Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together . . . through fractals. First, we iden...

Radial basis functions are traditional and powerful tools for multivariate interpolation from scattered data. This self-contained talk surveys both theoretical and practical aspects of scattered data fitting by radial basis functions. To this end, basic features of the radial basis function interpolation scheme are first reviewed, such as well-posedness, numerical stability and approximation or...

| Radial basis functions are presented as a practical solution to the problem of interpolating incomplete surfaces derived from three-dimensional (3-D) medical graphics. The speciic application considered is the design of cranial implants for the repair of defects, usually holes, in the skull. Radial basis functions impose few restrictions on the geometry of the interpolation centers and are su...

Radial basis function (RBFs) neural networks provide an attractive method for high dimensional nonparametric estimation for use in nonlinear control. They are faster to train than conventional feedforward networks with sigmoidal activation networks (\backpropagation nets"), and provide a model structure better suited for adaptive control. This article gives a brief survey of the use of RBFs and...

This paper proposes a Neural Network model using Generalised kernel functions for the hidden layer of a feed forward network. These functions are Generalised Radial Basis Functions (GRBF), and the architecture, weights and node topology are learned through an evolutionary algorithm. The proposed model is compared with the corresponding standard hidden-node models: Product Unit (PU) neural netwo...

There are multiple reasons why anisotropic basis functions may be needed or be more appropriate. The most obvious is that if the basis function is to be defined on Rn × T then there is no natural norm on this space that would reflect the unique properties of time. A second reason is that function being interpolated or approximated may incorporate a directional dependence. Thirdly, differentiabi...

In this paper, we present experiments comparing different training algorithms for Radial Basis Functions (RBF) neural networks. In particular we compare the classical training which consists of an unsupervised training of centers followed by a supervised training of the weights at the output, with the full supervised training by gradient descent proposed recently in same papers. We conclude tha...

In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clari cation and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline int...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

This paper presents a novel approach for developing simulation metamodels using Gaussian radial basis functions. This approach is based on some recently developed mathematical results for radial basis functions. It is systematic, explicitly controls the underfitting and overfitting tradeoff, and uses a fast computational algorithm that requires minimal human involvement. This approach is illust...