Foundations of Quantization for Probability Distributions

• Κύριοι συγγραφείς: Graf, Siegfried (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Luschgy, Harald (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Έκδοση: 1st ed. 2000.
• Σειρά: Lecture Notes in Mathematics, 1730
• Θέματα: Probabilities.; Statistics .; Pattern recognition.; Operations research.; Decision making.; Electrical engineering.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Pattern Recognition.; Operations Research/Decision Theory.; Communications Engineering, Networks.

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...

Πίνακας περιεχομένων:

• 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.