Reject option with multiple thresholds

can be obtained using the so-called “reject” option. Namely, the patterns that are the most likely to be misclassified are rejected (i.e., they are not classified); they are then handled by more sophisticated procedures (e.g., a manual classification is performed). However, handling high reject rates is usually too time-consuming for application purposes. Therefore, a trade-off between error and reject is mandatory. The formulation of the best error-reject trade-off and the related optimal reject rule was given by Chow [1]. According to Chow’s rule, a pattern x is rejected if: max P P T k N k i = ( ) = ( ) < 1, , | | K ω ω x x (3)