A study on cost behaviors of binary classification measures in class-imbalanced problems

TL;DR

This paper analyzes the cost behaviors of twelve binary classification measures in class-imbalanced problems, revealing their suitability based on theoretical cost functions related to class imbalance ratios.

Contribution

It introduces a new perspective by deriving cost functions for various measures, explaining their effectiveness or ineffectiveness in imbalanced classification tasks.

Findings

G-means of accuracy rates and BER are suitable measures.

F1, G-means of recall and precision, MCC, and Kappa are unsuitable.

Cost functions explain why some measures handle class imbalance better.

Abstract

This work investigates into cost behaviors of binary classification measures in a background of class-imbalanced problems. Twelve performance measures are studied, such as F measure, G-means in terms of accuracy rates, and of recall and precision, balance error rate (BER), Matthews correlation coefficient (MCC), Kappa coefficient, etc. A new perspective is presented for those measures by revealing their cost functions with respect to the class imbalance ratio. Basically, they are described by four types of cost functions. The functions provides a theoretical understanding why some measures are suitable for dealing with class-imbalanced problems. Based on their cost functions, we are able to conclude that G-means of accuracy rates and BER are suitable measures because they show "proper" cost behaviors in terms of "a misclassification from a small class will cause a greater cost than that from a large class". On the contrary, F1 measure, G-means of recall and precision, MCC and Kappa coefficient measures do not produce such behaviors so that they are unsuitable to serve our goal in dealing with the problems properly.