Author | Graf, Siegfried. author |
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Title | Foundations of Quantization for Probability Distributions [electronic resource] / by Siegfried Graf, Harald Luschgy |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |
Connect to | http://dx.doi.org/10.1007/BFb0103945 |
Descript | X, 230 p. online resource |
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