Constancy maximization based weight optimization in high dimensional model representation for multivariate functions

Burcu Tunga*, Metin Demiralp

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

High Dimensional Model Representation (HDMR) method is a technique that represents a multivariate function in terms of less-variate functions. Even though the method has a finite expansion, to determine the components of this expansion is very expensive due to integration based natures of the components. Hence, the HDMR expansion is generally truncated at certain multivariance level and such approximations are produced to represent the given multivariate function approximately. The weight function selection becomes an important issue for the HDMR based applications when it is desired to give different importances to function values at different points. An appropriately chosen weight function may increase the quality of the approximation incredibly. This work aims at a multivariate weight function optimization to obtain high quality approximations through the HDMR method to represent multivariate functions. The proposed optimization considers constancy measurer maximization which produces a quadratic vector equation to be solved. Another contribution of this work is to use a recently developed method, fluctuation free integration, with HDMR, to solve this equation easily. This work is an extension of a previous work about weight optimization in HDMR for univariate functions.

Original languageEnglish
Pages (from-to)1996-2012
Number of pages17
JournalJournal of Mathematical Chemistry
Volume49
Issue number9
DOIs
Publication statusPublished - Oct 2011

Keywords

  • Approximation
  • Fluctuation expansion
  • High Dimensional Model Representation
  • Multivariate functions
  • Optimization

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