The high resolution vector quantization problem with Orlicz norm distortion

Abstract

We derive a high-resolution formula for the quantization problem under Orlicz norm distortion. In this setting, the optimal point density solves a variational problem which comprises a function $g:{\mathbb{R}}_{+}\to [0,\infty )$ characterizing the quantization complexity of the underlying Orlicz space. Moreover, asymptotically optimal codebooks induce a tight sequence of empirical measures. The set of possible accumulation points is characterized and in most cases it consists of a single element. In that case, we find convergence as in the classical setting.

27 pages