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Variable selection in clustering via Dirichlet process mixture models

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  • Sinae Kim
  • Mahlet G. Tadesse
  • Marina Vannucci

Abstract

The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this paper, we propose a model-based method that addresses the two problems simultaneously. We introduce a latent binary vector to identify discriminating variables and use Dirichlet process mixture models to define the cluster structure. We update the variable selection index using a Metropolis algorithm and obtain inference on the cluster structure via a split-merge Markov chain Monte Carlo technique. We explore the performance of the methodology on simulated data and illustrate an application with a DNA microarray study. Copyright 2006, Oxford University Press.

Suggested Citation

  • Sinae Kim & Mahlet G. Tadesse & Marina Vannucci, 2006. "Variable selection in clustering via Dirichlet process mixture models," Biometrika, Biometrika Trust, vol. 93(4), pages 877-893, December.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:4:p:877-893
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    Cited by:

    1. Krzanowski, Wojtek J. & Hand, David J., 2009. "A simple method for screening variables before clustering microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2747-2753, May.
    2. Brian J. Reich & Howard D. Bondell, 2011. "A Spatial Dirichlet Process Mixture Model for Clustering Population Genetics Data," Biometrics, The International Biometric Society, vol. 67(2), pages 381-390, June.
    3. Claudia Angelini & Daniela De Canditiis & Marianna Pensky, 2012. "Clustering time-course microarray data using functional Bayesian infinite mixture model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 129-149, March.
    4. Chakraborty, Sounak, 2009. "Bayesian binary kernel probit model for microarray based cancer classification and gene selection," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4198-4209, October.
    5. Sun Jiehuan & Warren Joshua L. & Zhao Hongyu, 2017. "A Bayesian semiparametric factor analysis model for subtype identification," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(2), pages 145-158, April.
    6. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Cathy Maugis & Gilles Celeux & Marie-Laure Martin-Magniette, 2009. "Variable Selection for Clustering with Gaussian Mixture Models," Biometrics, The International Biometric Society, vol. 65(3), pages 701-709, September.
    8. Bettina Grün & Paul Hofmarcher, 2021. "Identifying groups of determinants in Bayesian model averaging using Dirichlet process clustering," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1018-1045, September.
    9. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 59-80, February.
    10. Subharup Guha & Rex Jung & David Dunson, 2022. "Predicting phenotypes from brain connection structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 639-668, June.
    11. repec:jss:jstsof:47:i05 is not listed on IDEAS
    12. Anoek Castelein & Dennis Fok & Richard Paap, 2020. "Heterogeneous variable selection in nonlinear panel data models: A semiparametric Bayesian approach," Tinbergen Institute Discussion Papers 20-061/III, Tinbergen Institute.
    13. Lian, Heng, 2010. "Sparse Bayesian hierarchical modeling of high-dimensional clustering problems," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1728-1737, August.
    14. Benhuai Xie & Wei Pan & Xiaotong Shen, 2008. "Variable Selection in Penalized Model‐Based Clustering Via Regularization on Grouped Parameters," Biometrics, The International Biometric Society, vol. 64(3), pages 921-930, September.
    15. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    16. Cozzini, Alberto & Jasra, Ajay & Montana, Giovanni & Persing, Adam, 2014. "A Bayesian mixture of lasso regressions with t-errors," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 84-97.
    17. Laura C. Dawkins & Daniel B. Williamson & Stewart W. Barr & Sally R. Lampkin, 2020. "‘What drives commuter behaviour?': a Bayesian clustering approach for understanding opposing behaviours in social surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 251-280, January.
    18. Crook Oliver M. & Gatto Laurent & Kirk Paul D. W., 2019. "Fast approximate inference for variable selection in Dirichlet process mixtures, with an application to pan-cancer proteomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(6), pages 1-20, December.
    19. Zhuang, Haoxin & Diao, Liqun & Yi, Grace Y., 2022. "A Bayesian nonparametric mixture model for grouping dependence structures and selecting copula functions," Econometrics and Statistics, Elsevier, vol. 22(C), pages 172-189.
    20. Thierry Chekouo & Alejandro Murua, 2018. "High-dimensional variable selection with the plaid mixture model for clustering," Computational Statistics, Springer, vol. 33(3), pages 1475-1496, September.

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