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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Rapport
2014
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https://hal.archives-ouvertes.fr/hal-01034196
Contributeur : Gilles Pagès <>
Soumis le : mardi 22 juillet 2014 - 18:40:06
Dernière modification le : mardi 11 octobre 2016 - 15:20:20
Document(s) archivé(s) le : mardi 25 novembre 2014 - 11:40:35

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  • HAL Id : hal-01034196, version 1

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PMA | UPMC | INSMI | LARA | USPC

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

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