The influence of the support functions on the quality of enhanced multivariance product representation

Tunga, Burcu; Demіralp, Metin

doi:10.1007/s10910-010-9714-2

Cited by 35 publications

(26 citation statements)

References 6 publications

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“…These constraints are defined also for EMPR under the existence of support functions which are univariate functions multiplied by components of HDMR and they are explained for EMPR of multi-way arrays in the next section. 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.…”

Section: Enhanced Multivariance Products Representationmentioning

confidence: 99%

Reductive enhanced multivariance product representation for multi-way arrays

Özay

Demіralp

2014

J Math Chem

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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.

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Section: Enhanced Multivariance Products Representationmentioning

confidence: 99%

Reductive enhanced multivariance product representation for multi-way arrays

Özay

Demіralp

2014

J Math Chem

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“…EMPR is an extension to the HDMR philosophy [26,33]. The following relation is given as the expansion of the EMPR algorithm:…”

Section: Enhanced Multivariance Product Representationmentioning

confidence: 99%

“…where the functions, s j (x j )s with 1 ≤ j ≤ N are the support functions and make the method a general purpose algorithm when compared with HDMR [26,33]. When each support function is set as 1, we get the HDMR expansion.…”

Section: Enhanced Multivariance Product Representationmentioning

confidence: 99%

“…In parallel to the HDMR philosophy, the weight function components and the support functions have the following normalization conditions for easy and simple calculations [33]:…”

Section: Enhanced Multivariance Product Representationmentioning

confidence: 99%

“…The numerical results of previous studies show that the HDMR philosophy works well for modelling purely and dominantly additive natures while it becomes worse as the multiplicativity dominancy of the problem increases. To this end, this work aims to use another approach which is a more general purpose method called enhanced multivariance product representation (EMPR) [33]. The expansion defined in this method has a number of support functions and appearance of the support functions gives a flexibility to the user and makes the method very efficient in representing any kind of structure appearing in data modelling problems.…”

Section: Introductionmentioning

confidence: 99%

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A new approach for multivariate data modelling in orthogonal geometry

Tunga

2014

International Journal of Computer Mathematics

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Decomposing multivariate functions in terms of less variate components such as univariate or bivariate structures is an efficient way to reduce the mathematical and computational complexity of the related problem in computer-based applications. The enhanced multivariance product representation (EMPR) method is an extension to high-dimensional model representation (HDMR) which has a divide-and-conquer philosophy. The EMPR method has some additional structures named as support functions in its expansion when compared with HDMR and we have an important flexibility in selecting these support function structures. This selection process makes the method more successful than HDMR in most cases. In this sense, this work aims to apply the EMPR method to the multivariate data modelling problems having orthogonal geometries. The numerical results also show that the idea of this work is successfully applied to the considered problems and we obtain good representations in data modelling.

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Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation

Tunga

Demіralp

2010

J Math Chem

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The influence of the support functions on the quality of enhanced multivariance product representation

Cited by 35 publications

References 6 publications

Reductive enhanced multivariance product representation for multi-way arrays

Reductive enhanced multivariance product representation for multi-way arrays

A new approach for multivariate data modelling in orthogonal geometry

Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation

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