# Intrinsic stationarity for vector quantization: Foundation of dual quantization

* Auteur correspondant
Abstract : We develop a new approach to vector quantization, which guarantees an intrinsic stationarity property that also holds, in contrast to regular quantization, for non-optimal quantization grids. This goal is achieved by replacing the usual nearest neighbor projection operator for Voronoi quantization by a random splitting operator, which maps the random source to the vertices of a triangle of $d$-simplex. In the quadratic Euclidean case, it is shown that these triangles or $d$-simplices make up a Delaunay triangulation of the underlying grid. Furthermore, we prove the existence of an optimal grid for this Delaunay -- or dual -- quantization procedure. We also provide a stochastic optimization method to compute such optimal grids, here for higher dimensional uniform and normal distributions. A crucial feature of this new approach is the fact that it automatically leads to a second order quadrature formula for computing expectations, regardless of the optimality of the underlying grid.
keyword :
Type de document :
Article dans une revue
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2012, pp.50(2), 747-780. <10.1137/110827041>
Domaine :

https://hal.archives-ouvertes.fr/hal-00528485
Contributeur : Benedikt Wilbertz <>
Soumis le : lundi 26 mars 2012 - 17:18:16
Dernière modification le : mardi 11 octobre 2016 - 15:20:22
Document(s) archivé(s) le : mercredi 27 juin 2012 - 02:41:30

### Fichiers

document.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Gilles Pagès, Benedikt Wilbertz. Intrinsic stationarity for vector quantization: Foundation of dual quantization. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2012, pp.50(2), 747-780. <10.1137/110827041>. <hal-00528485v2>

Consultations de
la notice

## 246

Téléchargements du document