Evolution of Fisher's discriminants

Series expansions on a fixed set of basis functions have a neat advantage over neural-like modeling: the absence of local minima. Polynomial regression constitutes the paradigm. Even when non-linear basis functions are used, the coefficients of the expansion are uniquely specified and easily calculated. However, the number of adjustable coefficients is not controlled by the complexity of the problem but by the input dimension. In this paper, an evolutionary approach is proposed as a means of alleviating this drawback. As a proof of concept, a genetic algorithm is used to evolve the inputs used to construct Fisher's discriminants. A varied group of UCI datasets is used to show that the evolved models perform 30% better than the discriminants constructed with the whole set of inputs.