A new approach for multivariate data modelling in orthogonal geometry

Abstract

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.

Keywords:

• high-dimensional model representation
• multivariate functions
• approximation
• interpolation
• data modelling

2010 AMS Subject Classifications:

• 41A05
• 41A10
• 41A63
• 65D05

Acknowledgements

The author is grateful to Professor Metin Demiralp for his contributions and invaluable comments.