Introduction to vector quantization and its applications for numerics

Gilles Pagès (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Optimal vector quantization; greedy quantization; quantization tree; Lloyd's I algorithm; Competitive Learning Vector Quantization; stochastic gradient descent; learning algorithms; Zador's Theorem; Feynman-Kac's formula; variational inequality; optimal stopping; quasi-Monte Carlo method; nearest neighbor search; partial distance search

Domaines: Probabilités [math.PR]

Gilles Pagès. Introduction to vector quantization and its applications for numerics. ESAIM: Proceedings and Surveys, 2015, CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches, 48, pp.29-79. ⟨10.1051/proc/201448002⟩. ⟨hal-01034196⟩