@article {DualQuantizationFoundation,
title = {Intrinsic stationarity for vector quantization: Foundation of dual quantization},
year = {2010},
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.},
keywords = {Delaunay triangulation, numerical integration, quantization, Stationarity, Voronoi tessellation},
attachments = {http://quantize.maths-fi.com/sites/default/files/Foundation of dual quantization.pdf},
author = {Gilles Pag{\`e}s and Benedikt Wilbertz}
}