Support Vector Machines are used for time series prediction and compared to radial basis function networks. We make use of two diierent cost functions for Support Vectors: training with (i) an insensitive loss and (ii) Huber's robust loss function and discuss how to choose the regularization parameters in these models. Two applications are considered: data from (a) a noisy (normal and uniform n...

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 investigate the decision making ability of a fully complex-valued radial basis function (FC-RBF) network in solving real-valued classification problems. The FC-RBF classifier is a single hidden layer fully complex-valued neural network with a nonlinear input layer, a nonlinear hidden layer, and a linear output layer. The neurons in the input layer of the classifier employ the ...

ÐThis is an elementary research for assigning color values to voxels of multichannel Magnetic Resonance Imaging (MRI) volume data. The MRI volume data sets obtained under different scanning conditions are transformed to the components by independent component analysis (ICA), which enhances physical characteristics of the tissue. The transfer functions for generating color values from independen...

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

We propose a method for optimizing the complexity of Radial basis function (RBF) networks. The method involves two procedures: adaptation (training) and selection. The first procedure adaptively changes the locations and the width of the basis functions and trains the linear weights. The selection procedure performs the elimination of the redundant basis functions using an objective function ba...

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geomerty have been succesfuly treated using sigmoidal multilayer perceptrons in previous works [1, 2]. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonabl...

We propose a method for optimizing the complexity of Radial basis function (RBF) networks. The method involves two procedures: adaptation (training) and selection. The first procedure adaptively changes the locations and the width of the basis functions and trains the linear weights. The selection procedure performs the elimination of the redundant basis functions using an objective function ba...