Orthogonal and successive projection methods for the learning of neurofuzzy GMDH

Abstract

A neural GMDH (group method of data handling) family of modelling algorithm emulates the self-organizing activity of the central nervous system, and discovers the structure (functional form) of empirical models that include many input variables. A generalized successive projection method is developed for the accelerated learning algorithm of the GMDH type model whose partial descriptions are represented by the radial basis functions network. (1) For the learning of partial descriptions of the perceptron type GMDH, a combined algorithm of the successive projection method and the orthogonal projection method is developed. (2) For the learning of the network type GMDH, a successive projection method is derived as the solution of an optimization problem in which the Minkowski norm of distance travelled (step size) is minimized. Their performances are compared with the instantaneous learning algorithms such as the least mean square. Several examples show the validity of the methods.