TUTORIAL I Hilbert Space, Orthogonality and Quality Measurement Milestones of HDMR, High Dimensional Model Representation

Demiralp M.

WSEAS Conference on Recent Advances in Systems Engineering and Applied Mathematics, İstanbul, Turkey, 27 - 30 May 2008, pp.14 identifier

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.14
  • Istanbul Technical University Affiliated: No


High Dimensional Model Representation is perhaps the most interesting and efficient tool developed in last fifteen years for multivariate analysis. The basic concept was proposed by Sobol. Rabitz brought the weight function and geometry extensions to the method although the orthogonality of the geometry proposed by Sobol was preserved. Later, Demiralp established the bridge between the vanishing conditions and the orthogonality conditions amongst the HDMR components. He also defined certain functionals to measure the contribution percentage of different variete HDMR components to norm square of the whole HDMR expansion. Sobol, Rabitz and his group, and Demiralp's group is continuing to make research in various aspects of HDMR. Today, a lot of new variants of HDMR are constructed and being successfully used. Quite recently constructed fluctuation expansion technique, which is proceeding in the way of becoming a theory, has facilitated to construct an approximate but integration free algorithm in HDMR. This tutorial will focus on the Hilbert space components of HDMR theory starting from its birth to the present form.