Discovering Polynomials to Fit Multivariate Data Having Numeric and Nominal Variables

This paper proposes an improved version of a method for discovering 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 approximated and learned by three-layer neural networks. The method selects the best from those trained neural networks with different numbers of hidden units by a newly introduced double layer of cross-validation, and restores the final rules from the best. Experiments using two data sets show that the proposed method works well in discovering very succinct and interesting rules even from data containing irrelevant variables and a small amount of noise.