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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
Citation:
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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