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.

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Sisältö

Preface
1
Inequalities and Alternate Distance Measures
21
Linear Discrimination
39
Problems and Exercises
56
Weighted Nearest Neighbor Rules
71
Problems and Exercises
83
Consistency
91
Problems and Exercises
107
Condensed and Edited Nearest Neighbor Rules 303
302
Tree Classifiers
315
DataDependent Partitioning
363
Splitting the Data 387
386
The Resubstitution Estimate
397
Deleted Estimates of the Error Probability
407
Automatic Kernel Rules 423
422
Automatic Nearest Neighbor Rules
451

Problems and Exercises
118
The Regular Histogram Rule
133
Problems and Exercises
142
Consistency of the kNearest Neighbor Rule 169
168
VapnikChervonenkis Theory
187
Combinatorial Aspects of VapnikChervonenkis Theory 215
214
Lower Bounds for Empirical Classifier Selection
233
The Maximum Likelihood Principle
249
Parametric Classification
263
Generalized Linear Discrimination
279
Complexity Regularization
289
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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