The local radial basis function (RBF) interpolation method enables very large-scale data sets to be handled efficiently, overcoming the drawbacks of global interpolation which produces highly ill-conditioned linear systems. Whereas there have been intensive studies on the accuracy of global RBF interpolation, the error analysis of local RBF interpolation is much less investigated. In this regar...

Two optimization aspects of the meshless method (MLM) based on nonsingular radial basis functions (RBFs) are considered in an acoustic indoor problem. The former is minimization mean value relative error solution domain. letter at selected points In both cases leads to finding relations between physical parameters and approximate parameters. room field with uniform, impedance walls considered. ...

The purpose of this paper is to explore the representation capability of radial basis function (RBF) neural networks. The main results are: 1) the necessary and sufficient condition for a function of one variable to be qualified as an activation function in RBF network is that the function is not an even polynomial, and 2) the capability of approximation to nonlinear functionals and operators b...

Functional equivalence of radial basis function (RBF) networks and a class of fuzzy inference systems is considered. The class of fuuy systems based on the Takagi-Sugeno model is referred to as TS-model of fuzzy inference. From the abstract mathematical viewpoint the functional equivalence between radial basis function networks and fuzzy inference systems is already shown. However, from the vie...

| Adaptive learning dynamics of the Radial Basis Function Network (RBFN) are compared with a scale-based clustering technique Won93] and a relationship between the two is pointed out. Using this link, it is shown how scale-based clustering can be done using the RBFN, with the Radial Basis Function (RBF) width as the scale parameter. The technique suggests the \right" scale at which the given da...

Hierarchical RBF networks consist of multiple RBF networks assembled in different level or cascade architecture. In this paper, an evolved hierarchical RBF network was employed to detect the breast cancel. For evolving a hierarchical RBF network model, Extended Compact Genetic Programming (ECGP), a tree-structure based evolutionary algorithm and the Differential Evolution (DE) are used to find ...

Convolutional Radial Basis Function (RBF) networks are introduced for smoothing out irregularly sampled signals. Our proposed technique involves training a RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need t...

This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBF's. The form of the RBF's is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ...

Learning in radial basis function (RBF) networks is the topic of this paper. Particularly we address the problem of intialisation the centers and scaling parameters in RBF networks utilizing classiication tree algorithms. This method was introduced by Kubat in 1998. Algorithms for the calculation of the centers and scaling parameters in an RBF network are presented and numerical results for the...

The Radial Basis Function method (RBF) can be used not only for reconstruction of a surface from scattered data but for reconstruction of damaged images, filling gaps and for restoring missing data in images, too. The basic idea of reconstruction algorithm with RBF and very interesting results from reconstruction of images damaged by noise are presented. Feasibility of the RBF method for image ...