Hybrid high dimensional model representation (HHDMR) on the partitioned data
Journal of Computational and Applied Mathematics
WSEAS Transactions on Mathematics
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
A gentle introduction to high dimensional model representation under nonproduct type weights
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
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This paper focuses on a new version of Hybrid High Dimensional Model Representation for multivariate functions. High Dimensional Model Representation (HDMR) was proposed to approximate the multivariate functions by the functions having less number of independent variables. Towards this end, HDMR disintegrates a multivariate function to components which are respectively constant, univariate, bivariate and so on in an ascending ordering of multivariance. HDMR method is a scheme truncating the representation at a prescribed multivariance. If the given multivariate function is purely additive then HDMR method spontaneously truncates at univariance, otherwise the highly multivariant terms are required. On the other hand, if the given function is dominantly multiplicative then the Logarithmic HDMR method which truncates the scheme at a prescribed multivariance of the HDMR of the logarithm of the given function is taken into consideration. In most cases the given multivariate function has both additive and multiplicative natures. If so then a new method is needed. Hybrid High Dimensional Model Representation method is used for these types of problems. This new representation method joins both plain High Dimensional Model Representation and Logarithmic High Dimensional Model Representation components via an hybridity parameter. This work focuses on the construction and certain details of this novel method.