Finding polynomials to fit multivariate data having numeric and nominal variables

Abstract

This paper proposes a new method for finding polynomials to fit multivariate data containing numeric and nominal variables. Each polynomial is accompanied with the corresponding nominal condition stating when to apply the polynomial. Such a nominally conditioned polynomial is called a rule. A set of such rules can be regarded as a single numeric function, and such a function can be closely approximated by a single three-layer neural network. After training single neural networks with different numbers of hidden units, the method selects the best trained network, and restores the final rules fromi t. Experiments using three data sets show that the proposed method works well in finding very succinct and interesting rules, even fromda ta containing irrelevant variables and a small amount of noise.