Category regions as new geometrical concepts in Fuzzy-ART and Fuzzy-ARTMAP

In this paper we introduce novel geometric concepts, namely category regions, in the original framework of Fuzzy-ART (FA) and FuzzyARTMAP (FAM). The definitions of these regions are based on geometric interpretations of the vigilance test and the F2 layer competition of committed nodes with uncommitted ones, that we call commitment test. It turns out that not only these regions have the same geometrical shape (polytope structure), but they also share a lot of common and interesting properties that are demonstrated in this paper. One of these properties is the shrinking of the volume that each one of these polytope structures occupies, as training progresses, which alludes to the stability of learning in FA and FAM, a well-known result. Furthermore, properties of learning of FA and FAM are also proven utilizing the geometrical structure and properties that these regions possess; some of these properties were proven before using counterintuitive, algebraic manipulations and are now demo...

• Type: Journal
• Year: 2002
• Where: NN
• Authors: Georgios C. Anagnostopoulos, Michael Georgiopoulos
• Keywords: Category Regions, Intuitive Geometrical Arguments, Neural Networks, NN 2002, Vigilance Test