A Probabilistic Theory of Pattern Recognition
by Devroye, Luc; Gyorfi, Laszlo; Lugosi, GaborFormat: Hardcover
Pub. Date: 1996-01-01
Publisher(s): Springer Verlag
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Summary
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.
Table of Contents
| Preface | |
| Introduction | p. 1 |
| The Bayes Error | p. 9 |
| Inequalities and Alternate Distance Measures | p. 21 |
| Linear Discrimination | p. 39 |
| Nearest Neighbor Rules | p. 61 |
| Consistency | p. 91 |
| Slow Rates of Convergence | p. 111 |
| Error Estimation | p. 121 |
| The Regular Histogram Rule | p. 133 |
| Kernel Rules | p. 147 |
| Consistency of the k-Nearest Neighbor Rule | p. 169 |
| Vapnik-Chervonenkis Theory | p. 187 |
| Combinatorial Aspects of Vapnik-Chervonenkis Theory | p. 215 |
| Lower Bounds for Empirical Classifier Selection | p. 233 |
| The Maximum Likelihood Principle | p. 249 |
| Parametric Classification | p. 263 |
| Generalized Linear Discrimination | p. 279 |
| Complexity Regularization | p. 289 |
| Condensed and Edited Nearest Neighbor Rules | p. 303 |
| Tree Classifiers | p. 315 |
| Data-Dependent Partitioning | p. 363 |
| Splitting the Data | p. 387 |
| The Resubstitution Estimate | p. 397 |
| Deleted Estimates of the Error Probability | p. 407 |
| Automatic Kernel Rules | p. 423 |
| Automatic Nearest Neighbor Rules | p. 451 |
| Hypercubes and Discrete Spaces | p. 461 |
| Epsilon Entropy and Totally Bounded Sets | p. 479 |
| Uniform Laws of Large Numbers | p. 489 |
| Neural Networks | p. 507 |
| Other Error Estimates | p. 549 |
| Feature Extraction | p. 561 |
| Appendix | p. 575 |
| Notation | p. 591 |
| References | p. 593 |
| Author Index | p. 619 |
| Subject Index | p. 627 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
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