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Erschienen in: Journal of Classification 2/2021

12.08.2020

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

verfasst von: Sharon M. McNicholas, Paul D. McNicholas, Daniel A. Ashlock

Erschienen in: Journal of Classification | Ausgabe 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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Literatur
Zurück zum Zitat Andrews, J.L., & McNicholas, P.D. (2013). Using evolutionary algorithms for model-based clustering. Pattern Recognition Letters, 34, 987–992.CrossRef Andrews, J.L., & McNicholas, P.D. (2013). Using evolutionary algorithms for model-based clustering. Pattern Recognition Letters, 34, 987–992.CrossRef
Zurück zum Zitat Ashlock, D. (2010). Evolutionary Computation for Modeling and Optimization. Springer-Verlag: New York.MATH Ashlock, D. (2010). Evolutionary Computation for Modeling and Optimization. Springer-Verlag: New York.MATH
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat Bouveyron, C., & Brunet-Saumard, C. (2014). Model-based clustering of high-dimensional data: a review. Computational Statistics and Data Analysis, 71, 52–78.MathSciNetMATHCrossRef Bouveyron, C., & Brunet-Saumard, C. (2014). Model-based clustering of high-dimensional data: a review. Computational Statistics and Data Analysis, 71, 52–78.MathSciNetMATHCrossRef
Zurück zum Zitat 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. (2014a). Estimating common principal components in high dimensions. Advances in Data Analysis and Classification, 8(2), 217–226.MathSciNetMATHCrossRef
Zurück zum Zitat 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. (2014b). Mixture: mixture models for clustering and classification. R package version 1.1.
Zurück zum Zitat 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 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
Zurück zum Zitat 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. (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14 (3), 315–332.MathSciNetMATHCrossRef
Zurück zum Zitat Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition, 28(5), 781–793.CrossRef Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition, 28(5), 781–793.CrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat Flury, B. (2012). Flury: data sets from flury, 1997. R package version 0.1–3. Flury, B. (2012). Flury: data sets from flury, 1997. R package version 0.1–3.
Zurück zum Zitat 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. 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.
Zurück zum Zitat 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. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–631.MathSciNetMATHCrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat 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. (2018). Finite mixtures of skewed matrix variate distributions. Pattern Recognition, 80, 83–93.CrossRef
Zurück zum Zitat 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. (2019). On fractionally-supervised classification: Weight selection and extension to the multivariate t-distribution. Journal of Classification, 36(2), 232–265.MathSciNetMATHCrossRef
Zurück zum Zitat 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. (2020a). Mixtures of skewed matrix variate bilinear factor analyzers. Advances in Data Analysis and Classification, 14(2), 415–434.MathSciNetMATHCrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat Ghahramani, Z., & Hinton, G.E. (1997). The EM algorithm for factor analyzers Technical Report CRG-TR-96-1. Toronto: University Of Toronto. Ghahramani, Z., & Hinton, G.E. (1997). The EM algorithm for factor analyzers Technical Report CRG-TR-96-1. Toronto: University Of Toronto.
Zurück zum Zitat Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193–218.MATHCrossRef Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193–218.MATHCrossRef
Zurück zum Zitat Hurley, C. (2004). Clustering visualizations of multivariate data. Journal of Computational and Graphical Statistics, 13(4), 788–806.MathSciNetCrossRef Hurley, C. (2004). Clustering visualizations of multivariate data. Journal of Computational and Graphical Statistics, 13(4), 788–806.MathSciNetCrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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. (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.
Zurück zum Zitat McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. New Jersey: John Wiley & Sons.MATHCrossRef McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. New Jersey: John Wiley & Sons.MATHCrossRef
Zurück zum Zitat McLachlan, G.J., & Peel, D. (2000a). Finite mixture models. New York: John Wiley & Sons.MATHCrossRef McLachlan, G.J., & Peel, D. (2000a). Finite mixture models. New York: John Wiley & Sons.MATHCrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat 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. (2010). Model-based classification using latent Gaussian mixture models. Journal of Statistical Planning and Inference, 140(5), 1175–1181.MathSciNetMATHCrossRef
Zurück zum Zitat McNicholas, P.D. (2016a). Mixture model-based classification. Boca Raton: Chapman & Hall/CRC Press.MATHCrossRef McNicholas, P.D. (2016a). Mixture model-based classification. Boca Raton: Chapman & Hall/CRC Press.MATHCrossRef
Zurück zum Zitat 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. (2008). Parsimonious gaussian mixture models. Statistics and Computing, 18(3), 285–296.MathSciNetCrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat Melnykov, V., & Zhu, X. (2018). On model-based clustering of skewed matrix data. Journal of Multivariate Analysis, 167, 181–194.MathSciNetMATHCrossRef Melnykov, V., & Zhu, X. (2018). On model-based clustering of skewed matrix data. Journal of Multivariate Analysis, 167, 181–194.MathSciNetMATHCrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat Pesevski, A., Franczak, B.C., & McNicholas, P.D. (2018). Subspace clustering with the multivariate-t distribution. Pattern Recognition Letters, 112(1), 297–302.CrossRef Pesevski, A., Franczak, B.C., & McNicholas, P.D. (2018). Subspace clustering with the multivariate-t distribution. Pattern Recognition Letters, 112(1), 297–302.CrossRef
Zurück zum Zitat R Core Team. (2018). R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. R Core Team. (2018). R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Zurück zum Zitat Rand, W.M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846–850.CrossRef Rand, W.M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846–850.CrossRef
Zurück zum Zitat Roeder, K., & Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894–902.MathSciNetMATHCrossRef Roeder, K., & Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894–902.MathSciNetMATHCrossRef
Zurück zum Zitat Sarkar, S., Zhu, X., Melnykov, V., & Ingrassia, S. (2020). On parsimonious models for modeling matrix data. Computational Statistics and Data Analysis, 142. Sarkar, S., Zhu, X., Melnykov, V., & Ingrassia, S. (2020). On parsimonious models for modeling matrix data. Computational Statistics and Data Analysis, 142.
Zurück zum Zitat Steinley, D. (2004). Properties of the Hubert-Arabie adjusted Rand index. Psychological Methods, 9, 386–396.CrossRef Steinley, D. (2004). Properties of the Hubert-Arabie adjusted Rand index. Psychological Methods, 9, 386–396.CrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat Titterington, D.M., Smith, A.F.M. , & Makov, U.E. (1985). Statistical analysis of finite mixture distributions. Chichester: John Wiley & Sons.MATH Titterington, D.M., Smith, A.F.M. , & Makov, U.E. (1985). Statistical analysis of finite mixture distributions. Chichester: John Wiley & Sons.MATH
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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. 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.
Metadaten
Titel
An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering
verfasst von
Sharon M. McNicholas
Paul D. McNicholas
Daniel A. Ashlock
Publikationsdatum
12.08.2020
Verlag
Springer US
Erschienen in
Journal of Classification / Ausgabe 2/2021
Print ISSN: 0176-4268
Elektronische ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-020-09371-4

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