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Introduction to optimal vector quantization and its applications for numerics

Abstract : We present an introductory survey to optimal vector quantization and its first applications to Numerical Probability and, to a lesser extent to Information Theory and Data Mining. Both theoretical results on the quantization rate of a random vector taking values in R^d (equipped with the canonical Euclidean norm) and the learning procedures that allow to design optimal quantizers (CLVQ and Lloyd's I procedures) are presented. We also introduce and investigate the more recent notion of {\em greedy quantization} which may be seen as a sequential optimal quantization. A rate optimal result is established. A brief comparison with Quasi-Monte Carlo method is also carried out.
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https://hal.archives-ouvertes.fr/hal-01034196
Contributor : Gilles Pagès <>
Submitted on : Tuesday, July 22, 2014 - 6:40:06 PM
Last modification on : Friday, March 27, 2020 - 4:01:27 AM
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  • HAL Id : hal-01034196, version 1

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Gilles Pagès. Introduction to optimal vector quantization and its applications for numerics. 2014. ⟨hal-01034196⟩

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