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Journal of Classification
Erschienen in: Journal of Classification 1/2023

15.02.2023

Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions

verfasst von: Utkarsh J. Dang, Michael P.B. Gallaugher, Ryan P. Browne, Paul D. McNicholas

Erschienen in: Journal of Classification | Ausgabe 1/2023

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Abstract

Families of mixtures of multivariate power exponential (MPE) distributions have already been introduced and shown to be competitive for cluster analysis in comparison to other mixtures of elliptical distributions, including mixtures of Gaussian distributions. A family of mixtures of multivariate skewed power exponential distributions is proposed that combines the flexibility of the MPE distribution with the ability to model skewness. These mixtures are more robust to variations from normality and can account for skewness, varying tail weight, and peakedness of data. A generalized expectation-maximization approach, which combines minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold, is used for parameter estimation. These mixtures are implemented both in the unsupervised and semi-supervised classification frameworks. Both simulated and real data are used for illustration and comparison to other mixture families.
Vorheriger Artikel DDCAL: Evenly Distributing Data into Low Variance Clusters Based on Iterative Feature Scaling
Nächster Artikel Classification Trees with Mismeasured Responses

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Literatur
Absil, P.-A., Mahony, R., & Sepulchre, R. (2009). Optimization algorithms on matrix manifolds. Princeton University Press.
Aitken, A.C. (1926). On Bernoulli’s numerical solution of algebraic equations. In Proceedings of the royal society of edinburgh (pp. 289–305).
Andrews, J. L., & McNicholas, P. D. (2012). Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions. Statistics and Computing, 22(5), 1021–1029.MathSciNetMATHCrossRef
Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica, 46(2), 199–208.MathSciNetMATH
Basford, K., Greenway, D., McLachlan, G., & Peel, D. (1997). Standard errors of fitted component means of normal mixtures. Computational Statistics, 12(1), 1–18.MATH
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. (2003). Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics & Data Analysis, 41(3–4), 561–575.MathSciNetMATHCrossRef
Böhning, D., & Lindsay, B. G. (1988). Monotonicity of quadratic-approximation algorithms. Annals of the Institute of Statistical Mathematics, 40(4), 641–663.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
Branco, M. D., & Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis, 79(1), 99–113.MathSciNetMATHCrossRef
Browne, R. P., & McNicholas, P. D. (2014). 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. (2015). A mixture of generalized hyperbolic distributions. Canadian Journal of Statistics, 43(2), 176–198.MathSciNetMATHCrossRef
Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition, 28(5), 781–793.CrossRef
Cho, D., & Bui, T. D. (2005). Multivariate statistical modeling for image denoising using wavelet transforms. Signal Processing: Image Communication, 20 (1), 77–89.
da Silva Ferreira, C., Bolfarine, H., & Lachos, V. H. (2011). Skew scale mixtures of normal distributions: Properties and estimation. Statistical Methodology, 8(2), 154–171.MathSciNetMATHCrossRef
Dang, U. J., Browne, R. P., & McNicholas, P. D. (2015). Mixtures of multivariate power exponential distributions. Biometrics, 71(4), 1081–1089.MathSciNetMATHCrossRef
Dang, U.J., Browne, R.P., Gallaugher, M.P., & Band McNicholas, P.D. (2021). mixSPE: Mixtures of power exponential and skew power exponential distributions for use in model-based clustering and classification. R package version 0.9.1.
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
DiCiccio, T. J., & Monti, A. C. (2004). Inferential aspects of the skew exponential power distribution. Journal of the American Statistical Association, 99 (466), 439–450.MathSciNetMATHCrossRef
Flury, B. (2012). Flury: data sets from Flury, 1997. R package version 0.1–3.
Forina, M., & Tiscornia, E. (1982). Pattern-recognition methods in the prediction of italian olive oil origin by their fatty-acid content. Annali di Chimica, 72(3-4), 143–155.
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, Washington.
Franczak, B. C., Browne, R. P., & McNicholas, P. D. (2014). Mixtures of shifted asymmetric Laplace distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(6), 1149–1157.CrossRef
Franczak, B. C., Browne, R. P., McNicholas, P. D., & Burak, K. L. (2018). MixSAL: Mixtures of multivariate shifted asymmetric Laplace (SAL) distributions. R package version, 1, 0.
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
Gómez, E., Gomez-Viilegas, M. A., & Marin, J. M. (1998). A multivariate generalization of the power exponential family of distributions. Communications in Statistics-Theory and Methods, 27(3), 589–600.MathSciNetMATHCrossRef
Hartigan, J. A., & Wong, M. A. (1979). A k-means clustering algorithm. Journal of the Royal Statistical Society: Series C, 28(1), 100–108.MATH
Hasselblad, V. (1966). Estimation of parameters for a mixture of normal distributions. Technometrics, 8(3), 431–444.MathSciNetCrossRef
Horst, A.M., Hill, A.P., & Gorman, K.B. (2020). Palmerpenguins: Palmer Archipelago (Antarctica) penguin data. R package version 0.1.0.
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193–218.MATHCrossRef
