A Probabilistic Theory of Pattern Recognition / Edition 1

by Luc Devroye, Laszlo Gyïrfi, Gabor Lugosi

Overview

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.

Product Details

ISBN-13:	9780387946184
Publisher:	Springer New York
Publication date:	04/04/1996
Series:	Stochastic Modelling and Applied Probability , #31
Edition description:	1996
Pages:	638
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

Preface * Introduction * The Bayes Error * Inequalities and alternate

distance measures * Linear discrimination * Nearest neighbor rules *

Consistency * Slow rates of convergence Error estimation * The regular

histogram rule * Kernel rules Consistency of the k-nearest neighbor

rule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-

Chervonenkis theory * Lower bounds for empirical classifier selection

* The maximum likelihood principle * Parametric classification *

Generalized linear discrimination * Complexity regularization *

Condensed and edited nearest neighbor rules * Tree classifiers * Data-

dependent partitioning * Splitting the data * The resubstitution

estimate * Deleted estimates of the error probability * Automatic

kernel rules * Automatic nearest neighbor rules * Hypercubes and

discrete spaces * Epsilon entropy and totally bounded sets * Uniform

laws of large numbers * Neural networks * Other error estimates *

Feature extraction * Appendix * Notation * References * Index