Generalized HDMR can be used to partition the given multivariate data set into less variate data sets to avoid the standard numerical methods' restrictions coming from the multivariance and to minimize the memory insufficiencies occured in the computer based applications when all nodes of the whole domain defined for given, that is, randomly selected nodes are given. Hovewer, this method has some disadvantages to obtain acceptable approximations in engineering problems. For this purpose, High Dimensional Model Representation (HDMR) method can be used in these types of problems. In fact, this method needs an orthogonal geometry. The main purpose of this work is to reconstruct the given multivariate data set by imposing an indexing scheme and to obtain an orthogonal geometry for the given problem. The introductory steps of this new method called Lumping HDMR are given in this work. The remaining details and the maturization of this new method is still under intense study.