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＜電子ブック＞
Foundations of Quantization for Probability Distributions / by Siegfried Graf, Harald Luschgy
(Lecture Notes in Mathematics. ISSN:16179692 ; 1730)

版	1st ed. 2000.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	X, 230 p : online resource
冊子体	Foundations of quantization for probability distributions / Siegfried Graf, Harald Luschgy
著者標目	*Graf, Siegfried author Luschgy, Harald author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Statistics  LCSH:Pattern recognition systems LCSH:Operations research LCSH:Telecommunication FREE:Probability Theory FREE:Statistical Theory and Methods FREE:Automated Pattern Recognition FREE:Operations Research and Decision Theory FREE:Communications Engineering, Networks
一般注記	I. General properties of the quantization for probability distributions: Voronoi partitions. Centers and moments of probability distributions. The quantization problem. Basic properties of optimal quantizers. Uniqueness and optimality in one dimension -- II. Asymptotic quantization for nonsingular probability distributions: Asymptotics for the quantization error. Asymptotically optimal quantizers. Regular quantizers and quantization coefficients. Random quantizers and quantization coefficients. Asymptotics for the covering radius -- III. Asymptotic quantization for singular probability distributions: The quantization dimension. Regular sets and measures of dimension D. Rectifiable curves. Self-similar sets and measures Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/BFb0103945

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