Foundations of quantization for probability distributions:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Lecture notes in mathematics
1730 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 230 S. graph. Darst. |
| ISBN: | 3540673946 |
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MARC
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Record in the Search Index
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| adam_text | Contents
List of Figures VIII
List of Tables IX
Introduction 1
I General properties of the quantization for probability distributions 7
1 Voronoi partitions 7
1.1 General norms 7
1.2 Euclidean norms 16
2 Centers and moments of probability distributions 20
2.1 Uniqueness and characterization of centers 20
2.2 Moments of balls 26
3 The quantization problem 30
4 Basic properties of optimal quantizers 37
4.1 Stationarity and existence 37
4.2 The functional Vn T 48
4.3 Quantization error for ball packings 50
4.4 Examples 52
4.5 Stability properties and empirical versions 57
5 Uniqueness and optimality in one dimension 64
5.1 Uniqueness 64
5.2 Optimal Quantizers 66
II Asymptotic quantization for nonsingular probability distributions 77
6 Asymptotics for the quantization error 77
vi Contents
7 Asymptotically optimal quantizers 93
7.1 Mixtures and partitions 93
7.2 Empirical measures 96
7.3 Asymptotic optimality in one dimension 99
7.4 Product quantizers 102
8 Regular quantizers and quantization coefficients 106
8.1 Ball lower bound 107
8.2 Space filling figures, regular quantizers and upper bounds . . . 107
8.3 Lattice quantizers Ill
8.4 Quantization coefficients of one dimensional distributions ... 121
9 Random quantizers and quantization coefficients 127
9.1 Asymptotics for random quantizers 127
9.2 Random quantizer upper bound 130
9.3 d asymptotics and entropy 132
10 Asymptotics for the covering radius 137
10.1 Basic properties 137
10.2 Asymptotic covering radius 141
10.3 Covering radius of lattices and bounds 146
10.4 Stability properties and empirical versions 151
III Asymptotic quantization for singular probability distributions 155
11 The quantization dimension 155
11.1 Definition and elementary properties 155
11.2 Comparison to the Hausdorff dimension 157
11.3 Comparison to the box dimension 158
11.4 Comparison to the rate distortion dimension 161
12 Regular sets and measures of dimension D 165
12.1 Definition and examples 165
12.2 Asymptotics for the quantization error 173
13 Rectifiable curves 180
14 Self similar sets and measures 190
14.1 Basic notion and facts 190
Contents vii
14.2 An. upper bound for the quantization dimension 192
14.3 A lower bound for the quantization dimension 195
14.4 The quantization dimension 199
14.5 The quantization coefficient 203
Appendix Univariate distributions 209
Bibliography 215
Symbols 225
Index 229
|
| any_adam_object | 1 |
| author | Graf, Siegfried Luschgy, Harald |
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| spelling | Graf, Siegfried Verfasser aut Foundations of quantization for probability distributions Siegfried Graf ; Harald Luschgy Berlin [u.a.] Springer 2000 X, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1730 Wahrscheinlichkeitsverteilung - Beste Approximation Wahrscheinlichkeitsverteilung - Quantisierung <Nachrichtentechnik> Cluster analysis Coding theory Distribution (Probability theory) Fractals Quantisierung Nachrichtentechnik (DE-588)4391959-5 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantisierung Nachrichtentechnik (DE-588)4391959-5 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Luschgy, Harald Verfasser aut Lecture notes in mathematics 1730 (DE-604)BV000676446 1730 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008944510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graf, Siegfried Luschgy, Harald Foundations of quantization for probability distributions Lecture notes in mathematics Wahrscheinlichkeitsverteilung - Beste Approximation Wahrscheinlichkeitsverteilung - Quantisierung <Nachrichtentechnik> Cluster analysis Coding theory Distribution (Probability theory) Fractals Quantisierung Nachrichtentechnik (DE-588)4391959-5 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4391959-5 (DE-588)4121894-2 (DE-588)4113937-9 |
| title | Foundations of quantization for probability distributions |
| title_auth | Foundations of quantization for probability distributions |
| title_exact_search | Foundations of quantization for probability distributions |
| title_full | Foundations of quantization for probability distributions Siegfried Graf ; Harald Luschgy |
| title_fullStr | Foundations of quantization for probability distributions Siegfried Graf ; Harald Luschgy |
| title_full_unstemmed | Foundations of quantization for probability distributions Siegfried Graf ; Harald Luschgy |
| title_short | Foundations of quantization for probability distributions |
| title_sort | foundations of quantization for probability distributions |
| topic | Wahrscheinlichkeitsverteilung - Beste Approximation Wahrscheinlichkeitsverteilung - Quantisierung <Nachrichtentechnik> Cluster analysis Coding theory Distribution (Probability theory) Fractals Quantisierung Nachrichtentechnik (DE-588)4391959-5 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Wahrscheinlichkeitsverteilung - Beste Approximation Wahrscheinlichkeitsverteilung - Quantisierung <Nachrichtentechnik> Cluster analysis Coding theory Distribution (Probability theory) Fractals Quantisierung Nachrichtentechnik Wahrscheinlichkeitsverteilung Hochschulschrift |
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