Revised GMDH Algorithm Using Principal Component-Regression Analysis

Abstract

In this paper, a revised GMDH (Group Method of Data Handling) of multiinput-singleoutput type algorithm is developed by using principal component-regression analysis.
In previous GMDH algorithms, the optimal partial polynomials, which are generated by using the second degree polynomial of the two variables in each selection layer, are accumulated in multilayerd structure to construct the complete polynomial. But, in a high order selection layer, many combinations of two variables generate multicolinearity in partial polynomials and this presents a severe problem in estimation accuracy of model parameters. The nonlinear models which contain multicolinearity in the partial polynomials lack in stability and can not be used in prediction problems.
The revised GMDH in this paper generates some optimal partial polynomials which are identified by using principal component-regression analysis in each selection layer, and the complete description of the system is constructed by combining these optimal partial polynomials in multilayerd structure. The principal components which construct the partial polynomials are perendicular each other and so the partial polynomials generate no multicolinearity.
The revised GMDH algorithm is applied to a simple illustrative example and compared with the result obtained by the previous GMDH algorithm.