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

By M. Alper Tunga, Metin Demiralp. 2006

49 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/69c9f6f836281a48a9a01e4a46b96d34d348e737

How researchers see this paper

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In Artificial Intelligence

1. S. Shan
2. G. G. Wang

In Control and Systems Engineering

1. S. Shan
2. G. G. Wang

In Statistics and Probability

1. S. Shan
2. G. G. Wang
3. Amir H. Gandomi
4. Géraud Blatman
5. Bruno Sudret

Citations in the corpus

• Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions (2010, background): “If the problem has a hybrid nature (neither additive nor multiplicative ), HHDMR (Tunga and Demiralp 2006; hybrid HDMR) has been developed.”