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Manuscript Title: Fitting sparse multidimensional data with low-dimensional terms | ||

Authors: Sergei Manzhos, Koichi Yamashita, Tucker Carrington Jr. | ||

Program title: RS_HDMR_NN | ||

Catalogue identifier: AEEI_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 180(2009)2002 | ||

Programming language: MatLab R2007b. | ||

Computer: any computer running MatLab. | ||

Operating system: Windows XP, Windows Vista, UNIX, Linux. | ||

Keywords: neural networks, high dimensional model representation, functional approximation, fitting and interpolation. | ||

PACS: 31.50.Bc, 31.50.Df. | ||

Classification: 4.9. | ||

External routines: Neural Network Toolbox Version 5.1 (R2007b). | ||

Nature of problem:Fitting a smooth, easily integratable and differentiatable, function to a very sparse (~2-3 points per dimension) multidimensional (D ≥ 6) large (~10 ^{4}-10^{5} data) dataset. | ||

Solution method:A multivariate function is represented as a sum of a small number of terms each of which is a low-dimensional function of optimised coordinates. The optimal coordinates reduce both the dimensionality and the number of the terms. Neural networks (including exponential neurons) are used to obtain a general and robust method and a functional form which is easily differentiated and integrated (in the case of exponential neurons). | ||

Running time:Depends strongly on the dataset to be modelled and the chosen structure of the approximating function, ranges from about a minute for ~10 ^{3} data in 3-D to about a day for ~10^{5} data in 15-D. |

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