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A hierarchical modeling approach for clustering probability density functions

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  • Calò, Daniela G.
  • Montanari, Angela
  • Viroli, Cinzia

Abstract

The problem of clustering probability density functions is emerging in different scientific domains. The methods proposed for clustering probability density functions are mainly focused on univariate settings and are based on heuristic clustering solutions. New aspects of the problem associated with the multivariate setting and a model-based perspective are investigated. The novel approach relies on a hierarchical mixture modeling of the data. The method is introduced in the univariate context and then extended to multivariate densities by means of a factorial model performing dimension reduction. Model fitting is carried out using an EM-algorithm. The proposed method is illustrated through simulated experiments and applied to two real data sets in order to compare its performance with alternative clustering strategies.

Suggested Citation

  • Calò, Daniela G. & Montanari, Angela & Viroli, Cinzia, 2014. "A hierarchical modeling approach for clustering probability density functions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 79-91.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:79-91
    DOI: 10.1016/j.csda.2013.04.013
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    References listed on IDEAS

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    1. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    2. Vermunt, Jeroen K., 2007. "A hierarchical mixture model for clustering three-way data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5368-5376, July.
    3. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
    4. Inna Chervoneva & Tingting Zhan & Boris Iglewicz & Walter W. Hauck & David E. Birk, 2012. "Two-stage hierarchical modeling for analysis of subpopulations in conditional distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 445-460, June.
    5. Calò, Daniela G. & Viroli, Cinzia, 2010. "A dimensionally reduced finite mixture model for multilevel data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2543-2553, November.
    6. Bouveyron, C. & Girard, S. & Schmid, C., 2007. "High-dimensional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 502-519, September.
    7. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.
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