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 ...

This paper proves the convergence of applying the radial basis functions as a global spatial approximation method for solving the option pricing models. The computational advantage of this method is illustrated by giving numerical examples on solving both the European and American options pricing models whereas the latter is a free boundary value problem.

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...

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...

As the support vector (SV) number of a support vector machine (SVM) determines the execution speed of the testing phase, there have been diverse methods to reduce it. Although iterative preimage addition (IPA), belonging to the ‘reduced set construction’, is reported to be able to reduce a large portion of the SV number of a standard SVM when the kernel is a radial basis function (RBF), the fac...