New Geometrical Concepts In Fuzzy-Art And Fuzzy-Artmap: Category Regions

We introduce new geometric concepts regarding categories in Fuzzy ART (FA) and Fuzzy ARTMAP (FAM), which add a geometric facet to the process of node selection in the F2 layer by patterns. Apart from providing the means to better understand the training and performance phase of these two architectures, the new concepts, namely the category regions, lead us to interesting theoretical results, when training either architecture. First, we define the Commitment Test as a novelty detection mechanism similar to the Vigilance Test. Next we define various category regions. Via those definitions and 3 derived lemmas we identify areas in the vigilance-choice parameter space, for which 4 results are stated that are applicable to both FA and the FAM classifier training phase