Relevance-Based Evaluation Metrics for Multi-class Imbalanced Domains

The class imbalance problem is a key issue that has received much attention. This attention has been mostly focused on two-classes problems. Fewer solutions exist for the multi-classes imbalance problem. From an evaluation point of view, the class imbalance problem is challenging because a non-uniform importance is assigned to the classes. In this paper, we propose a relevance-based evaluation framework that incorporates user preferences by allowing the assignment of differentiated importance values to each class. The presented solution is able to overcome difficulties detected in existing measures and increases discrimination capability. The proposed framework requires the assignment of a relevance score to the problem classes. To deal with cases where the user is not able to specify each class relevance, we describe three mechanisms to incorporate the existing domain knowledge into the relevance framework. These mechanisms differ in the amount of information available and assumptions made regarding the domain. They also allow the use of our framework in common settings of multi-class imbalanced problems with different levels of information available.