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<p>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.</p>
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

A. Djouadi and F. Garber, "Bounds on the Bayes Classification Error Based on Pairwise Risk Functions," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 10, no. , pp. 281-288, 1988.
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