A granular-oriented development of functional radial basis function neural networks

In this study, we develop a design methodology for generalized radial basis function neural networks. In contrast with the plethora of existing approaches, here we promote a development strategy in which a topology of the network is predominantly based upon a collection of information granules formed on a basis of available experimental data. The output space is granulated making use of the K-means clustering while the input space is clustered with the aid of a so-called context-based fuzzy clustering. The number of information granules produced for each context is adjusted so that we satisfy a certain reconstructability criterion that helps us minimize an error between the original data and the ones resulting from their reconstruction involving prototypes of the clusters and the corresponding membership values. In contrast to “standard” radial basis function neural networks, the output neuron of the network exhibits a certain functional nature as its connections are realized as local linear or quadratic functions whose location is determined by the values of the context and the prototypes in the input space. The other parameters of these local functions are subject to further parametric optimization. Numeric examples involve some low-dimensional synthetic data and selected data coming from the Machine Learning repository.