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Journal of Classification
Published in: Journal of Classification 2/2021

12-08-2020

An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering

Authors: Sharon M. McNicholas, Paul D. McNicholas, Daniel A. Ashlock

Published in: Journal of Classification | Issue 2/2021

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Abstract

An evolutionary algorithm (EA) is developed as an alternative to the EM algorithm for parameter estimation in model-based clustering. This EA facilitates a different search of the fitness landscape, i.e., the likelihood surface, utilizing both crossover and mutation. Furthermore, this EA represents an efficient approach to “hard” model-based clustering and so it can be viewed as a sort of generalization of the k-means algorithm, which is itself equivalent to a restricted Gaussian mixture model. The EA is illustrated on several datasets, and its performance is compared with that of other hard clustering approaches and model-based clustering via the EM algorithm.
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Literature
Andrews, J.L., & McNicholas, P.D. (2013). Using evolutionary algorithms for model-based clustering. Pattern Recognition Letters, 34, 987–992.CrossRef
Ashlock, D. (2010). Evolutionary Computation for Modeling and Optimization. Springer-Verlag: New York.MATH
Bagnato, L., Punzo, A., & Zoia, M.G. (2017). The multivariate leptokurtic-normal distribution and its application in model-based clustering. Canadian Journal of Statistics, 45(1), 95–119.MathSciNetMATHCrossRef
Biernacki, C., Celeux, G., & 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.CrossRef
Bouveyron, C., & Brunet-Saumard, C. (2014). Model-based clustering of high-dimensional data: a review. Computational Statistics and Data Analysis, 71, 52–78.MathSciNetMATHCrossRef
Browne, R.P., & McNicholas, P.D. (2014a). Estimating common principal components in high dimensions. Advances in Data Analysis and Classification, 8(2), 217–226.MathSciNetMATHCrossRef
Browne, R.P., & McNicholas, P.D. (2014b). Mixture: mixture models for clustering and classification. R package version 1.1.
Browne, R.P., & McNicholas, P.D. (2014c). Orthogonal Stiefel manifold optimization for eigen-decomposed covariance parameter estimation in mixture models. Statistics and Computing, 24(2), 203–210.MathSciNetMATHCrossRef
Celeux, G., & Govaert, G. (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14 (3), 315–332.MathSciNetMATHCrossRef
Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition, 28(5), 781–793.CrossRef
Dasgupta, A., & 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.MATHCrossRef
Dean, N., Murphy, T.B., & Downey, G. (2006). Using unlabelled data to update classification rules with applications in food authenticity studies. Journal of the Royal Statistical Society: Series C, 55(1), 1–14.MathSciNetMATH
Dempster, A.P., Laird, N.M., & 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.MathSciNetMATH
Flury, B. (2012). Flury: data sets from flury, 1997. R package version 0.1–3.
Forina, M., Armanino, C., Castino, M., & Ubigli, M. (1986). Multivariate data analysis as a discriminating method of the origin of wines. Vitis, 25, 189–201.
Fraley, C., & Raftery, A.E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–631.MathSciNetMATHCrossRef
Fraley, C., Raftery, A.E., Murphy, T.B., & Scrucca, L. (2012). Mclust version 4 for R: Normal mixture modeling for model-based clustering, classification, and density estimation. Technical Report 597, Department of Statistics, University of Washington, Seattle, WA.
Gallaugher, M.P.B., & McNicholas, P.D. (2018). Finite mixtures of skewed matrix variate distributions. Pattern Recognition, 80, 83–93.CrossRef
Gallaugher, M.P.B., & McNicholas, P.D. (2019). On fractionally-supervised classification: Weight selection and extension to the multivariate t-distribution. Journal of Classification, 36(2), 232–265.MathSciNetMATHCrossRef
Gallaugher, M.P.B., & McNicholas, P.D. (2020a). Mixtures of skewed matrix variate bilinear factor analyzers. Advances in Data Analysis and Classification, 14(2), 415–434.MathSciNetMATHCrossRef
Gallaugher, M.P.B., & McNicholas, P.D. (2020b). Parsimonious mixtures of matrix variate bilinear factor analyzers. In Imaizumi, T., Nakayama, A., & Yokoyama, S. (Eds.) Advanced studies in behaviormetrics and data science: Essays in honor of Akinori Okada (pp. 177–196). Singapore: Springer.
Ghahramani, Z., & Hinton, G.E. (1997). The EM algorithm for factor analyzers Technical Report CRG-TR-96-1. Toronto: University Of Toronto.
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193–218.MATHCrossRef
