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High-dimensional variable selection with the plaid mixture model for clustering

Author

Listed:
  • Thierry Chekouo

    (University of Minnesota Duluth)

  • Alejandro Murua

    (Université de Montréal)

Abstract

With high-dimensional data, the number of covariates is considerably larger than the sample size. We propose a sound method for analyzing these data. It performs simultaneously clustering and variable selection. The method is inspired by the plaid model. It may be seen as a multiplicative mixture model that allows for overlapping clustering. Unlike conventional clustering, within this model an observation may be explained by several clusters. This characteristic makes it specially suitable for gene expression data. Parameter estimation is performed with the Monte Carlo expectation maximization algorithm and importance sampling. Using extensive simulations and comparisons with competing methods, we show the advantages of our methodology, in terms of both variable selection and clustering. An application of our approach to the gene expression data of kidney renal cell carcinoma taken from The Cancer Genome Atlas validates some previously identified cancer biomarkers.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-018-0818-7
    DOI: 10.1007/s00180-018-0818-7
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. 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.
    3. 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.
    4. Sijian Wang & Ji Zhu, 2008. "Variable Selection for Model-Based High-Dimensional Clustering and Its Application to Microarray Data," Biometrics, The International Biometric Society, vol. 64(2), pages 440-448, June.
    5. Tadesse, Mahlet G. & Sha, Naijun & Vannucci, Marina, 2005. "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 602-617, June.
    6. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    7. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    8. Thierry Chekouo & Alejandro Murua, 2015. "The penalized biclustering model and related algorithms," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(6), pages 1255-1277, June.
    9. Li, Fan & Zhang, Nancy R., 2010. "Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces With Applications in Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1202-1214.
    10. Witten, Daniela M. & Tibshirani, Robert, 2010. "A Framework for Feature Selection in Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 713-726.
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    Cited by:

    1. Weibing Li & Thierry Chekouo, 2022. "Bayesian group selection with non-local priors," Computational Statistics, Springer, vol. 37(1), pages 287-302, March.

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