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...

The quality of Radial Basis Functions (RBF) and other nonlinear learning networks such as Multi Layer Perceptrons (MLP) depend significantly on issues in architecture, learning algorithms, initialisation heuristics and regularization techniques. Little attention has been given to the effect of mixture transfer functions in RBF networks on model quality and efficiency of parameter optimisation. ...

A general and efficient design approach using a radial basis function (RBF) neural classifier to cope with small training sets of high dimension, which is a problem frequently encountered in face recognition, is presented. In order to avoid overfitting and reduce the computational burden, face features are first extracted by the principal component analysis (PCA) method. Then, the resulting fea...

Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly illconditioned as the RBF shape parameter becomes small, corresponding to flat RBFs. Two stable approaches that overco...

Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly illconditioned as the RBF shape parameter becomes small, corresponding to flat RBFs. Two stable approaches that overco...

In this paper we present an integer programming formulation of the minimum sphere covering problem that seeks to construct a minimum number of spheres to represent the training data. Using soft threshold functions, we further derive a linear programming problem whose solution gives rise to radial basis function classifiers and sigmoid function classifiers. In contrast to traditional RBF and sig...

This paper investigates the problem of multiuser detector (MUD) for direct sequence code division multiple access (DS-CDMA) system. A radial basis function (RBF) receiver provides the optimum receiver performance. We propose a fuzzy implementation of the RBF receiver. This fuzzy receiver provides considerable computational complexity reduction with respect to RBF receivers. The fuzzy receiver p...

A systematic method for the diagnosis of planar antenna arrays from far field radiation pattern using neural networks is presented. Two types of neural networks, Radial basis function (RBF) and Probabilistic neural network (PNN) are considered for the performance comparison. Deviation pattern is used as input to the neural network to determine the location of the faulty element and error in exc...

The appropriate operation of a radial basis function (RBF) neural network depends mainly upon an adequate choice of the parameters of its basis functions. The simplest approach to train an RBF network is to assume fixed radial basis functions defining the activation of the hidden units. Once the RBF parameters are fixed, the optimal set of output weights can be determined straightforwardly by u...