Global and local modelling in RBF networks

Radial basis function networks are traditionally known as local approximation networks as they are composed by a number of elements which, individually, mainly take care of the approximation about a specific area of the input space. Then, the joint global output of the network is obtained as a linear combination of the individual elements' output. However, in the network optimization, the performance of the global model is normally the only objective to optimize. This might cause a deficient local modelling of the input space, thus partially losing the local character of this type of models. This work presents a modified radial basis function network that maintains the approximation capabilities of the local sub-models whereas the model is globally optimized. This property is obtained thanks to a special partitioning of the input space, that leads to a direct global-local optimization. A learning methodology adapted to the proposed model is used in the simulations, consisting of a clustering algorithm for the initialization of the centers and a local search technique. In the experiments, the proposed model shows satisfactory local and global modelling capabilities both in artificial and real applications.