On functional relation between class-selective rejection error and average number of classes

The paper first reviews the recently proposed optimum class-selective rejection rule. This rule provides an optimum trade-off between the error rate and the average number of (selected) classes. Then, a new general relation between the error rate and the average number of classes is presented. The error rate can directly be computed from the class-selective reject function, which in turn can be estimated from unlabelled patterns, by simply counting the rejected classes. Theoretical as well as practical implications are discussed and some future research directions are proposed.