The EM Algorithm and Extensions New York: Wiley-Interscience. , 2nd ed..
    [Google Scholar]
  91. McLachlan GJ, Lee SX, Rathnayake SI. 2019. Finite mixture models. Annu. Rev. Stat. Appl. 6:355–78
    [Google Scholar]
  92. McLachlan GJ, Peel D, Basford KE, Adams P 1999. The EMMIX software for the fitting of mixtures of normal and t-components. J. Stat. Softw. 4:21–14
    [Google Scholar]
  93. McLachlan GJ, Peel D, Bean RW. 2003. Modelling high-dimensional data by mixtures of factor analyzers. Comput. Stat. Data Anal. 41:3–4379–88
    [Google Scholar]
  94. McNicholas PD 2016a. Mixture Model–Based Classification Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  95. McNicholas PD. 2016b. Model-based clustering. J. Classif. 33:331–73
    [Google Scholar]
  96. McNicholas PD, ElSherbiny A, McDaid AF, Murphy TB. 2021. pgmm: Parsimonious Gaussian mixture models. R Package version 1.2.5
    [Google Scholar]
  97. McNicholas PD, Jampani KR, Subedi S. 2019. longclust: Model-based clustering and classification for longitudinal data. R Package version 1.2.3
    [Google Scholar]
  98. McNicholas PD, Murphy TB. 2008. Parsimonious Gaussian mixture models. Stat. Comput. 18:3285–96
    [Google Scholar]
  99. McNicholas PD, Murphy TB. 2010. Model-based clustering of longitudinal data. Can. J. Stat. 38:1153–68
    [Google Scholar]
  100. McParland D, Gormley IC. 2016. Model based clustering for mixed data: clustMD. Adv. Data Anal. Classif. 10:2155–69
    [Google Scholar]
  101. McParland D, Gormley IC. 2017. clustMD: Model based clustering for mixed data. R Package version 1.2.1
    [Google Scholar]
  102. McParland D, Gormley IC, McCormick TH, Clark SJ, Kabudula CW, Collinson MA. 2014. Clustering South African households based on their asset status using latent variable models. Ann. Appl. Stat. 8:2747–76
    [Google Scholar]
  103. McParland D, Murphy TB 2019. Mixture modelling of high-dimensional data. Handbook of Mixture Analysis S Frühwirth-Schnatter, G Celeux, CP Robert 39–70 Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  104. McParland D, Phillips CM, Brennan L, Roche HM, Gormley IC. 2017. Clustering high-dimensional mixed data to uncover sub-phenotypes: joint analysis of phenotypic and genotypic data. Stat. Med. 36:284548–69
    [Google Scholar]
  105. Melnykov V. 2016a. ClickClust: an R package for model-based clustering of categorical sequences. J. Stat. Softw. 74:91–34
    [Google Scholar]
  106. Melnykov V. 2016b. Model-based biclustering of clickstream data. Comput. Stat. Data Anal. 93:31–45
    [Google Scholar]
  107. Mengersen KL, Robert CP 1996. Testing for mixtures: a Bayesian entropic approach. Bayesian Statistics 5: Proceedings of the Fifth Valencia International Meeting JM Bernardo, JO Berger, AP Dawid, AFM Smith 255–76 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  108. Mollica C, Tardella L. 2014. Epitope profiling via mixture modeling of ranked data. Stat. Med. 33:213738–58
    [Google Scholar]
  109. Mollica C, Tardella L. 2017. Bayesian Plackett-Luce mixture models for partially ranked data. Psychometrika 82:2442–58
    [Google Scholar]
  110. Mollica C, Tardella L. 2020. PLMIX: an R package for modelling and clustering partially ranked data. J. Stat. Comput. Simul. 90:5925–59
    [Google Scholar]
  111. Mollica C, Tardella L. 2021. Bayesian analysis of ranking data with the extended Plackett-Luce model. Stat. Methods Appl. 30:1175–94
    [Google Scholar]
  112. Montanari A, Viroli C. 2010. Heteroscedastic factor mixture analysis. Stat. Model. 10:4441–60
    [Google Scholar]
  113. Morris K, McNicholas PD. 2016. Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures. Comput. Stat. Data Anal. 97:133–50
    [Google Scholar]
  114. Murphy K, Murphy TB. 2020. Gaussian parsimonious clustering models with covariates and a noise component. Adv. Data Anal. Classif. 14:2293–325
    [Google Scholar]
  115. Murphy K, Murphy TB, Piccarreta R, Gormley IC. 2021. Clustering longitudinal life-course sequences using mixtures of exponential-distance models. J. R. Stat. Soc. Ser. A 184:41414–51
    [Google Scholar]
  116. Murphy K, Murphy TB, Piccarreta R, Gormley IC. 2022. MEDseq: Mixtures of exponential-distance models with covariates. R Package version 1.3.3
