Categorical classifiers in multiclass classification with imbalanced datasets

This paper discusses, in a multiclass classification setting, the issue of the choice of the so-called categorical classifier, which is the procedure or criterion that transforms the probabilities produced by a probabilistic classifier into a single category or class. The standard choice is the Bayes Classifier (BC), but it has some limits with rare classes. This paper studies the classification performance of the BC versus two alternatives, that are the Max Difference Classifier (MDC) and Max Ratio Classifier (MRC), through an extensive simulation and some case studies. The results show that both MDC and MRC are preferable to BC in a multiclass setting with imbalanced data.