A new approach for data partitioning through high dimensional model representation

Abstract

A multivariate function f(x1, ..., xN) can be evaluated via interpolation if its values are given at a finite number nodes of a hyperprismatic grid in the space of independent variables x1, x2, ..., xN. Interpolation is a way to characterize an infinite data structure (function) by a finite number of data approximately. Hence it leaves an infinite arbitrariness unless a mathematical structure with finite number of flexibilities is imposed for the unknown function. Imposed structure has finite dimensionality. When the dimensionality increases unboundedly, the complexities grow rapidly in the standard methods. The main purpose here is to partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula. As a result, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease. © 2013 Elsevier B.V., All rights reserved.