A Multiclass ROC Curve

Abstract: This paper introduces a novel methodology for constructing multiclass ROC curves using the multidimensional Gini index. The proposed methodology leverages the established relationship between the Gini coefficient and the ROC Curve and extends it to multiclass settings through the multidimensional Gini index. The framework is validated by means of two comprehensive case studies in health care and finance. The paper provides a theoretically grounded solution to multiclass performance evaluation, particularly valuable for imbalanced datasets, for which a prudential assessment should take precedence over class frequency considerations.