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. |
Kirjan sisältä
Tulokset 1 - 5 kokonaismäärästä 21
Sivu 2
... vector equation is the equivalent of three scalar equations . A vector is said to be equal to zero , when its magnitude is zero . Such vectors may be set equal to one ... VECTOR ANALYSIS . Addition and Subtraction of Vectors . 3 2 ...
... vector equation is the equivalent of three scalar equations . A vector is said to be equal to zero , when its magnitude is zero . Such vectors may be set equal to one ... VECTOR ANALYSIS . Addition and Subtraction of Vectors . 3 2 ...
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Sivu 9
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Sivu 2
... vector â multiplied by the magnitude of a ; i.e. , a = a â . Two vectors a and b are parallel if and only if a = mb for some scalar m . 4. Scalar Multiplication ... vector will have different components in 2 TOPICS IN VECTOR ANALYSIS.
... vector â multiplied by the magnitude of a ; i.e. , a = a â . Two vectors a and b are parallel if and only if a = mb for some scalar m . 4. Scalar Multiplication ... vector will have different components in 2 TOPICS IN VECTOR ANALYSIS.
Sivu xiii
... VECTOR ANALYSIS . 1. Definitions - Vector Scalar .. PAGE 2. Graphical Representation of a Vector ... 3. Equality of Vectors ― Reciprocal Vector ... Negative Vector Unit Vector 4. Composition of Vectors - Addition and Subtraction Sum as ...
... VECTOR ANALYSIS . 1. Definitions - Vector Scalar .. PAGE 2. Graphical Representation of a Vector ... 3. Equality of Vectors ― Reciprocal Vector ... Negative Vector Unit Vector 4. Composition of Vectors - Addition and Subtraction Sum as ...
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
A Probabilistic Theory of Pattern Recognition Luc Devroye,Laszlo Györfi,Gabor Lugosi Rajoitettu esikatselu - 2013 |
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 |
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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