HyperPattern Recognition and SuperHyperPattern Recognition with some applications

Abstract

A hyperfunction maps each input to a subset of outputs, generalizing classical functions to represent multi-valued or uncertain outcomes [1]. A superhyperfunction extends this concept by mapping collections of sets to higher-order powerset values, thereby capturing layered hierarchical uncertainties [2]. A Pattern Recognizer assigns labels to instances by minimizing empirical loss on training data. In this paper, we introduce and analyze HyperPattern Recognition and SuperHyperPattern Recognition, which extend the Pattern Recognizer framework via hyperfunctions and superhyperfunctions. Our treatment is purely theoretical, and we anticipate future computational experiments on real-world datasets to empirically validate the proposed models.