Robustness in statistical pattern recognition:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Mathematics and its applications
380 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 302 S. |
| ISBN: | 0792342674 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 Probability Models of Data and Optimal Decision Rules 1
1.1 Probability Models of Observation Data 1
1.2 Elements of Statistical Decision Theory 8
1.3 Optimal Decision Rules in Space of Continuous Feature Variables . . 12
1.4 Optimal Classification of Multivariate Gaussian Observations 19
1.5 Optimal Decision Rules in Discrete Space of Feature Variables .... 24
1.6 Regular Families of Probability Distributions 27
2 Violations of Model Assumptions and Basic Notions in Decision
Rule Robustness 31
2.1 Construction of Decision Rules Using Training Sample 31
2.1.1 Structural Minimization of Empirical Risk for Given Paramet¬
ric Family of Decision Rules 33
2.1.2 Statistical Hypothesis Testing with Parametric Model of Prob¬
ability Distributions {/ ,(•)} and Classified Training Sample
Available 33
2.1.3 Decision Rules Minimizing Lower and Upper Bounds of Risk
Density 34
2.1.4 Plug in Decision Rules (PDR) 36
2.2 Types of Distortions 38
2.3 Decision Rule Robustness Characteristics 47
3 Robustness of Parametric Decision Rules and Small sample Effects 51
3.1 Asymptotic Risk Expansion for Decision Rules Using Minimum Con¬
trast Estimators 51
3.2 Optimization and Robustness Analysis for Decision Rules Based on
MC estimators 62
3.3 Adaptive Decision Rule Robustness for Gaussian Observations .... 68
4 Robustness of Nonparametric Decision Rules and Small sample
Effects 77
4.1 Robustness of Nonparametric Rosenblatt Parzen Decision Rules . . 77
4.2 Robustness of Nonparametric k Nearest
Neighbor Decision Rules 87
viii CONTENTS
4.3 Comparative Analysis of Robustness for Adaptive Decision Rules . . 93
4.3.1 Application of Rosenblatt Parzen ADR 94
4.3.2 Application of NN Decision Rules 97
4.3.3 Performance Comparison for Parametric and Nonparametric
ADR 100
5 Decision Rule Robustness under Distortions of Observations to be
Classified 101
5.1 Robustness to Tukey Huber Type Contaminations 101
5.2 Distortions in /^ metric Ill
5.3 Robustness of Error Probability for Distortions in Variation Metric . 119
5.4 Decision Rule Robustness to Random Distortions of Densities . . . .125
5.5 Additive Distortions of Observations 127
5.6 Distortions Induced by Finite Mixtures 135
5.7 Errors in Assignment of Distribution Parameters 142
6 Decision Rule Robustness under Distortions of Training Samples 149
6.1 Risk Robustness under Statistical Dependence of Sample Elements . 149
6.2 Robustness under Misclassification Errors in Training Sample .... 159
6.3 Parametric e nonhomogeneity of Training Samples 178
6.4 Classification of Gaussian Observations with Outliers in Training
Sample 187
7 Cluster Analysis under Distorted Model Assumptions 193
7.1 Small sample Effects and Robustness of Unsupervised Decision Rules 193
7.2 Cluster Analysis for Random length Runs of Observations 206
7.3 Cluster Analysis of T° runs : 218
7. 3.1 Mathematical Model 218
7.3.2 Classification by Maximum Likelihood Rule 220
7.3.3 Classification by Homogeneity Criterion 222
7.3.4 The Case of Unknown Parameters {0?} 228
7.3.5 Performance Analysis 231
7.4 Cluster Analysis of Random Runs using Statistical Estimators of In
terclass Distances 240
7.4.1 Mathematical Model 240
7.4.2 Interclass Distance Functional: Case of Parametric Prior Un¬
certainty 242
7.4.3 Nonparametric Estimator of Interclass Distance 245
7.4.4 Decision Rules 247
7.4.5 Computer Experiments 249
7.5 Case of Markov Dependence of Class Indices 250
7.5.1 Mathematical Model 250
7.5.2 Optimal Decision Rules 252
7.5.3 Unknown Probability Characteristics w°, P° 256
7.5.4 Parametric Prior Uncertainty Case 262
CONTENTS ix
7.5.5 Case of Gaussian Observations 268
7.5.6 Performance Analysis 270
7.6 Asymptotic Robustness under Tukey Huber Distortions 272
7.6.1 Mathematical Model 272
7.6.2 Asymptotic Expansions of Risk 275
7.6.3 Robustness under Contaminated Fisher Model 280
Bibliography 283
Index 297
Main Notations and Abbreviations 301
|
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| isbn | 0792342674 |
| language | English |
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| physical | XIV, 302 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Charin, Jurij S. Verfasser aut Robustness in statistical pattern recognition by Yurij Kharin Dordrecht [u.a.] Kluwer 1996 XIV, 302 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 380 Mustererkennung - Robuste Statistik Pattern perception Statistical methods Mustererkennung (DE-588)4040936-3 gnd rswk-swf Robustheit (DE-588)4126481-2 gnd rswk-swf Mustererkennung (DE-588)4040936-3 s Robustheit (DE-588)4126481-2 s DE-604 Mathematics and its applications 380 (DE-604)BV008163334 380 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007440293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Charin, Jurij S. Robustness in statistical pattern recognition Mathematics and its applications Mustererkennung - Robuste Statistik Pattern perception Statistical methods Mustererkennung (DE-588)4040936-3 gnd Robustheit (DE-588)4126481-2 gnd |
| subject_GND | (DE-588)4040936-3 (DE-588)4126481-2 |
| title | Robustness in statistical pattern recognition |
| title_auth | Robustness in statistical pattern recognition |
| title_exact_search | Robustness in statistical pattern recognition |
| title_full | Robustness in statistical pattern recognition by Yurij Kharin |
| title_fullStr | Robustness in statistical pattern recognition by Yurij Kharin |
| title_full_unstemmed | Robustness in statistical pattern recognition by Yurij Kharin |
| title_short | Robustness in statistical pattern recognition |
| title_sort | robustness in statistical pattern recognition |
| topic | Mustererkennung - Robuste Statistik Pattern perception Statistical methods Mustererkennung (DE-588)4040936-3 gnd Robustheit (DE-588)4126481-2 gnd |
| topic_facet | Mustererkennung - Robuste Statistik Pattern perception Statistical methods Mustererkennung Robustheit |
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