A vigilance-free ART network with general geometry internal categories

ART neural networks are important tools for online supervised pattern recognition. They use internal categories with pre-defined geometry, given by the category choice function. Pre-defined geometry limits the ability of the categories to fit complex borders among output predictions for a given data set, and may contribute to the category proliferation problem. This work proposes Polytope ARTMAP (PTAM), whose category representation regions have general geometry-polytopes in Rⁿ whose vertices are selected training patterns. The category borders compose a piece-wise linear approximation to the borders among predictions. Overlapping among categories is avoided in PTAM because they do not need to overlap in order to keep their geometry during learning. The choice function does not depend on the category size. Category growing is only limited by the other categories, and the vigilance parameter can be removed, so that PTAM learns a training data set without any parameter tuning.