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Clustering sparse binary data with hierarchical Bayesian Bernoulli mixture model

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  • Ye, Mao
  • Zhang, Peng
  • Nie, Lizhen

Abstract

Sparsity in features presents a big technical challenge to existing clustering methods for categorical data. Hierarchical Bayesian Bernoulli mixture model (HBBMM) incorporates constrained empirical Bayes priors for model parameters, so the resulting Expectation Maximization (EM) algorithm of estimator searching is confined in a proper region. The EM algorithm enables to obtain the maximum a posterior (MAP) estimation, in which cluster labels are simultaneously assigned. Three criteria are proposed to identify defining features of individual clusters, leading to understanding of the underlying data structures. Information based model selection criterion is applied to determine the number of clusters. Estimation consistency and performance of model selection criteria are investigated. Two real-world sparse categorical datasets are analyzed with the proposed method.

Suggested Citation

  • Ye, Mao & Zhang, Peng & Nie, Lizhen, 2018. "Clustering sparse binary data with hierarchical Bayesian Bernoulli mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 32-49.
    • Handle: RePEc:eee:csdana:v:123:y:2018:i:c:p:32-49
    DOI: 10.1016/j.csda.2018.01.020
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    References listed on IDEAS

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    1. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    2. Gerhard Moser & Sang Hong Lee & Ben J Hayes & Michael E Goddard & Naomi R Wray & Peter M Visscher, 2015. "Simultaneous Discovery, Estimation and Prediction Analysis of Complex Traits Using a Bayesian Mixture Model," PLOS Genetics, Public Library of Science, vol. 11(4), pages 1-22, April.
    3. Zhang, Peng & Wang, Xiaogang & Song, Peter X.K., 2006. "Clustering Categorical Data Based on Distance Vectors," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 355-367, March.
    4. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
    5. Arias-Castro, Ery & Pu, Xiao, 2017. "A simple approach to sparse clustering," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 217-228.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. White, Arthur & Murphy, Thomas Brendan, 2014. "BayesLCA: An R Package for Bayesian Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i13).
    8. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
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