Bounds on the Bayes classification error based on pairwise risk functions

Author

Garber, F.D. ; Djouadi, A.

Author_Institution

Dept. of Electr. Eng., Ohio State Univ., Columbus, OH, USA

Volume

10

Issue

2

fYear

1988

fDate

3/1/1988 12:00:00 AM

Firstpage

281

Lastpage

288

Abstract

Upper and lower bounds on the Bayes risk for multiple, composite-hypothesis classification are obtained. Bounds on the Bayes risk for M simple classes are derived in terms of the risk functions for (M-1) classes, and so on, until the desired result depends only on the pairwise (M=2) Bayes risks. A method of computing upper and lower bounds on the pairwise Bayes risk for composite classes is developed. Algorithms for computing the upper and lower bounds for the general M-class case and for composite-hypothesis classes are presented. Numerical examples of the application of the bounding techniques to a problem involving the classification of aircraft are discussed. Results for the bounds and other performance measures are compared for the most interesting cases

Keywords

Bayes methods; decision theory; error statistics; pattern recognition; Bayes classification error; composite-hypothesis classification; lower bounds; pairwise Bayes risk; pairwise risk functions; pattern recognition; upper bounds; Aircraft; Algorithm design and analysis; Bayesian methods; Classification algorithms; Nearest neighbor searches; Pattern analysis; Pattern recognition; Performance analysis; Prototypes; System performance;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.3891

Filename

3891