Convex Mixture Criterion Based Evidential Set-Valued Classification

Imperfect data have to be processed in a different way when they are involved in classification or regression tasks. For instance, in sensitive domains, e.g., medical field, predicting a subset of candidate classes when imperfect data are present is preferable to predicting a single class using point prediction methods which offer less guarantee. Of course, the corresponding classifier should be cautious, i.e., the predicted subset of candidate classes contains the true class, but also relevant or precise, i.e., its size is not too large. This paper focuses on the adaptation of the Strong Dominance criterion (SD) to a more flexible classifier by combining it to the pignistic criterion (PC) within the framework of belief functions. Indeed, SD is a good candidate for cautious classification tasks as a robust method but in some situations it predicts subsets that are too large. The proposed set-valued classifier, based on a convex mixture (CM) between SD and PC, allows the control of the granularity of the partial order that is returned by SD regarding the desire of the decision-maker. The outputs of PC, SD and CM classifiers are theoretically studied and compared. Experimental results on fashion mnist data show that the proposed classifier might lead to better performances for the measures that more reward precision.