Fluctuation Free Matrix Representation Based HDMR Method to Model Multivariate Data

摘要

When a multivariate data set in which the sought function values are known only at a number of scattered nodes of the problem's grid is given and it is asked to determine an analytical structure to have the ability of evaluating the function values at the given testing points then High Dimensional Model Representation method is one of the best choice over the standard numerical methods since it is a divide-and-conquer method and an approximation can be obtained. Only disadvantage of this method is an orthogonal geometry need in the given data structure as there exist nonorthogonal structures for the training data sets of real life problems. To bypass this disadvantage we use the Fluctuation Free Approximation Method in the determination process of the HDMR expansion's components. This work deals with this process and builds an algorithm for the univariate approximation through the HDMR method to model the given multivariate data.