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- catalog abstract "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.".
- catalog contributor b11702894.
- catalog contributor b11702895.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "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.".
- catalog description "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.".
- catalog description "Includes bibliographical references (pages 215-224) and index.".
- catalog extent "x, 230 p. :".
- catalog identifier "3540673946 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1730.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1730".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 519.2/4 21".
- catalog subject "Cluster analysis.".
- catalog subject "Coding theory.".
- catalog subject "Distribution (Probability theory)".
- catalog subject "Fractals.".
- catalog subject "Mathematical statistics.".
- catalog subject "Mathematics.".
- catalog subject "Optical pattern recognition.".
- catalog subject "QA3.L28 no. 1730 QA273.6".
- catalog subject "Telecommunication.".
- catalog tableOfContents "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.".
- catalog title "Foundations of quantization for probability distributions / Siegfried Graf, Harald Luschgy.".
- catalog type "text".