A Probabilistic Theory of Pattern Recognition

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.

Pattern recognition presents a significant challege for scientists and engineers, and many different approaches have been proposed. This book provides a self-contained account of probabilistic techniques that have been applied to the subject. Researchers and graduate students will benefit from this wide-ranging account of the field.

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