Good Classification Measures and How to Find Them

TL;DR

This paper systematically analyzes various classification performance measures, defining desirable properties, proving an impossibility theorem, and proposing a new family of measures including Matthews Correlation Coefficient and Symmetric Balanced Accuracy.

Contribution

It introduces a formal framework for evaluating classification measures, proves an impossibility theorem, and proposes a new family of measures satisfying most desirable properties.

Findings

Identified which measures satisfy which properties

Proved an impossibility theorem for measure properties

Proposed a new family of classification measures

Abstract

Several performance measures can be used for evaluating classification results: accuracy, F-measure, and many others. Can we say that some of them are better than others, or, ideally, choose one measure that is best in all situations? To answer this question, we conduct a systematic analysis of classification performance measures: we formally define a list of desirable properties and theoretically analyze which measures satisfy which properties. We also prove an impossibility theorem: some desirable properties cannot be simultaneously satisfied. Finally, we propose a new family of measures satisfying all desirable properties except one. This family includes the Matthews Correlation Coefficient and a so-called Symmetric Balanced Accuracy that was not previously used in classification literature. We believe that our systematic approach gives an important tool to practitioners for adequately evaluating classification results.