    [Google Scholar]
  117. Murphy K, Viroli C, Gormley IC. 2020. Infinite mixtures of infinite factor analysers. Bayesian Anal. 15:3937–63
    [Google Scholar]
  118. Murphy TB, Martin D. 2003. Mixtures of distance-based models for ranking data. Comput. Stat. Data Anal. 41:3–4645–55
    [Google Scholar]
  119. Murray PM, Browne RP, McNicholas PD. 2020. Mixtures of hidden truncation hyperbolic factor analyzers. J. Classif. 37:2366–79
    [Google Scholar]
  120. Murtagh F, Raftery AE. 1984. Fitting straight lines to point patterns. Pattern Recognit. 17:5479–83
    [Google Scholar]
  121. Ng TLJ, Murphy TB. 2021. Model-based clustering of count processes. J. Classif. 38:2188–211
    [Google Scholar]
  122. Nowicki K, Snijders TAB. 2001. Estimation and prediction of stochastic blockstructures. J. Am. Stat. Assoc. 96:4551077–87
    [Google Scholar]
  123. O'Hagan A, Murphy TB, Gormley IC. 2012. Computational aspects of fitting mixture models via the expectation–maximization algorithm. Comput. Stat. Data Anal. 56:123843–64
    [Google Scholar]
  124. O'Hagan A, Murphy TB, Gormley IC, McNicholas PD, Karlis D. 2016. Clustering with the multivariate normal inverse Gaussian distribution. Comput. Stat. Data Anal. 93:18–30
    [Google Scholar]
  125. Papastamoulis P. 2018. Overfitting Bayesian mixtures of factor analyzers with an unknown number of components. Comput. Stat. Data Anal. 124:220–34
    [Google Scholar]
  126. Pearson K. 1894. Contributions to the mathematical theory of evolution. Philos. Trans. R. Soc. A 185:71–110
    [Google Scholar]
  127. Plackett RL. 1975. The analysis of permutations. J. R. Stat. Soc. Ser. C 24:2193–202
    [Google Scholar]
  128. Pyne S, Hu X, Wang K, Rossin E, Lin TI et al. 2009. Automated high-dimensional flow cytometric data analysis. PNAS 106:218519–24
    [Google Scholar]
  129. Quintana FA, Iglesias PL. 2003. Bayesian clustering and product partition models. J. R. Stat. Soc. Ser. B 65:2557–74
    [Google Scholar]
  130. Raftery AE 1996. Hypothesis testing and model selection. Markov Chain Monte Carlo in Practice WR Gilks, S Richardson, DJ Spiegelhalter 163–88 London: Chapman and Hall
    [Google Scholar]
  131. Raftery AE, Dean N. 2006. Variable selection for model-based clustering. J. Am. Stat. Assoc. 101:473168–78
    [Google Scholar]
  132. Raftery AE, Newton M, Satagopan J, Krivitsky P 2007. Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Bayesian Statistics 8 JM Bernardo, MJ Bayarri, JO Berger, AP Dawid, D Heckerman et al.1–45 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  133. Richardson S, Green PJ. 1997. On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Stat. Soc. Ser. B 59:4731–92
    [Google Scholar]
  134. Roick T, Karlis D, McNicholas PD. 2021. Clustering discrete-valued time series. Adv. Data Anal. Classif. 15:1209–29
    [Google Scholar]
  135. Rost J. 1990. Rasch models in latent classes: an integration of two approaches to item analysis. Appl. Psychol. Meas. 14:3271–82
    [Google Scholar]
  136. Rousseau J, Mengersen K. 2011. Asymptotic behaviour of the posterior distribution in overfitted mixture models. J. R. Stat. Soc. Ser. B 73:5689–710
    [Google Scholar]
  137. Salter-Townshend M, White A, Gollini I, Murphy TB. 2012. Review of statistical network analysis: models, algorithms, and software. Stat. Anal. Data Min. 5:4243–64
    [Google Scholar]
  138. Schwarz G. 1978. Estimating the dimension of a model. Ann. Stat. 6:2461–64
    [Google Scholar]
  139. Scrucca L, Fop M, Murphy TB, Raftery AE. 2016. mclust 5: Clustering, classification and density estimation using Gaussian finite mixture models. R J. 8:1289–317
    [Google Scholar]
  140. Scrucca L, Fraley C, Murphy TB, Raftery AE. 2022. Model-Based Clustering, Classification and Density Estimation Using mclust in R Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  141. Scrucca L, Raftery AE. 2018. clustvarsel: A package implementing variable selection for Gaussian model-based clustering in R. J. Stat. Softw. 84:11–28
    [Google Scholar]
  142. Sneath PHA. 1957. The application of computers to taxonomy. J. Gen. Microbiol. 17:201–6
