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A RADIAL BASIS FUNCTION ALGORITHM WITH AUTOMATIC MODEL ORDER DETERMINATION
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DOI：10.1137/130948252.png)
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We present a new radial basis function (RBF) algorithm for constructing nonlinear models from data that may be sparsely scattered in high dimensions. We propose a simplified method for identifying function locations that is based on an approximation to the autocorrelation function. Local regions are now defined based on zero crossings of the modified autocorrelation contribution. The resulting local spatiotemporal data appear to capture increased structure as evidenced by the reduced number of basis functions required to achieve algorithm convergence and the fact that the resulting approximations have significantly improved accuracy. We prove a zero crossing lemma and convergence of the algorithm in the norm for continuous functions over a compact domain. Further, we show that several hypotheses tests can be used to detect this convergence. The model parameters and the number of basis functions are determined automatically from the given data. The only user parameter is the confidence level of the hypotheses tests which we fix at 95%. We apply the algorithm to modeling data on manifolds and the prediction of a chaotic time series using compactly supported skew RBFs in the setting of the overdetermined data fitting problem.
Keyword:
radial basis functions
convergence analysis
nonlinear function approximation
scattered data
data driven modeling
low order models
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Towards a black box algorithm for nonlinear function approximation over high-dimensional domains
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