A Probabilistic Theory of Pattern RecognitionSpringer 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. |
Kirjan sisältä
Tulokset 1 - 5 kokonaismäärästä 89
Sivu x
... Nearest Neighbor Rules : Even k 74 5.7 Inequalities for the Probability of Error 75 5.8 5.9 6.1 Behavior When L * Is Small 5.10 Admissibility of the Nearest Neighbor Rule 5.11 The ( k , l ) -Nearest Neighbor Rule Problems and Exercises ...
... Nearest Neighbor Rules : Even k 74 5.7 Inequalities for the Probability of Error 75 5.8 5.9 6.1 Behavior When L * Is Small 5.10 Admissibility of the Nearest Neighbor Rule 5.11 The ( k , l ) -Nearest Neighbor Rule Problems and Exercises ...
Sivu xi
... k - Nearest Neighbor Rule 169 11.1 Strong Consistency 170 11.2 Breaking Distance Ties 174 11.3 Recursive Methods 176 11.4 Scale - Invariant Rules 177 11.5 Weighted Nearest Neighbor Rules 178 11.6 Rotation - Invariant Rules 179 11.7 ...
... k - Nearest Neighbor Rule 169 11.1 Strong Consistency 170 11.2 Breaking Distance Ties 174 11.3 Recursive Methods 176 11.4 Scale - Invariant Rules 177 11.5 Weighted Nearest Neighbor Rules 178 11.6 Rotation - Invariant Rules 179 11.7 ...
Sivu xii
... Principle 249 15.1 Maximum Likelihood : The Formats 249 15.2 The Maximum ... Nearest Neighbor Rules 303 19.1 Condensed Nearest Neighbor Rules 303 19.2 Edited ... k - d Tree 328 20.6 The Deep k - d Tree 332 20.7 Quadtrees 333 20.8 Best ...
... Principle 249 15.1 Maximum Likelihood : The Formats 249 15.2 The Maximum ... Nearest Neighbor Rules 303 19.1 Condensed Nearest Neighbor Rules 303 19.2 Edited ... k - d Tree 328 20.6 The Deep k - d Tree 332 20.7 Quadtrees 333 20.8 Best ...
Sivu xiv
... Nearest Neighbor Rules 26.1 Consistency 26.2 Data Splitting 445 446 451 451 452 26.3 Data Splitting for Weighted NN Rules 453 26.4 Reference Data and Data Splitting 454 26.5 Variable Metric NN Rules 455 26.6 Selection of k Based on the ...
... Nearest Neighbor Rules 26.1 Consistency 26.2 Data Splitting 445 446 451 451 452 26.3 Data Splitting for Weighted NN Rules 453 26.4 Reference Data and Data Splitting 454 26.5 Variable Metric NN Rules 455 26.6 Selection of k Based on the ...
Sivu 3
... rule — not a classifier — is good if it is consistent , that is , if lim EL , = L * n → ∞ or equivalently , if Ln ... k - nearest neighbor rule with k = k ( n ) and k / n → 0. The k - nearest neighbor classifier gn ( x ) takes a ...
... rule — not a classifier — is good if it is consistent , that is , if lim EL , = L * n → ∞ or equivalently , if Ln ... k - nearest neighbor rule with k = k ( n ) and k / n → 0. The k - nearest neighbor classifier gn ( x ) takes a ...
Sisältö
1 | |
4 | |
21 | |
27 | |
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 |
Muita painoksia - Näytä kaikki
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |
A Probabilistic Theory of Pattern Recognition Luc Devroye,Laszlo Gyorfi,Gábor Lugosi Esikatselu ei käytettävissä - 2014 |
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Esikatselu ei käytettävissä - 2013 |
Yleiset termit ja lausekkeet
a₁ algorithm Assume asymptotic b₁ Bayes error binary Cauchy-Schwarz inequality cells Chapter class of classifiers classification rule condition converges to zero Corollary data points decision defined deleted estimate denotes density Devroye distribution empirical error error estimate error probability example finite fixed function HINT histogram rule Hoeffding's inequality hyperplane hyperrectangles inequality integer Jensen's inequality k-d tree k-nearest k-NN rule kernel rule L(gn Lemma linear classifier maximum likelihood minimizing the empirical nearest neighbor rule neural network node obtained otherwise pairs parameters partition pattern recognition probability of error proof of Theorem Prove random variables rate of convergence rectangles risk minimization rule gn sample selected shatter coefficients Show sigmoid split squared error structural risk minimization subsets tree classifiers universally consistent upper bound values vc dimension vector X₁ Y₁ фес