Evaluating the classifier behavior with noisy data considering performance and robustness: The Equalized Loss of Accuracy measure

Noise is common in any real-world data set and may adversely affect classifiers built under the effect of such type of disturbance. Some of these classifiers are widely recognized for their good performance when dealing with imperfect data. However, the noise robustness of the classifiers is an important issue in noisy environments and it must be carefully studied. Both performance and robustness are two independent concepts that are usually considered separately, but the conclusions reached with one of these metrics do not necessarily imply the same conclusions with the other. Therefore, involving both concepts seems to be crucial in order determine the expected behavior of the classifiers against noise. Existing measures fail to properly integrate these two concepts, and they are also not well suited to compare different techniques over the same data. This paper proposes a new measure to establish the expected behavior of a classifier with noisy data trying to minimize the problems of considering performance and robustness individually: the Equalized Loss of Accuracy (ELA). The advantages of ELA against other robustness metrics are studied and all of them are also compared. Both the analysis of the distinct measures and the empirical results show that ELA is able to overcome the aforementioned problems that the rest of the robustness metrics may produce, having a better behavior when comparing different classifiers over the same data set. & 2015 Elsevier B.V. All rights reserved.