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A Matrix Based Indexing HDMR method for multivariate data modelling

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Abstract

Modelling multivariate data of real life problems from engineering, chemistry, physics, mathematics or other related sciences, in which function values are known only at arbitrarily distributed points of the problem domain, is an important and complicated issue since there exist mathematical and computational complexities in the analytical structure construction process coming from the multivariance. The Plain High Dimensional Model Representation (HDMR) method expresses a multivariate problem in terms of less-variate problems. In this work, a Matrix Based Indexing HDMR method is developed to make the Plain HDMR philosophy employable for the multivariate data partitioning process. This new method will have the ability of dealing with less-variate data sets by partitioning the given data set into univariate, bivariate and trivariate data sets. Interpolating these partitioned data sets will construct an approximate analytical structure as the model of the given multivariate data modelling problem.

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Authors and Affiliations

  1. Engineering Faculty, Software Engineering Department, Bahçeşehir University, Beşiktaş, 34349, İstanbul, Turkey

    M. Alper Tunga

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  1. M. Alper Tunga
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Correspondence to M. Alper Tunga.

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Tunga, M.A. A Matrix Based Indexing HDMR method for multivariate data modelling. J Math Chem 49, 1092–1114 (2011). https://doi.org/10.1007/s10910-011-9800-0

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