Constancy maximization based weight optimization in high dimensional model representation

This work focuses on the weight function optimization in high dimensional model representation (HDMR) via constancy maximization. There are a lot of circumstances where HDMR’s weight function becomes completely flexible in its factors. The univariate coordinate changes which can be constructed to pr...

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Bibliographic Details
Published in:Numerical algorithms 2009-11, Vol.52 (3), p.435-459
Main Authors: Tunga, Burcu, Demiralp, Metin
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
Basis functions
Computer Science
Hilbert space
Mathematical analysis
Mathematical models
Matrix representation
Maximization
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Representations
Theory of Computation
Weight function
Weighting functions
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Summary:This work focuses on the weight function optimization in high dimensional model representation (HDMR) via constancy maximization. There are a lot of circumstances where HDMR’s weight function becomes completely flexible in its factors. The univariate coordinate changes which can be constructed to produce nonnegative factors in the integrands of HDMR component, are perhaps the most important ones of these cases. Here, the weight function is considered as the square of a linear combination of certain basis functions spanning an appropriately chosen Hilbert space. Then, the coefficients of these linear combinations are determined to maximize the HDMR’s constant term contribution to the function. Although the resulting equations are nonlinear we could have been able to approximate the solutions by using recently proven fluctuationlessness theorem on matrix representations appearing in the equations.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-009-9291-2