New geometrical perspective of fuzzy ART and fuzzy ARTMAP learning
Georgios C. Anagnostopoulos, Michael Georgiopoulos · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
In this paper we introduce new useful, geometric concepts regarding categories in Fuzzy ART and Fuzzy ARTMAP, which shed more light into the process of category competition eligibility upon the presentation of input patterns. First, we reformulate the competition of committed nodes with uncommitted nodes in an F2 layer as a commitment test very similar to the vigilance test. Next, we introduce a category's match and choice regions, which are the geometric interpretation of the vigilance and commitment test respectively. After examining properties of these regions we reach three results applicable to both Fuzzy ART and Fuzzy ARTMAP. More specifically, we show that only one out of these two tests is required; which test needs to be performed depends on the values of the vigilance parameter (rho) and the choice parameter (alpha) . Also, we show that for a specific relation of (rho) and (alpha) , the vigilance (rho) does not influence the training or performance phase of Fuzzy ART and Fuzzy ARTMAP. Finally, we refine a previously published upper bound on the size of the categories created during training in Fuzzy ART and Fuzzy ARTMAP.