A Probabilistic Theory of Pattern RecognitionSpringer Science & Business Media, 20.2.1997 - 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
Introduction | 1 |
The Bayes Error | 9 |
Inequalities and Alternate Distance Measures | 21 |
Linear Discrimination | 39 |
Nearest Neighbor Rules | 61 |
Consistency | 91 |
Slow Rates of Convergence | 111 |
Error Estimation | 121 |
Tree Classifiers | 315 |
DataDependent Partitioning | 363 |
Splitting the Data | 387 |
The Resubstitution Estimate | 397 |
Deleted Estimates of the Error Probability | 407 |
Automatic Kernel Rules | 423 |
Automatic Nearest Neighbor Rules | 451 |
Hypercubes and Discrete Spaces | 461 |
The Regular Histogram Rule | 133 |
Kernel Rules | 147 |
Consistency of the fcNearest Neighbor Rule | 169 |
VapnikChervonenkis Theory | 187 |
Combinatorial Aspects of VapnikChervonenkis Theory | 215 |
Lower Bounds for Empirical Classifier Selection | 233 |
The Maximum Likelihood Principle | 249 |
Parametric Classification | 263 |
Generalized Linear Discrimination | 279 |
Complexity Regularization | 289 |
Condensed and Edited Nearest Neighbor Rules | 303 |
Epsilon Entropy and Totally Bounded Sets | 479 |
Uniform Laws of Large Numbers | 489 |
Neural Networks | 507 |
Other Error Estimates | 549 |
Feature Extraction | 561 |
Appendix | 575 |
Notation | 591 |
| 619 | |
| 627 | |
Muita painoksia - Näytä kaikki
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apply Assume Bayes bound called cells Chapter classification rule classifier Clearly close coefficients complexity components computational Consider constant contains continuous convergence corresponding covering cuts decision defined definition denotes density depends discrimination distance distribution empirical error error probability estimate example exists expected fact Figure finite fixed function given hyperplane implies independent inequality integer introduce Lemma linear measure method minimizing nearest neighbor rule Note Observe obtained otherwise pairs parameters partition performance pick points positive possible probability of error Problem proof Prove random variables rectangles regions Remark respect result risk sample satisfies selected sequence shatter Show simple smoothing space split subsets suffices term Theorem tree uniform universally consistent upper bound values vc dimension vector weights zero