High Dimensional Model Representation
from Beginning to Present Status
    
within the
9th WSEAS International Conference on
APPLIED MATHEMATICS (MATH '06)
Istanbul, Turkey, May 27-29, 2006
http://www.worldses.org/conferences/2006/istanbul/math/index.html
 

High Dimensional Model Representation (HDMR) seems to be a powerful agent in the representation of multivariate functions. Although it finds its roots in Kolmogorov's works the first important steps are taken via Sobol's and Rabitz's works. Later Demiralp's group contributed to the topics by de defining several different methods. Today, there is more tendency to deal with HDMR than the beginning of its history. Different varieties are proposed and the applicability of the representation to many different problem seems to be possible now. There is still a long way to walk but many aspects of the issue is now more clear than before.
Tutorial will cover standing well established parts of the theory for high dimensional model representation. It will not focus only on the High Dimensional Model Representation in its original form but the following varieties will also be considered:

• Factorized High Dimensional Model Representation (FHDMR)

• Hybrid High Dimensional Model Representation (HHDMR)

• Generalized High Dimensional Model Representation (GHDMR)

• Interval HDMR Varieties

The presentation will also cover the basic applications of HDMR and its varieties to many application areas. Amongst these, perhaps, the most important one is the data partitioning and the following multivariate interpolation. A special emphasize will be given to this focus since it has a lot of openings starting from atmospheric science and geographic information systems to data recovery, data mining and so on.

Organizer:

Prof. Metin Demiralp, Informatics Institute, Istanbul Technical University, Turkey.
E-mail: demiralp@be.itu.edu.tr