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Hierarchical clustering of continuous variables based on the empirical copula process and permutation linkages

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  • Kojadinovic, Ivan
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    Abstract

    The agglomerative hierarchical clustering of continuous variables is studied in the framework of the likelihood linkage analysis method proposed by Lerman. The similarity between variables is defined from the process comparing the empirical copula with the independence copula in the spirit of the test of independence proposed by Deheuvels. Unlike more classical similarity coefficients for variables based on rank statistics, the comparison measure considered in this work can also be sensitive to non-monotonic dependencies. As aggregation criteria, besides classical linkages, permutation-based linkages related to procedures for combining dependent p-values are considered. The performances of the corresponding clustering algorithms are compared through thorough simulations. In order to guide the choice of a partition, a natural probabilistic selection strategy, related to the use of the gap statistic in object clustering, is proposed and empirically compared with classical ordinal approaches. The resulting variable clustering procedure can be equivalently regarded as a potentially less computationally expensive alternative to more powerful tests of multivariate independence.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 1 (January)
    Pages: 90-108

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:90-108

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    Web page: http://www.elsevier.com/locate/csda

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    1. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    2. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    3. Plasse, Marie & Niang, Ndeye & Saporta, Gilbert & Villeminot, Alexandre & Leblond, Laurent, 2007. "Combined use of association rules mining and clustering methods to find relevant links between binary rare attributes in a large data set," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 596-613, September.
    4. Kojadinovic, Ivan, 2004. "Agglomerative hierarchical clustering of continuous variables based on mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 269-294, June.
    5. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer, vol. 50(2), pages 159-179, June.
    6. Loughin, Thomas M., 2004. "A systematic comparison of methods for combining p-values from independent tests," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 467-485, October.
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