A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid

2009

Numer Algor

Self Cite

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.

“…If the weight function given above is used to calculate the constancy measurer given in (10) we obtain the following relation.…”

Section: The Weight Optimization Through Constancy Measurermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constancy maximization based weight optimization in high dimensional model representation

Tunga

2009

Numer Algor

Self Cite

“…Enhanced multivariance products representation was developed by Demiralp to get better approximation and to overcome some weaknesses of HDMR [25,26]. Although different methods based on HDMR have been developed for different kind of functions [27][28][29], EMPR can be considered as a generalization of HDMR. The main reason for developing EMPR is additive nature of HDMR.…”

Section: Enhanced Multivariance Products Representationmentioning

confidence: 99%

Reductive enhanced multivariance product representation for multi-way arrays

Özay

2014

J Math Chem

Self Cite

The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as a multi-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR's efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.

“…These are the HDMR components of a given multivariate function. Then, several other new algorithms based on this method were proposed in more comprehensive forms for different types of engineering problems by H. Rabitz, M. Demiralp and their groups [2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…These methods work well for the sought functions having additive nature as a result of the additive structure of the HDMR expansion. For the sought functions having dominantly or entirely multiplicative nature Factorized HDMR (FHDMR) is used [9,10]. Hybrid HDMR (HHDMR) method is used when the sought function has intermediate nature, that is, it has neither a dominantly additive nor a dominantly multiplicative nature [11].…”

Section: Introductionmentioning

confidence: 99%

Computational complexity investigations for high-dimensional model representation algorithms used in multivariate interpolation problems

Tunga

Lecture Notes in Electrical Engineering

2009

Abstract:In multivariate interpolation problems, increase in both the number of independent variables of the sought function and the number of nodes appearing in the data set cause computational and mathematical difficulties. It may be a better way to deal with less variate partitioned data sets instead of an N -dimensional data set in a multivariate interpolation problem. New algorithms such as High Dimensional Model Representation (HDMR), Generalized HDMR, Factorized HDMR, Hybrid HDMR are developed or rearranged for these types of problems. Up to now, the efficiency of the methods in mathematical sense were discussed in several papers. In this work, the efficiency of these methods in computational sense will be discussed. This investigation will be done by using several numerical implementations.