A Probabilistic Theory of Pattern Recognition

Etukansi
Springer Science & Business Media, 27.11.2013 - 638 sivua
Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, free classifiers, and neural networks. Wherever possible, distribution-free properties and inequalities are derived. A substantial portion of the results or the analysis is new. Over 430 problems and exercises complement the material.
 

Sisältö

Preface
1
Linear Discrimination
4
Inequalities and Alternate Distance Measures
21
6
27
1
54
Nearest Neighbor Rules
60
4
67
6
74
Parametric Classification
263
Generalized Linear Discrimination
279
Complexity Regularization
289
Condensed and Edited Nearest Neighbor Rules 303
302
Tree Classifiers
315
DataDependent Partitioning
363
Splitting the Data 387
386
The Resubstitution Estimate
397

11
81
2
92
6
100
8
106
2
113
Error Estimation
120
The Regular Histogram Rule
133
Kernel Rules
153
Consistency of the kNearest Neighbor Rule
168
VapnikChervonenkis Theory
187
Combinatorial Aspects of VapnikChervonenkis Theory
214
4
224
1
234
The Maximum Likelihood Principle
249
Deleted Estimates of the Error Probability
407
Automatic Kernel Rules 423
422
Automatic Nearest Neighbor Rules
451
Hypercubes and Discrete Spaces 461
460
Epsilon Entropy and Totally Bounded Sets
479
Uniform Laws of Large Numbers 489
488
Neural Networks
507
Other Error Estimates
549
Feature Extraction 561
560
Appendix
575
Notation
591
Author Index
619
Subject Index
627
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