Performance measures for classification systems with rejection. (March 2017) - Condessa, Filipe; Bioucas-Dias, José; Kovačević, Jelena
Abstract: Classifiers with rejection are essential in real-world applications where misclassifications and their effects are critical. However, if no problem specific cost function is defined, there are no established measures to assess the performance of such classifiers. We introduce a set of desired properties for performance measures for classifiers with rejection, based on which we propose a set of three performance measures for the evaluation of the performance of classifiers with rejection. The nonrejected accuracy measures the ability of the classifier to accurately classify nonrejected samples; the classification quality measures the correct decision making of the classifier with rejector; and the rejection quality measures the ability to concentrate all misclassified samples onto the set of rejected samples. We derive the concept of relative optimality that allows us to connect the measures to a family of cost functions that take into account the trade-off between rejection and misclassification. We illustrate the use of the proposed performance measures on classifiers with rejection applied to synthetic and real-world data. Abstract : Graphical abstract: Abstract : Highlights: A set of three performance measures for classifier with rejection is proposed. Nonrejected accuracy measures ability to accurately classify nonrejected samples. Classification quality measures correct decisions by classifier with rejection. Rejection quality measures ability to reject misclassified samples. The performance measures are connected to general cost functions.