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Quantization and clustering with Bregman divergences

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  • Fischer, Aurélie

Abstract

This paper deals with the problem of quantization of a random variable X taking values in a separable and reflexive Banach space, and with the related question of clustering independent random observations distributed as X. To this end, we use a quantization scheme with a class of distortion measures called Bregman divergences, and provide conditions ensuring the existence of an optimal quantizer and an empirically optimal quantizer. Rates of convergence are also discussed.

Suggested Citation

  • Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2207-2221
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    References listed on IDEAS

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    1. Marta Horvath & Gábor Lugosi, 1996. "A data-dependent skeleton estimate and a scale-sensitive dimension for classification," Economics Working Papers 199, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Y. Alber & D. Butnariu, 1997. "Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 33-61, January.
    3. Peter L. Bartlett & Stéphane Boucheron & Gábor Lugosi, 2000. "Model selection and error estimation," Economics Working Papers 508, Department of Economics and Business, Universitat Pompeu Fabra.
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    Cited by:

    1. Isabelle Charlier & Davy Paindaveine, 2014. "Conditional Quantile Estimation through Optimal Quantization," Working Papers ECARES ECARES 2014-28, ULB -- Universite Libre de Bruxelles.
    2. Katzur, Alexander & Kamps, Udo, 2016. "Classification into Kullback–Leibler balls in exponential families," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 75-90.

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