Granular self-organizing map (grSOM) for structure identification

This work presents a useful extension of Kohonen's Self-Organizing Map (KSOM) for structure identification in linguistic (fuzzy) system modeling applications. More specifically the granular SOM neural model is presented for inducing a distribution of nonparametric fuzzy interval numbers (FINs) from the data. A FIN can represent a local probability distribution function and/or a conventional fuzzy set; moreover, a FIN is interpreted as an information granule. Learning is based on a novel metric distance d(K)(.,.) between FINs. The metric d(K)(.,.) can be tuned nonlinearly by a mass function m(x), the latter attaches a weight of significance to a real number 'x' in a data dimension. Rigorous analysis is based on mathematical lattice theory. A grSOM can cope with ambiguity by processing linguistic (fuzzy) input data and/or intervals. This work presents a simple grSOM variant, namely greedy grSOM, for classification. A genetic algorithm (GA) introduces tunable nonlinearities during training. Extensive comparisons are shown with related work from the literature. The practical effectiveness of the greedy grSOM is demonstrated comparatively in three benchmark classification problems. Statistical evidence strongly suggests that the proposed techniques improve classification performance. In addition, the greedy grSOM induces descriptive decision-making knowledge (fuzzy rules) from the training data.