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arXiv · 1010.4248

The high resolution vector quantization problem with Orlicz norm distortion

Steffen Dereich·Christian Vormoor
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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.

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Steffen Dereich, Christian Vormoor. 2010-10-20. The high resolution vector quantization problem with Orlicz norm distortion. https://arxiv.org/abs/1010.4248

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