Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtalk task. In RBF, a new example is classiied by computing its Euclidean distance to a set of centers chosen by unsupervised methods. The application of supervised learning to learn a non-Euclidean distance metric was found to reduce the error rate of RBF networks, while supervis...

We propose a simple but efficient method to extract rules from the radial basis function (RBF) neural network. Firstly, the data are classified by an RBF classifier. During training the RBF network, we allow for large overlaps between clusters corresponding to the same class to reduce the number of hidden neurons while maintaining classification accuracy. Secondly, centers of the kernel functio...

A well-performing set of radial basis functions (RBFs) can emerge from genetic competition among individual RBFs. Genetic selection of the individual RBFs is based on credit sharing which localizes competition within orthogonal niches. These orthogonal niches are derived using singular value decomposition and are used to apportion credit for the overall performance of the RBF network among indi...

RBF approximations would appear to be very attractive for approximating spatial derivatives in numerical simulations of PDEs. RBFs allow arbitrarily scattered data, generalize easily to several space dimensions, and can be spectrally accurate. However, accuracy degradations near boundaries in many cases severely limit the utility of this approach. With that as motivation, this study aims at gai...

In this paper we provide a short overview of the Radial Basis Functions (RBF), their properties, the motivations behind their use and some of their applications. RBF’s have been employed for functional approximation in time-series modeling and in pattern classification. They have been shown to implement the Bayesian rule and to model any continuous inputoutput mapping. RBF’s are embedded in a t...

A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (source points). The new approach clusters evaluation points instead and is therefore easily able to cope with basis functions that have different mul...

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) met...

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 ...

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non uniform grids and mesh adaptation. We focus o...

When radial basis functions (RBFs) are made increasingly flat, the interpolation error typically decreases steadily until some point when Runge-type oscillations either halt or reverse this trend. Because the most obvious method to calculate an RBF interpolant becomes a numerically unstable algorithm for a stable problem in case of near-flat basis functions, there will typically also be a separ...