000 | 04009nam a22005895i 4500 | ||
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001 | 978-3-540-45577-6 | ||
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007 | cr nn 008mamaa | ||
008 | 121227s2000 gw | s |||| 0|eng d | ||
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_a9783540455776 _9978-3-540-45577-6 |
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024 | 7 |
_a10.1007/BFb0103945 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBT _2bicssc |
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072 | 7 |
_aMAT029000 _2bisacsh |
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_aPBT _2thema |
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_aPBWL _2thema |
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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. |
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300 |
_aX, 230 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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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 _d11607 |