TY - JOUR

T1 - Constancy maximization based weight optimization in high dimensional model representation for multivariate functions

AU - Tunga, Burcu

AU - Demiralp, Metin

PY - 2011/10

Y1 - 2011/10

N2 - 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.

AB - 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.

KW - Approximation

KW - Fluctuation expansion

KW - High Dimensional Model Representation

KW - Multivariate functions

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=80052304088&partnerID=8YFLogxK

U2 - 10.1007/s10910-011-9870-z

DO - 10.1007/s10910-011-9870-z

M3 - Article

AN - SCOPUS:80052304088

SN - 0259-9791

VL - 49

SP - 1996

EP - 2012

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 9

ER -