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Introduction to vector quantization and its applications for numerics
Ist Teil von
ESAIM. Proceedings and surveys, 2015-01, Vol.48, p.29-79
Ort / Verlag
Les Ulis: EDP Sciences
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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.