Factorized form of the indexing HDMR method for multivariate data modeling

A multivariate data set including a number of scattered nodes with associated function values is given in data modeling problems to construct a rule for the estimation process of unknown function values. To reduce the mathematical and computational complexity of the given problem coming from the multivariance, the given multivariate data set may be partitioned into less-variate data sets with one or two variables. The indexing HDMR method, which is a very recently developed divide-and-conquer method, can be used for this data partitioning process. However, we know that this method works well for the problems with either a dominantly or purely additive nature. To improve the overall performance of the method for different cases, this work offers the factorized form of the Indexing HDMR method. The Factorized Indexing HDMR method uses the Indexing HDMR components to construct the analytical models for the given multivariate problems and impressive numerical results are obtained.