COM NETWORKS ART CATEGORIES INTERNAL IRREGULAR GEOMETRYSummary: This thesis proposes several models of neural networks ART (Adaptive Resonance Theory), which explores the possibility of using categories irregular geometries with internal problems supervised classification of patterns. The networks ART traditional categories used internal geometries pre-definidas (hiper-rectángulos or hiperelipsoides basically), which have a limited capacity to approximate the boundaries between classes in classification problems. The objective of this thesis is to equip these networks internal geometries generic categories, so that the geometric shape of the class learn during the entrenamento monitored, adapted to the geometrical characteristics of joint training. The first model has been proposed ARTMAP Simplex, which uses categories internal geometry of símplexes and functions based on activation functions gaussianas taking only non-zero values in the interior volume of símplex. The second approach proposed PolyTope ARTMAP (PTAM), is based on categories polytope -- polygon n-dimensional -- featuring activation based hiperplanos delimiting the borders of polytope. In this model, learning is done through internal expansion of the categories only in the direction of the pattern of entry, without overlap between them. Thus, limiting their own categories including expansion, without any maximum size or parameter monitoring. This allows PTAM operate out fully automatically, without any parameter optimizable. PTAM has been validated on several standard problems of classification, showing a greater capacity to learn and adapt to different geometries that networks ART classic tune without oversight. It has also experimented with using categories internal geometry polytope allowing overlap between them in the model Overlapping PTAM. However, the behavior of this model is more volatile and the results have generally been worse, in addition to optimizing require monitoring. Future research will focus on reducing the computational complexity of PTAM, increasing its efficiency and robustness in the presence of noise.
