Entropic Regularization Schemes for Learning Fuzzy Similarity Measures Based on the d-Choquet Integral

We consider the problem of learning one of three possible fuzzy generalizations of the Jaccard similarity measure, based on the d-Choquet integral. Each of the resulting fuzzy similarity measures is parameterized by a capacity and by a real parameter. The capacity describes the weights assigned to groups of attributes and their interactions, while the real parameter is related to the restricted dissimilarity function used to evaluate differences among attributes. To face identifiability issues and in view of an XAI use of the learned capacity, the parameters’ set is restricted to the set of (at most) 2-additive completely monotone capacities. Next, under a suitable definition of entropy for completely monotone capacities, we address different entropic regularization schemes to single out interactions between groups of attributes. This is done by taking as reference a local uniform Mobius inverse over sets of attributes with the same cardinality.