Dimension reduction as a part of function approximation problem

Abstract

Usually in case of approximation of high-dimensional unknown dependencies the "curse of dimensionality" problem arises. In order to deal with such problem preliminary dimension reduction of input vector should be done. In this paper the methodology for integration of dimension reduction procedure into the method for construction of function approximation is proposed. Developed method al¬lows choosing optimal combination of dimension of compression transformation and complexity of a model used for approximation avoiding overtraining of approximating function. Application of proposed method to real and artificial data shows good performance in terms of accuracy.