Multiclass ROC curves: a proposal based on the multidimensional Gini Index

This article 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 a comprehensive case study in credit rating, a challenging problem. The article 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.