An Optimal Reject Rule for Binary Classifiers

Binary classifiers are used in many complex classification problems in which the classification result could have serious consequences. Thus, they should ensure a very high reliability to avoid erroneous decisions. Unfortunately, this is rarely the case in real situations where the cost for a wrong classification could be so high that it should be convenient to reject the sample which gives raise to an unreliable result. However, as far as we know, a reject option specifically devised for binary classifiers has not been yet proposed. This paper presents an optimal reject rule for binary classifiers, based on the Receiver Operating Characteristic curve. The rule is optimal since it maximizes a classification utility function, defined on the basis of classification and error costs peculiar for the application at hand. Experiments performed with a data set publicly available confirmed the effectiveness of the proposed reject rule.