rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Foundations of Quantization for Probability Distributions
  name:
    name part: Graf, Siegfried.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Luschgy, Harald.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2000
    edition: 1st ed. 2000.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 230 p. online resource.
  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.
  table of contents: 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.
  note: by Siegfried Graf, Harald Luschgy.
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  subject:
    topic: Pattern recognition
  subject:
    topic: Operations research
  subject:
    topic: Decision making
  subject:
    topic: Electrical engineering
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Statistical Theory and Methods
  subject:
    topic: Pattern Recognition
  subject:
    topic: Operations Research/Decision Theory
  subject:
    topic: Communications Engineering, Networks
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 1730
  identifier: 9783540455776
  identifier: https://doi.org/10.1007/BFb0103945
  record info:
    record creation date: 121227
    record change date: 20191024193556.0
    record identifier: 978-3-540-45577-6