Neural Comput - Modeling multivariate time series on manifolds with skew radial basis functions.

Tópicos

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Resumo

We present an approach for constructing nonlinear empirical mappings from high-dimensional domains to multivariate ranges. We employ radial basis functions and skew radial basis functions for constructing a model using data that are potentially scattered or sparse. The algorithm progresses iteratively, adding a new function at each step to refine the model. The placement of the functions is driven by a statistical hypothesis test that accounts for correlation in the multivariate range variables. The test is applied on training and validation data and reveals nonstatistical or geometric structure when it fails. At each step, the added function is fit to data contained in a spatiotemporally defined local region to determine the parameters--in particular, the scale of the local model. The scale of the function is determined by the zero crossings of the autocorrelation function of the residuals. The model parameters and the number of basis functions are determined automatically from the given data, and there is no need to initialize any ad hoc parameters save for the selection of the skew radial basis functions. Compactly supported skew radial basis functions are employed to improve model accuracy, order, and convergence properties. The extension of the algorithm to higher-dimensional ranges produces reduced-order models by exploiting the existence of correlation in the range variable data. Structure is tested not just in a single time series but between all pairs of time series. We illustrate the new methodologies using several illustrative problems, including modeling data on manifolds and the prediction of chaotic time series.

Resumo Limpo

present approach construct nonlinear empir map highdimension domain multivari rang employ radial basi function skew radial basi function construct model use data potenti scatter spars algorithm progress iter ad new function step refin model placement function driven statist hypothesi test account correl multivari rang variabl test appli train valid data reveal nonstatist geometr structur fail step ad function fit data contain spatiotempor defin local region determin parametersin particular scale local model scale function determin zero cross autocorrel function residu model paramet number basi function determin automat given data need initi ad hoc paramet save select skew radial basi function compact support skew radial basi function employ improv model accuraci order converg properti extens algorithm higherdimension rang produc reducedord model exploit exist correl rang variabl data structur test just singl time seri pair time seri illustr new methodolog use sever illustr problem includ model data manifold predict chaotic time seri

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