A method of evaluating matrix elements between polynomial basis functions is proposed involving the explicit expansion of the operator in terms of the polynomial. The method is shown to have several advantages over the direct evaluation of these matrix elements by Gaussian quadrature, including savings of up to a factor of 6N for an N-dimensional integral. Application to the calculation of poly...

2D curve representations usually take algebraic forms in ways not related to visual perception. This poses great difficulties in connecting curve representation with object recognition where information computed from raw images must be manipulated in a perceptually meaningful way and compared to the representation. In this paper we show that 2D curves can be represented compactly by imposing sh...

Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtaik task. In RBF, a new example is classified 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 supervi...

Abstract: The performances of Normalised RBF (NRBF) nets and standard RBF nets are compared in simple classification and mapping problems. In Normalized RBF networks, the traditional roles of weights and activities in the hidden layer are switched. Hidden nodes perform a function similar to a Voronoi tessellation of the input space, and the output weights become the network's output over the pa...

In this study, we are mainly interested in error estimates of interpolation, using smooth radial basis functions such as multiquadrics. The current theories of radial basis function interpolation provide optimal error bounds when the basis function φ is smooth and the approximand f is in a certain reproducing kernel Hilbert space Fφ. However, since the space Fφ is very small when the function φ...

We study p-sets and (i)-p-sets for a real function space A and compare them with p-sets for its complexification. We also discuss the relation of p-sets and (i)-p-sets with weak peak sets and weak (i)-peak sets which generalize our result of [7]. Using some of the results, we generalize a result of Izzo [2] (proved for a complex function algebra) for a real function space A. Mathematics Subject...

Radial basis function networks (RBF) are efficient general function approximators. They show good generalization performance and they are easy to train. Due to theoretical considerations RBFs commonly use Gaussian activation functions. It has been shown that these tight restrictions on the choice of possible activation functions can be relaxed in practical applications. As an alternative differ...

The behavior of Radial Basis Function (RBF) Networks greatly depends on how the center points of the basis functions are selected. In this work we investigate the use of instance reduction techniques, originally developed to reduce the storage requirements of instance based learners, for this purpose. Five Instance-Based Reduction Techniques were used to determine the set of center points, and ...