Hybrid high dimensional model representation (HHDMR) on the partitioned data

Authors:
M. Alper Tunga;Metin Demiralp
Affiliations:
Department of Computer Science and Engineering, Isik University, Engineering Faculty, Maslak, Istanbul, Turkey;Istanbul Technical University, Informatics Institute, Computational Science and Engineering Program, Maslak, Istanbul, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 1
Cited 8

Distribution theory and transform analysis: an introduction to generalized functions, with applications

Distribution theory and transform analysis: an introduction to generalized functions, with applications

A tool to improve the execution time of air quality models

Environmental Modelling & Software
Weight parameters optimization to get maximum constancy in high dimensional model representation

SMO'06 Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization
Computational complexity investigations for high dimensional model representation algorithms used in multivariate interpolation problems

MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
A novel hybrid high dimensional model representation (HHDMR) based on the combination of plain and logarithmic high dimensional model representations

MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
Data partitioning via high dimensional model representation by using paralel computing

MAASE'08 Proceedings of the 1st WSEAS International Conference on Multivariate Analysis and its Application in Science and Engineering
Bound analysis in univariately truncated Generalized High Dimensional Model Representation for random-data partitioning: Interval GHDMR

Applied Numerical Mathematics
Additivity and deviation multiplicativity measurers for uniform discrete multivariate data via high dimensional model representation varieties

ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
A modified method of calculating High Dimensional Model Representation (HDMR) Terms for parallelization with MPI and CUDA

The Journal of Supercomputing

Quantified Score

Hi-index	7.29

Visualization

Abstract

A multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid. One way to construct the solution of this problem is to partition the given multivariate data into low-variate data. High dimensional model representation (HDMR) and generalized high dimensional model representation (GHDMR) methods are used to make this partitioning. Using the components of the HDMR or the GHDMR expansions the multivariate data can be partitioned. When a cartesian product set in the space of the independent variables is given, the HDMR expansion is used. On the other hand, if the nodes are the elements of a random discrete data the GHDMR expansion is used instead of HDMR. These two expansions work well for the multivariate data that have the additive nature. If the data have multiplicative nature then factorized high dimensional model representation (FHDMR) is used. But in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature. They have a hybrid nature. So, a new method is developed to obtain better results and it is called hybrid high dimensional model representation (HHDMR). This new expansion includes both the HDMR (or GHDMR) and the FHDMR expansions through a hybridity parameter. In this work, the general structure of this hybrid expansion is given. It has tried to obtain the best value for the hybridity parameter. According to this value the analytical structure of the sought multivariate function can be determined via HHDMR.