Hunter, D. R., & Lange, K. (2000). Rejoinder to discussion of optimization transfer using surrogate objective functions. Journal of Computational and Graphical Statistics, 9(1), 52–59.
Hurley, C. (2012). gclus: clustering Graphics. R package version 1.3.1.
Karlis, D., & Santourian, A. (2009). Model-based clustering with non-elliptically contoured distributions. Statistics and Computing, 19(1), 73–83.MathSciNetCrossRef
Lee, S., & McLachlan, G. J. (2014). Finite mixtures of multivariate skew t-distributions: some recent and new results. Statistics and Computing, 24 (2), 181–202.MathSciNetMATHCrossRef
Lee, S. X., & McLachlan, G. J. (2016). Finite mixtures of canonical fundamental skew t-distributions: The unification of the restricted and unrestricted skew t-mixture models. Statistics and Computing, 26(3), 573–589.MathSciNetMATHCrossRef
Lin, T. -I. (2010). Robust mixture modeling using multivariate skew t distributions. Statistics and Computing, 20(3), 343–356.MathSciNetCrossRef
Lin, T. -I., Ho, H. J., & Lee, C -R. (2014). Flexible mixture modelling using the multivariate skew-t-normal distribution. Statistics and Computing, 24(4), 531–546.MathSciNetMATHCrossRef
Lindsay, B. G. (1995). Mixture models: Theory, geometry and applications. In NSF-CBMS regional conference series in probability and statistics (pp. 1–163).
Lindsey, J. K. (1999). Multivariate elliptically contoured distributions for repeated measurements. Biometrics, 55(4), 1277–1280.MATHCrossRef
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., McDaid, A. F., & Frost, D. (2010). Serial and parallel implementations of model-based clustering via parsimonious gaussian mixture models. Computational Statistics & Data Analysis, 54(3), 711–723.MathSciNetMATHCrossRef
McNicholas, P.D., ElSherbiny, A., McDaid, A.F., & Murphy, T. B. (2022). pgmm: Parsimonious Gaussian Mixture Models. R package version 1.2.6-2.
McNicholas, S.M., McNicholas, P.D., & Browne, R.P. (2017). A mixture of variance-gamma factor analyzers. In Big and complex data analysis (pp 369–385). Springer international publishing, Cham.
Morris, K., & McNicholas, P. D. (2013). Dimension reduction for model-based clustering via mixtures of shifted asymmetric Laplace distributions. Statistics and Probability Letters, 83(9), 2088–2093.MathSciNetMATHCrossRef
Murray, P. M., Browne, R. B., & McNicholas, P. D. (2014). Mixtures of skew-t factor analyzers. Computational Statistics and Data Analysis, 77, 326–335.MathSciNetMATHCrossRef
Murray, P. M., Browne, R. B., & McNicholas, P. D. (2017). Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering. Journal of Multivariate Analysis, 161, 141–156.MathSciNetMATHCrossRef
Nakai, K., & Kanehisa, M. (1991). Expert system for predicting protein localization sites in gram-negative bacteria. Proteins: Structure. Function, and Bioinformatics, 11(2), 95–110.CrossRef
Nakai, K., & Kanehisa, M. (1992). A knowledge base for predicting protein localization sites in eukaryotic cells. Genomics, 14(4), 897–911.CrossRef
O’Hagan, A., Murphy, T. B., Gormley, I. C., McNicholas, P. D., & Karlis, D. (2016). Clustering with the multivariate normal inverse gaussian distribution. Computational Statistics and Data Analysis, 93, 18–30.MathSciNetMATHCrossRef
Peel, D., & McLachlan, G. J. (2000). Robust mixture modelling using the t distribution. Statistics and Computing, 10(4), 339–348.CrossRef
Pocuca, N., Browne, R.P., & McNicholas, P.D. (2022). Mixture: Mixture models for clustering and classification. R package version 2.0.5.
Steinley, D. (2004). Properties of the Hubert-Arabie adjusted Rand index. Psychological Methods, 9, 386–396.CrossRef
Streuli, H. (1973). Der heutige stand der kaffeechemie. In 6th international colloquium on coffee chemisrty (pp. 61–72).
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
Tipping, M. E., & Bishop, C. M. (1999). Mixtures of probabilistic principal component analysers. Neural Computation, 11(2), 443–482.CrossRef
Tortora, C., ElSherbiny, A., Browne, R. P., Franczak, B.C., McNicholas, P.D., & Amos, D.D. (2018). MixGHD: Model based clustering, classification and discriminant analysis using the mixture of generalized hyperbolic distributions. R package version 2.2.
Venables, W.N., & Ripley, B.D. (2002). Modern applied statistics with S, fourth edn. New York: Springer. ISBN 0-387-95457-0.MATHCrossRef
Verdoolaege, G., De Backer, S., & Scheunders, P. (2008). Multiscale colour texture retrieval using the geodesic distance between multivariate generalized Gaussian models. In 2008 15th IEEE international conference on image processing (pp. 169–172).
Vrbik, I., & McNicholas, P. D. (2014). Parsimonious skew mixture models for model-based clustering and classification. Computational Statistics and Data Analysis, 71, 196–210.MathSciNetMATHCrossRef
Wolfe, J.H. (1965). A computer program for the maximum likelihood analysis of types. U.S. Naval personnel research activity, technical bulletin:65-15.
Zhu, X., Sarkar, S., & Melnykov, V. (2022). Mattransmix: An r package for matrix model-based clustering and parsimonious mixture modeling. Journal of Classification, 39(1), 147–170.MathSciNetMATHCrossRef
Metadaten
Titel
Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions
verfasst von
Utkarsh J. Dang
Michael P.B. Gallaugher
Ryan P. Browne
Paul D. McNicholas
Publikationsdatum
15.02.2023
Verlag
Springer US
Erschienen in
Journal of Classification / Ausgabe 1/2023
Print ISSN: 0176-4268
Elektronische ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-022-09427-7

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