AUCμ: A Performance Metric for Multi-Class Machine Learning Models

The area under the receiver operating characteristic curve (AUC) is arguably the most common metric in machine learning for assessing the quality of a two-class classification model. As the number and complexity of machine learning applications grows, so too does the need for measures that can gracefully extend to classification models trained for more than two classes. Prior work in this area has proven computationally intractable and/or inconsistent with known properties of AUC, and thus there is still a need for an improved multi-class efficacy metric. We provide in this work a multi-class extension of AUC that we call AUC{\textmu} that is derived from first principles of the binary class AUC. AUC{\textmu} has similar computational complexity to AUC and maintains the properties of AUC critical to its interpretation and use.