Good Classification Measures and How to Find Them
This provides a tool for practitioners to evaluate classification results more effectively, though it is incremental in refining existing measures.
The paper tackles the problem of selecting the best performance measures for classification by systematically analyzing desirable properties and proving an impossibility theorem, resulting in a new family of measures including Symmetric Balanced Accuracy that satisfies most properties.
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.