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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_0
Distribution 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 (~104-105 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 ~103 data in 3-D to about a day for ~105 data in 15-D.