We propose a network architecture based on adaptive receptive fields and a learning algorithm that combines both supervised learning of centers and unsupervised learning of output layer weights. This algorithm causes each group of radial basis functions to adapt to regions of the clustered input space. Networks produced by this algorithm appear to have better generalization performance on predi...

Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the reg...

Finite differences was the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD ...

A novel descriptor for pattern recognition is proposed by using dual-tree complex wavelet features and SVM. The approximate shiftinvariant property of the dual-tree complex wavelet and its good directional selectivity in 2D make it a very appealing choice for pattern recognition. Recently, SVM has been shown to be very successful in pattern recognition. By combining these two tools we find that...

In this paper we focus on an interpretation of Gaussian radial basis functions (GRBF) which motivates extensions and learning strategies. Specifically, we show that GRBF regression equations naturally result from representing the input-output joint probability density function by a finite mixture of Gaussians. Corollaries of this interpretation are: some special forms of GRBF representations ca...

In this study, two novel learning algorithms have been applied on Radial Basis Function Neural Network (RBFNN) to approximate the functions with high non-linear order. The Probabilistic Evolutionary (PE) and Gaussian Mixture Model (GMM) techniques are proposed to significantly minimize the error functions. The main idea is concerning the various strategies to optimize the procedure of Gradient ...

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than whe...

This paper presents a sum-of-product neural network (SOPNN) structure. The SOPNN can learn to implement static mapping that multilayer neural networks and radial basis function networks normally perform. The output of the neural network has the sum-of-product form +Np i/1 <Nv j/1 f ij (x j ), where x j 's are inputs, N v is the number of inputs, f ij ( ) is a function generated through network ...