Abstract
An investigation has been made of the relation between the optimal classification error for two composite classes and the optimal classification error for certain pairs of subclasses (one from each composite class). Two kinds of inequalities have been derived: 1. (1) an inequality involving the classification error for the two composite classes and the classification error for a pair of subclasses averaged in an appropriate way on all possible pairs and 2. (2) a second inequality that differs from the first by replacing the average on all possible pairs by an average on a subset of pairs put into one-to-one correspondence. The relations between the two kinds of inequalities are investigated.
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