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Foundations of Quantization for Probability Distributions [[electronic resource] /] / by Siegfried Graf, Harald Luschgy



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Autore: Graf Siegfried Visualizza persona
Titolo: Foundations of Quantization for Probability Distributions [[electronic resource] /] / by Siegfried Graf, Harald Luschgy Visualizza cluster
Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Edizione: 1st ed. 2000.
Descrizione fisica: 1 online resource (X, 230 p.)
Disciplina: 519.24
Soggetto topico: Probabilities
Statistics 
Pattern recognition
Operations research
Decision making
Electrical engineering
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Pattern Recognition
Operations Research/Decision Theory
Communications Engineering, Networks
Soggetto genere / forma: Electronic books.
Persona (resp. second.): LuschgyHarald
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references (pages [215]-224) and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Foundations of quantization for probability distributions  Visualizza cluster
ISBN: 3-540-45577-9
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910146314003321
Lo trovi qui: Univ. Federico II
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Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1730