Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Quantization of probability distributions under norm-based distortion measures


Code(s) de Classification MSC:

Résumé: For a probability measure $P$ on $\R^d$ and $n\!\! \in \! \N$ consider $e_n = \inf \displaystyle \int \min_{a \in \alpha} V(\| x-a \| )dP(x)$ where the infimum is taken over all subsets $\alpha$ of $\R^d$ with $\mbox{card} (\alpha) \leq n$ and $V$ is a nondecreasing function. Under certain conditions on $V$, we derive the precise $n$-asymptotics of $e_n$ for nonsingular and for (singular) self-similar distributions $P$ and we find the asymptotic performance of optimal quantizers using weighted empirical measures.

Mots Clés: High-rate vector quantization ; norm-difference distortion ; empirical measure ; weak convergence ; local distortion ; point density measure

Date: 2004-09-06

Prépublication numéro: PMA-924