Bounds on the Bayes Classification Error Based on Pairwise Risk Functions

Authors:
F. D. Garber;A. Djouadi
Affiliations:
Ohio State Univ., Columbus;Ohio State Univ., Columbus
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1988

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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.