An optimum class-selective rejection rule for pattern recognition

The concept of rejection is extended to that of class-selective rejection. That is, when an input pattern cannot be reliably assigned to one of the N classes in a N-class problem, it is assigned to a subset of classes that are most likely to issue the pattern, instead of simply being rejected. First, a new optimality criterion is appropriately defined to accommodate the newly introduced decision outcomes. Then, a new decision rule is proposed and its optimality proven. Various upper-bounds of error rate are obtained. Next, an example is provided to illustrate various aspects of the optimum decision rule. Finally, the implications of the new decision rule are discussed