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L1-Quantization and clustering in Banach spaces

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Abstract

LetX be a random variable with distribution µ taking values in a Banach spaceH. First, we establish the existence of an optimal quantization of µ with respect to the L 1-distance. Second, we propose several estimators of the optimal quantizer in the potentially infinite-dimensional space H, with associated algorithms. Finally, we discuss practical results obtained from real-life data sets.

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Authors and Affiliations

  1. Univ. de Lyon, Univ. de Lyon 1, ISFA, Laboratoire SAF, Lyon, France

    T. Laloë

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  1. T. Laloë
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Laloë, T. L1-Quantization and clustering in Banach spaces. Math. Meth. Stat. 19, 136–150 (2010). https://doi.org/10.3103/S1066530710020031

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  • DOI: https://doi.org/10.3103/S1066530710020031

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