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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. 281288, March, 1988.  
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@article{ 10.1109/34.3891, author = {F.D. Garber and A. Djouadi}, title = {Bounds on the Bayes Classification Error Based on Pairwise Risk Functions}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {10}, number = {2}, issn = {01628828}, year = {1988}, pages = {281288}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.3891}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Bounds on the Bayes Classification Error Based on Pairwise Risk Functions IS  2 SN  01628828 SP281 EP288 EPD  281288 A1  F.D. Garber, A1  A. Djouadi, PY  1988 KW  upper bounds; pattern recognition; Bayes classification error; pairwise risk functions; lower bounds; compositehypothesis classification; pairwise Bayes risk; Bayes methods; decision theory; error statistics; pattern recognition VL  10 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Upper and lower bounds on the Bayes risk for multiple, compositehypothesis classification are obtained. Bounds on the Bayes risk for M simple classes are derived in terms of the risk functions for (M1) 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 Mclass case and for compositehypothesis 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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