Numerical Studies on the Use of Enhanced Multivariance Product Representation as a Multiway Array Decomposer

Abstract

High dimensional model representation (HDMR) is a method to approximate a multivariate function by the sum of a constant, univariate, bivariate and other higher variate functions. HDMR philosophy may also be used as a multiway array decomposer approximating an N‐way array by the sum of a constant, vector, matrix and higher way arrays. Enhanced multivariance product representation (EMPR) provides univariate factors for each term of the representation and the choice of the factors affect the quality of the truncation. In multiway array decomposition case, this approach coincides with taking the outer product of the components by certain predetermined vectors instead of vectors with all elements that are 1. This work focuses on this case, investigating the application of EMPR to multiway array decomposition.