Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Radial basis functions for multivariable interpolation: a review
Algorithms for approximation
Universal approximation using radial-basis-function networks
Neural Computation
Approximation and radial-basis-function networks
Neural Computation
Regularization theory and neural networks architectures
Neural Computation
Matrix computations (3rd ed.)
A new approach to dimensionality reduction: theory and algorithms
SIAM Journal on Applied Mathematics
Regularized radial basis functional networks: theory and applications
Regularized radial basis functional networks: theory and applications
A general class of multivariate skew-elliptical distributions
Journal of Multivariate Analysis
Radial Basis Functions
A multivariate skew normal distribution
Journal of Multivariate Analysis
On fundamental skew distributions
Journal of Multivariate Analysis
The Whitney Reduction Network: A Method for Computing Autoassociative Graphs
Neural Computation
A note on the Gibbs phenomenon with multiquadric radial basis functions
Applied Numerical Mathematics
Towards a Black Box Algorithm for Nonlinear Function Approximation over High-Dimensional Domains
SIAM Journal on Scientific Computing
Fast learning in networks of locally-tuned processing units
Neural Computation
Comparing support vector machines with Gaussian kernels to radialbasis function classifiers
IEEE Transactions on Signal Processing
Robust radial basis function neural networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On the construction and training of reformulated radial basis function neural networks
IEEE Transactions on Neural Networks
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We propose a skew-radial basis function (sRBF) expansion for the empirical model fitting problem. sRBFs employ a standard radial term, which is now made asymmetric by modulating, or skewing it with another function. The additional parameters in the skewing function permit the composite radial basis function to more flexibly adapt its shape to the data. We present several examples that illustrate the utility of sRBF representations for both the overdetermined data fitting problem and the data interpolation problem. We derive conditions under which skew perturbations of positive definite interpolation matrices remain positive definite. We observe that the sRBFs are particularly effective for producing uniform approximations and fitting jump discontinuities. We present an application to the time-series prediction of the maximum wind intensity of a hurricane and outline future work in image processing. The resulting sRBF models have reduced order, improved accuracy, and interpolation matrices with lower condition numbers.