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Infinite Dirichlet mixture models learning via expectation propagation

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  • Wentao Fan
  • Nizar Bouguila

Abstract

In this article, we propose a novel Bayesian nonparametric clustering algorithm based on a Dirichlet process mixture of Dirichlet distributions which have been shown to be very flexible for modeling proportional data. The idea is to let the number of mixture components increases as new data to cluster arrive in such a manner that the model selection problem (i.e. determination of the number of clusters) can be answered without recourse to classic selection criteria. Thus, the proposed model can be considered as an infinite Dirichlet mixture model. An expectation propagation inference framework is developed to learn this model by obtaining a full posterior distribution on its parameters. Within this learning framework, the model complexity and all the involved parameters are evaluated simultaneously. To show the practical relevance and efficiency of our model, we perform a detailed analysis using extensive simulations based on both synthetic and real data. In particular, real data are generated from three challenging applications namely images categorization, anomaly intrusion detection and videos summarization. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Wentao Fan & Nizar Bouguila, 2013. "Infinite Dirichlet mixture models learning via expectation propagation," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 465-489, December.
  • Handle: RePEc:spr:advdac:v:7:y:2013:i:4:p:465-489
    DOI: 10.1007/s11634-013-0152-4
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    References listed on IDEAS

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    1. Nizar Bouguila & Jian Han Wang & A. Ben Hamza, 2010. "Software modules categorization through likelihood and bayesian analysis of finite dirichlet mixtures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(2), pages 235-252.
    2. Chris Fraley & Adrian E. Raftery, 2003. "Enhanced Model-Based Clustering, Density Estimation, and Discriminant Analysis Software: MCLUST," Journal of Classification, Springer;The Classification Society, vol. 20(2), pages 263-286, September.
    3. Shen X. & Ye J., 2002. "Adaptive Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 210-221, March.
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