Hurley, C. (2004). Clustering visualizations of multivariate data. Journal of Computational and Graphical Statistics, 13(4), 788–806.MathSciNetCrossRef
Kass, R.E., & Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90(431), 928–934.MathSciNetMATHCrossRef
Lin, T.-I., Wang, W.-L., McLachlan, G.J., & Lee, S.X. (2018). Robust mixtures of factor analysis models using the restricted multivariate skew-t distribution. Statistical Modelling, 18, 50–72.MathSciNetMATHCrossRef
McGrory, C., & Titterington, D. (2007). Variational approximations in Bayesian model selection for finite mixture distributions. Computational Statistics and Data Analysis, 51(11), 5352–5367.MathSciNetMATHCrossRef
McLachlan, G.J. (1982). The classification and mixture maximum likelihood approaches to cluster analysis. In Krishnaiah, P.R., & Kanal, L. (Eds.) Handbook of statistics, vol. 2, pp 199–208. Amsterdam: North-Holland.
McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. New Jersey: John Wiley & Sons.MATHCrossRef
McLachlan, G.J., & Peel, D. (2000b). Mixtures of factor analyzers. In Proceedings of the seventh international conference on machine learning, San Francisco, pp 599–606. Morgan Kaufmann.
McNicholas, P.D. (2010). Model-based classification using latent Gaussian mixture models. Journal of Statistical Planning and Inference, 140(5), 1175–1181.MathSciNetMATHCrossRef
McNicholas, P.D. (2016a). Mixture model-based classification. Boca Raton: Chapman & Hall/CRC Press.MATHCrossRef
McNicholas, P.D., & Murphy, T.B. (2008). Parsimonious gaussian mixture models. Statistics and Computing, 18(3), 285–296.MathSciNetCrossRef
McNicholas, P.D., & Murphy, T.B. (2010). Model-based clustering of microarray expression data via latent gaussian mixture models. Bioinformatics, 26 (21), 2705–2712.CrossRef
Melnykov, V., & Zhu, X. (2019). Studying crime trends in the USA over the years 2000–2012. Advances in Data Analysis and Classification, 13(1), 325–341.MathSciNetMATHCrossRef
Morris, K., Punzo, A., McNicholas, P.D., & Browne, R.P. (2019). Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions. Computational Statistics and Data Analysis, 132, 145–166.MathSciNetMATHCrossRef
Murray, P.M., Browne, R.P., & McNicholas, P.D. (2020). Mixtures of hidden truncation hyperbolic factor analyzers. Journal of Classification, 37(2), 366–379.MathSciNetMATHCrossRef
Pesevski, A., Franczak, B.C., & McNicholas, P.D. (2018). Subspace clustering with the multivariate-t distribution. Pattern Recognition Letters, 112(1), 297–302.CrossRef
R Core Team. (2018). R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Rand, W.M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846–850.CrossRef
Roeder, K., & Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894–902.MathSciNetMATHCrossRef
Sarkar, S., Zhu, X., Melnykov, V., & Ingrassia, S. (2020). On parsimonious models for modeling matrix data. Computational Statistics and Data Analysis, 142.
Steinley, D. (2004). Properties of the Hubert-Arabie adjusted Rand index. Psychological Methods, 9, 386–396.CrossRef
Subedi, S., & 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.MathSciNetMATHCrossRef
Titterington, D.M., Smith, A.F.M. , & Makov, U.E. (1985). Statistical analysis of finite mixture distributions. Chichester: John Wiley & Sons.MATH
Tortora, C., Franczak, B.C., Browne, R.P., & McNicholas, P.D. (2019). A mixture of coalesced generalized hyperbolic distributions. Journal of Classification, 36(1), 26–57.MathSciNetMATHCrossRef
Vermunt, J.K. (2011). K-means may perform as well as mixture model clustering but may also be much worse: Comment on Steinley and Brusco. Psychological Methods, 16(1), 82–88.CrossRef
Wallace, M.L., Buysse, D.J., Germain, A., Hall, M.H., & Iyengar, S. (2018). Variable selection for skewed model-based clustering: Application to the identification of novel sleep phenotypes. Journal of the American Statistical Association, 113(521), 95–110.MathSciNetMATHCrossRef
Wei, Y., Tang, Y., & McNicholas, P.D. (2020). Flexible high-dimensional unsupervised learning with missing data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(3), 610–621.CrossRef
Wolfe, J.H. (1965). A computer program for the maximum-likelihood analysis of types. USNPRA Technical Bulletin 65-15, U.S.Naval Personal Research Activity, San Diego.
Metadata
Title
An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering
Authors
Sharon M. McNicholas
Paul D. McNicholas
Daniel A. Ashlock
Publication date
12-08-2020
Publisher
Springer US
Published in
Journal of Classification / Issue 2/2021
Print ISSN: 0176-4268
Electronic ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-020-09371-4

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