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Bounds on the Bayes classification error based on pairwise risk functions

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2 Author(s)
Garber, F.D. ; Dept. of Electr. Eng., Ohio State Univ., Columbus, OH, USA ; Djouadi, A.

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

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:10 ,  Issue: 2 )