Multivariate interpolation using radial basis function networks

There is, hitherto, no efficient method to interpolate multivariate functions, for especially dynamic problems in which new training data are often added in real-time. In order to construct an efficient method, this paper considers local interpolation RBF networks, where artificial neural network approach and instance-based learning are combined. In these networks, training data are clustered into relatively small sub-clusters and on each sub-cluster, an interpolation RBF network is trained by using a new algorithm recently proposed by the authors; it is a two-phase algorithm for training interpolation RBF networks using Gaussian basis functions and it has the complexity O(N²), where N is the number of nodes. The training time of this new architecture is effectively short and its generality is superior to global RBF networks. Furthermore its universal approximation property is proven. Especially, this new architecture can be efficiently used for dynamic training.