Performance measures for classification systems with rejection

TL;DR

This paper introduces a set of performance measures for classifiers with rejection, addressing the lack of evaluation tools when no specific cost function is defined, and demonstrates their effectiveness on synthetic and real data.

Contribution

The paper proposes three novel performance measures for classifiers with rejection that satisfy desired properties and links them to cost functions through the concept of relative optimality.

Findings

The measures effectively evaluate classifiers with rejection on synthetic data.

The measures provide meaningful insights on real-world classification tasks.

The approach connects performance evaluation to cost-sensitive decision-making.

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 that satisfy the desired properties. 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. From the measures, 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.