A nonlinear perturbative scheme to solve weight optimization problem of High Dimensional Model Representation (HDMR)

One way to increase the approximating quality of the High Dimensional Model Representation (HDMR) truncations is to increase the truncation order. However this is not generally desired for practical reasons if the order climbs to the multivariances beyond the bivariance. In these circumstances the other alternative is preferred. It is to change the structure of HDMR. This can be done either by using a different but again orthogonal geometry or by changing the structure of the weight function. Weight optimization is based on the constancy maximization and in fact gives different importances to the function values at different points of the HDMR domain. Weight function is considered as the square of a linear combination of certain basis functions and the linear combination coefficients are determined to maximize the constancy. The resulting equations are nonlinear. This work attempts to solve these equations by expanding unknowns around their certain nominal values.