Fitting sparse multidimensional data with low-dimensional terms

An algorithm that fits a continuous function to sparse multidimensional data is presented. The algorithm uses a representation in terms of lower-dimensional component functions of coordinates defined in an automated way and also permits dimensionality reduction. Neural networks are used to construct the component functions. Program summary Program title: RS_HDMR_NN Catalogue identifier. AEEI_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence. http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 566 No. of bytes in distributed program, including test data, etc.: 327 856 Distribution format. tar.gz Programming language: MatLab R2007b Computer: any computer running MatLab Operating system: Windows XR Windows Vista, UNIX, Linux 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 (similar to 2-3 points per dimension) multidimensional (D >= 6) large (similar to 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 similar to 10(3) data in 3-D to about a day for similar to 10(5) data in 15-D. (C) 2009 Elsevier B.V. All rights reserved.