Art networks with geometrical distances

In this paper, ART networks (Fuzzy ART and Fuzzy ARTMAP) with geometrical norms are presented. The category choice of these networks is based on the LpLp norm. Geometrical properties of these architectures are presented. Comparisons between this category choice and the category choice of the ART networks are illustrated. And simulation results on the databases taken from the UCI repository are performed. It will be shown that using the LpLp norm is geometrically more attractive. It will operate directly on the input patterns without the need for doing any preprocessing. It should be noted that the ART architecture requires two preprocessing steps: normalization and complement coding. Simulation results on different databases show the good generalization performance of the Fuzzy ARTMAP with LpLp norm compared to the performance of a typical Fuzzy ARTMAP.