The high resolution vector quantization problem with Orlicz norm distortion

Details The high resolution vector quantization problem with Orlicz norm distortion The high resolution vector quantization problem with Orlicz norm distortion

2010-10-20

arxiv.org/abs/1010.4248v1

Mathematics

Probability

27 pages

Scientific paper

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.

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