LEADER 04698nam 22008175 450 001 9910146314003321 005 20200702160230.0 010 $a3-540-45577-9 024 7 $a10.1007/BFb0103945 035 $a(CKB)1000000000437284 035 $a(SSID)ssj0000323273 035 $a(PQKBManifestationID)11244407 035 $a(PQKBTitleCode)TC0000323273 035 $a(PQKBWorkID)10299819 035 $a(PQKB)10398498 035 $a(DE-He213)978-3-540-45577-6 035 $a(MiAaPQ)EBC6295580 035 $a(MiAaPQ)EBC5586114 035 $a(Au-PeEL)EBL5586114 035 $a(OCoLC)1066188068 035 $a(PPN)155164120 035 $a(EXLCZ)991000000000437284 100 $a20121227d2000 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFoundations of Quantization for Probability Distributions$b[electronic resource] /$fby Siegfried Graf, Harald Luschgy 205 $a1st ed. 2000. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000. 215 $a1 online resource (X, 230 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1730 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-67394-6 320 $aIncludes bibliographical references (pages [215]-224) and index. 327 $aI. 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. 330 $aDue to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1730 606 $aProbabilities 606 $aStatistics  606 $aPattern recognition 606 $aOperations research 606 $aDecision making 606 $aElectrical engineering 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aPattern Recognition$3https://scigraph.springernature.com/ontologies/product-market-codes/I2203X 606 $aOperations Research/Decision Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/521000 606 $aCommunications Engineering, Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/T24035 615 0$aProbabilities. 615 0$aStatistics . 615 0$aPattern recognition. 615 0$aOperations research. 615 0$aDecision making. 615 0$aElectrical engineering. 615 14$aProbability Theory and Stochastic Processes. 615 24$aStatistical Theory and Methods. 615 24$aPattern Recognition. 615 24$aOperations Research/Decision Theory. 615 24$aCommunications Engineering, Networks. 676 $a519.24 700 $aGraf$b Siegfried$4aut$4http://id.loc.gov/vocabulary/relators/aut$062624 702 $aLuschgy$b Harald$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146314003321 996 $aFoundations of quantization for probability distributions$9262272 997 $aUNINA