Revised GMDH Algorithm of Self-Selecting Optimal Intermediate Polynomials Using AIC

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Abstract
In this paper, a revised GMDH (Group Method of Data Handling) algorithm, which automatically selects optimal intermediate polynomials instead of partial polynomials in each selection layer, is developed. In the previous GMDH algorithms, the partial polynomials, in which the intermediate variables are the input variables in each selection layer, have been estimated and accumulated in the multilayered structure. So, in general, it is difficult to identify exactly the physically meaningful structure between the input and the output variables. The revised GMDH algorithm in this paper generates optimal intermediate polynomials in each selection layer, which express the direct relationship between the input and the output variables, so as to minimize the Akaike's Information Criterion (AIC) evaluated by using all the data. Therefore, the physically meaningful structure can be identified when the characteristics of the system are well reflected in the data. The revised GMDH algorithm is applied to the input-output data observed in a simple kinematic system, and we try to discover the Newton's second law. The result obtained is compared with that obtained by the previous GMDH algorithm of using partial polynomials.

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