Radial Basis Function (RBF) neuron network is being applied widely in multivariate function regression. However, selection of neuron number for hidden layer and definition of suitable centre in order to produce a good regression network are still open problems which have been researched by many people. This article proposes to apply grid equally space nodes as the centre of hidden layer. Then, ...

Suppose is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal function L (x) = P k2Z c k exp(?(x ? k) 2), x 2 R, satisfying the interpolatory conditions L (k) = 0k , k 2 Z. One objective of this paper is to derive several additional properties of L. For example, it is shown that L possesses the sign-regularity property sgnnL (x)] = sgnnsin(x...

1 Radial Basis Functions 2 1.1 Multivariate Interpolation and Positive Definiteness . . . . . . 3 1.2 Stability and Scaling . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Solving Partial Differential Equations . . . . . . . . . . . . . . 7 1.4 Comparison of Strong and Weak Problems . . . . . . . . . . . 8 1.5 Collocation Techniques . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Method ...

Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...

This paper presents a provably convergent multifidelity optimization algorithm for unconstrained problems that does not require high-fidelity gradients. The method uses a radial basis function interpolation to capture the error between a high-fidelity function and a low-fidelity function. The error interpolation is added to the low-fidelity function to create a surrogate model of the high-fidel...

In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis function (RBF) interpolation. Given a target function sampled on some node set, an approximation of the m derivative is obtained by m successive applications of the operator “interpolate, then differentiate” this process is known in the spline com...

To restore a degraded image, which has been corrupted by some kinds of noise and motion blur, a model for restoration is first presented and then an algorithm based on this model and the radial basis function network (RBFN) is proposed in this paper. In the first step of this algorithm, noise is removed by using the RBFN interpolation with variable regularization parameters. In the second step,...

This paper presents a novel technique which may be used to determine an appropriate threshold for interpreting the outputs of a trained Radial Basis Function (RBF) classifier. Results from two experiments demonstrate that this method can be used to improve the performance of RBF classifiers in practical applications.