In this paper, we discuss multiscale radial basis function collocation methods for solving certain elliptic partial differential equations on the unit sphere. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. Two variants of the collocation method are considered (sometimes ...

We propose a method of function approximation by radial basis function networks. We will demonstrate that this approximation method can be improved by a pre-treatment of data based on a linear model. This approximation method will be applied to option pricing. This choice justifies itself through the known nonlinear nature of the behavior of options price and through the effective contribution ...

Radial Basis Function (RBF) networks typically use a distance function designed for numeric attributes, such as Euclidean or city-block distance. This paper presents a heterogeneous distance function which is appropriate for applications with symbolic attributes, numeric attributes, or both. Empirical results on 30 data sets indicate that the heterogeneous distance metric yields significantly i...

Extracting rules from RBFs is not a trivial task because of nonlinear functions or high input dimensionality. In such cases, some of the hidden units of the RBF network have a tendency to be “shared” across several output classes or even may not contribute to any output class. To address this we have developed an algorithm called LREX (for Local Rule EXtraction) which tackles these issues by ex...

Spatial prediction needs to account for spatial information, which makes conventional radial basis function (RBF) networks inappropriate, for they assume independent and identical distribution. In this paper, we fuse spatial information at different layers of RBF. Experiments show fusion at hidden layer gives the best result and suggest that the optimal value is around one for the coefficient, ...

We present a mixture of experts (ME) approach to interpolate sparse, spatially correlated earth-science data. Kriging is an interpolation method which uses a global covariation model estimated from the data to take account of the spatial dependence in the data. Based on the close relationship between kriging and the radial basis function (RBF) network (Wan & Bone, 1996), we use a mixture of gen...

Recent progress in acquisition technology has increased the availability and quality of measured appearance data. Although representations based on dimensionality reduction provide the greatest fidelity to measured data, they require assembling a high-resolution and regularly sampled matrix from sparse and non-uniformly scattered input. Constructing and processing this immense matrix becomes a ...

This paper presents a new cooperative-coevolutive algorithm for the design of Radial Basis Function Networks (RBFNs) for classification problems. The algorithm promotes a coevolutive environment where each individual represents a radial basis function (RBF) and the entire population is responsible for the final solution. As credit assignment three quality factors are considered which measure th...

We present the weighted minimum variance distortionless response (WMVDR), which is a steered response power (SRP) algorithm, for near-field speaker localization in a reverberant environment. The proposed WMVDR is based on a machine learning approach for computing the incoherent frequency fusion of narrowband power maps. We adopt a radial basis function network (RBFN) classifier for the estimati...