| Fuzzy ART and Fuzzy ARTMAP are two prominent neural network architectures based on the principles of Grossberg's Adaptive Resonance Theory (ART). While the former architecture employs unsupervised learning to perform clustering tasks, the latter one associates clusters belonging to an input and output domain in a supervised manner. As a special case, Fuzzy ARTMAP can also be used as a classifier. Both networks implement an exemplar-based learning method and summarize training patterns into categories (exemplars), whose geometric representation are hyper-rectangles embedded in the input domain.; We introduce two novel ART-based neural network architectures, namely Ellipsoid ART and Ellipsoid ARTMAP, which utilize hyper-ellipsoids for category representation. We have designed these two architectures, so that they share all essential properties and characteristics of their Fuzzy counterparts. Of foremost importance, they are capable of fast, stable learning, meaning that learning completes in a finite number of steps. We also present selected experimental results that illustrate the potential of Ellipsoid ARTMAP to successfully perform classification tasks by exhibiting high prediction accuracy, while maintaining a relatively small number of categories.; Next, we introduce category regions as novel concepts that enrich the geometric facet of Fuzzy ART and Fuzzy ARTMAP operations. Their definition stems from the geometric interpretation of two particular conditions that are examined, in order to assess the degree to which an input pattern matches the characteristics of an existing category already memorized by a Fuzzy ART or Fuzzy ARTMAP network. Apart from aiding us in gaining a clearer understanding of the networks' training and performance phases, based on the regions' properties we arrive at several results that are primarily of theoretical interest. Furthermore, due to the underlying similarity, all these results are shown to be applicable to Ellipsoid ART and Ellipsoid ARTMAP as well. |
