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020 _a9783540455776
_9978-3-540-45577-6
024 7 _a10.1007/BFb0103945
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
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072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aGraf, Siegfried.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFoundations of Quantization for Probability Distributions
_h[electronic resource] /
_cby Siegfried Graf, Harald Luschgy.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2000.
300 _aX, 230 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1730
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aMathematical statistics.
650 0 _aOptical pattern recognition.
650 0 _aOperations research.
650 0 _aTelecommunication.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistical Theory and Methods.
_0http://scigraph.springernature.com/things/product-market-codes/S11001
650 2 4 _aPattern Recognition.
_0http://scigraph.springernature.com/things/product-market-codes/I2203X
650 2 4 _aOperations Research/Decision Theory.
_0http://scigraph.springernature.com/things/product-market-codes/521000
650 2 4 _aCommunications Engineering, Networks.
_0http://scigraph.springernature.com/things/product-market-codes/T24035
700 1 _aLuschgy, Harald.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662168271
776 0 8 _iPrinted edition:
_z9783540673941
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1730
856 4 0 _uhttps://doi.org/10.1007/BFb0103945
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11607
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