Hierarchical Polytope ARTMAP for Supervised Learning

The recent Polytope ARTMAP (PTAM) suggests that irregular polytopes are more flexible than the predefined category geometries to approximate the borders among the desired output predictions. However, category expansion and adjustment steps without statistical information make PTAM not robust to noise and category overlap. In order to push the learning problem towards Structural Risk Minimization (SRM), this paper proposes Hierarchical Polytope ARTMAP (HPTAM) to use a hierarchical structure with different levels, which are determined by the complexity of regions incorporating the input pattern. Besides, overlapping of simplexes from the same desired prediction is designed to reduce category proliferation. Although HPTAM is still inevitably sensible to noisy outliers in the presence of noise, main experimental results show that HPTAM can achieve a balance between representation error and approximation error, which ameliorates the overall generalization capabilities.