Optimal quantization for uniform distributions on Cantor-like sets

  • In this paper, the problem of optimal quantization is solved for uniform distributions on some higher dimensional, not necessarily self-similar $N-$adic Cantor-like sets. The optimal codebooks are determined and the optimal quantization error is calculated. The existence of the quantization dimension is characterized and it is shown that the quantization coefficient does not exist. The special case of self-similarity is also discussed. The conditions imposed are a separation property of the distribution and strict monotonicity of the first $N$ quantization error differences. Criteria for these conditions are proved and as special examples modified versions of classical fractal distributions are discussed.

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Author:Wolfgang Kreitmeier
Document Type:Preprint
Year of Completion:2008
Date of Publication (online):2008/07/14
Publishing Institution:Universität Passau
Release Date:2008/07/14
Tag:optimal quantization; quantization coefficient; quantization dimension; self-similar probabilities
GND Keyword:Fraktale Dimension; Iteriertes Funktionensystem; Maßtheorie; Quantisierung
Source:This is a preprint of an article accepted for publication in Acta Applicandae Mathematicae, ISSN (Print) 0167-8019 ISSN (Online) 1572-9036 Copyright (c) by Springer. The original publication is available at www.springerlink.com. digital object identifier DOI: 10.1007/s10440-008-9278-3
Institutes:Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx]
62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10]
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung

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