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Bounds on the Bayes Classification Error Based on Pairwise Risk Functions
March 1988 (vol. 10 no. 2)
pp. 281-288

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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Index Terms:
upper bounds; pattern recognition; Bayes classification error; pairwise risk functions; lower bounds; composite-hypothesis classification; pairwise Bayes risk; Bayes methods; decision theory; error statistics; pattern recognition
F.D. Garber, A. Djouadi, "Bounds on the Bayes Classification Error Based on Pairwise Risk Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 2, pp. 281-288, March 1988, doi:10.1109/34.3891
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