Class-Selective Rejection Rules Based on the Aggregation of Pattern Soft Labels

Let Ω = {ω1, · · · , ωc} be a set of c classes and let x be a pattern described by p features, namely a vector x = (x1 · · · xp) in a p-dimensional real space R p. Classifier design aims at defining rules that allow to associate an incoming pattern x with one class of Ω. Let Lhc be the set of c-dimensional binary vectors whose components sum up to one. Then, such a rule, defined as a mapping D: Rp → Lhc, x → h(x), is called a crisp classifier. In most theoretical approaches to pattern classification, it is convenient to define a classifier as a couple (L, H) where: L is a labeling function: Rp → L•c, x → u(x), L•c depending on the mathematical framework the classifier relies on, Lpc = [0, 1]c for degrees of typicality or L f c =