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We discuss a strategy for polychotomous classification that involves coupling the estimating class probabilities for each pair of classes, and estimates together. The coupling model is similar to the Bradley-Terry method for paired comparisons. We study the nature of the class probability estimates that arise, and examine the performance of the procedure in real and simulated data sets. Classifiers used include linear discriminants, nearest neighbors, adaptive nonlinear methods and the support vector machine.
Hastie et al. (Wed,) studied this question.