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 71
Sivu 1
... vector of weather data , an electrocardiogram , or a signature on a check suitably digitized . More formally , an observation is a d - dimensional vector x . The unknown nature of the observation is called a class . It is denoted by y ...
... vector of weather data , an electrocardiogram , or a signature on a check suitably digitized . More formally , an observation is a d - dimensional vector x . The unknown nature of the observation is called a class . It is denoted by y ...
Sivu 4
... vector . The reader should be aware that many results given here may be painlessly extended to certain metric spaces of infinite dimension . Let us return to our novice's questions . We know that there are good rules , but just how good ...
... vector . The reader should be aware that many results given here may be painlessly extended to certain metric spaces of infinite dimension . Let us return to our novice's questions . We know that there are good rules , but just how good ...
Sivu 6
... vector X that are cut at the early stages of the tree are most crucial in reaching a decision . Expert systems ... vector X that represents character are true measurements involving only vector differences between se- 6 1. Introduction.
... vector X that are cut at the early stages of the tree are most crucial in reaching a decision . Expert systems ... vector X that represents character are true measurements involving only vector differences between se- 6 1. Introduction.
Sivu 7
Luc Devroye, Laszlo Györfi, Gabor Lugosi. character are true measurements involving only vector differences between ... vectors are denoted by lowercase letters such as a , b , c , x , and y . Sets are also denoted by roman capitals , but ...
Luc Devroye, Laszlo Györfi, Gabor Lugosi. character are true measurements involving only vector differences between ... vectors are denoted by lowercase letters such as a , b , c , x , and y . Sets are also denoted by roman capitals , but ...
Sivu 30
... vector , and p = 1 − p is a mixture parameter . If Σ1 = Σ0 = σ21 , where I is the identity matrix , then - || mi - mo || A = σ is a scaled version of the distance between the means . If Σ1 then || mi - moll A = √ po2 + ( 1 − p ) o ...
... vector , and p = 1 − p is a mixture parameter . If Σ1 = Σ0 = σ21 , where I is the identity matrix , then - || mi - mo || A = σ is a scaled version of the distance between the means . If Σ1 then || mi - moll A = √ po2 + ( 1 − p ) o ...
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