    [Google Scholar]
  143. Snijders TAB, Nowicki K. 1997. Estimation and prediction for stochastic blockmodels for graphs with latent block structure. J. Classif. 14:175–100
    [Google Scholar]
  144. Sokal RR, Michener CD. 1958. A statistical method for evaluating systematic relationships. Univ. Kans. Sci. Bull. 38:1409–38
    [Google Scholar]
  145. Sørensen Ø, Crispino M, Liu Q, Vitelli V. 2020. BayesMallows: an R package for the Bayesian Mallows model. R J. 12:1324–42
    [Google Scholar]
  146. Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. 2002. Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B 64:4583–639
    [Google Scholar]
  147. Steele RJ, Raftery AE. 2010. Performance of Bayesian model selection criteria for Gaussian mixture models. In Frontiers of Statistical Decision Making and Bayesian Analysis ed. M-H Chen, P Müller, D Sun, K Ye, DK Dey, pp. 113–30. New York: Springer
    [Google Scholar]
  148. Stephens M. 2000a. Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods. Ann. Stat. 28:140–74
    [Google Scholar]
  149. Stephens M. 2000b. Dealing with label switching in mixture models. J. R. Stat. Soc. Ser. B 62:4795–809
    [Google Scholar]
  150. Subedi S, Browne RP. 2020. A family of parsimonious mixtures of multivariate Poisson-lognormal distributions for clustering multivariate count data. Stat 9:1e310
    [Google Scholar]
  151. Tang Y, Browne RP, McNicholas PD. 2018. Flexible clustering of high-dimensional data via mixtures of joint generalized hyperbolic distributions. Stat 7:1e177
    [Google Scholar]
  152. Tanner MA, Wong WH. 1987. The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82:398528–40
    [Google Scholar]
  153. Teicher H. 1963. Identifiability of finite mixtures. Ann. Math. Stat. 34:41265–69
    [Google Scholar]
  154. Van Havre Z, White N, Rousseau J, Mengersen K. 2015. Overfitting Bayesian mixture models with an unknown number of components. PLOS ONE 10:7e0131739
    [Google Scholar]
  155. Vermunt J. 2007. Multilevel mixture item response theory models: an application in education testing. Proceedings of the 56th Session of the International Statistical Institute, Lisbon, Portugal Voorburg, Neth: Int. Stat. Inst.
    [Google Scholar]
  156. Viroli C, Anderlucci L. 2021. Deep mixtures of unigrams for uncovering topics in textual data. Stat. Comput. 31:31–10
    [Google Scholar]
  157. Viroli C, McLachlan GJ. 2019. Deep Gaussian mixture models. Stat. Comput. 29:143–51
    [Google Scholar]
  158. Vitelli V, Sørensen Ø, Crispino M, Frigessi A, Arjas E. 2017. Probabilistic preference learning with the Mallows rank model. J. Mach. Learn. Res. 18:1–49
    [Google Scholar]
  159. Wasserman S, Robins G, Steinley D 2007. Statistical models for networks: a brief review of some recent research. Statistical Network Analysis: Models, Issues, and New Directions EM Airoldi, DM Blei, SE Fienberg, A Goldenberg, EP Xing, AX Zheng 45–56 New York: Springer
    [Google Scholar]
  160. White A, Murphy TB. 2014. BayesLCA: an R package for Bayesian latent class analysis. J. Stat. Softw. 61:131–28
    [Google Scholar]
  161. Wolfe JH. 1965. A computer program for the maximum-likelihood analysis of types USNPRA Tech. Bull. 65-15 US Naval Pers. Res. Act. San Diego, CA:
    [Google Scholar]
  162. Wolfe JH. 1967. NORMIX: computational methods for estimating the parameters of multivariate normal mixture distributions of types. USNPRA Tech. Bull. 68-2 US Naval Pers. Res. Act. San Diego, CA:
    [Google Scholar]
  163. Wolfe JH. 1970. Pattern clustering by multivariate mixture analysis. Multivar. Behav. Res. 5:3329–50
    [Google Scholar]
  164. Yuksel SE, Wilson JN, Gader PD. 2012. Twenty years of mixture of experts. IEEE Trans. Neural Netw. Learn. Syst. 23:81177–93
    [Google Scholar]
  165. Zhang Y, Melnykov V, Zhu X. 2021. Model-based clustering of time-dependent categorical sequences with application to the analysis of major life event patterns. Stat. Anal. Data Min. 14:3230–40
    [Google Scholar]
/content/journals/10.1146/annurev-statistics-033121-115326
Loading
/content/journals/10.1146/annurev-statistics-033121-115326
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error