Volume 48, January 2015CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches
|Page(s)||29 - 79|
|Published online||09 March 2015|
Introduction to vector quantization and its applications for numerics*
Laboratoire de Probabilités et
Modèles aléatoires, UMR 7599, UPMC, case 188, 4, pl. Jussieu, F-75252
Paris Cedex 5,
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 ℝd (equipped with the canonical Euclidean norm) and the learning procedures that allow to design optimal quantizers (CLVQ and Lloyd’s procedures) are presented. We also introduce and investigate the more recent notion of 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.
© EDP Sciences, SMAI 2015
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