Evolutionary discriminant analysis

An evolutionary approach to the supervised reduction of dimensions is introduced in this paper. Traditionally, such reduction has been accomplished by maximizing one or another measure of class separation. Quite often, the rank deficiency of the involved covariance matrices precludes the application of this classical approach to real situations. Besides, the number of projections cannot be chosen freely, but it is bounded to be equal to the number of classes minus one. By contrast, our evolution strategy reduces dimensions by the direct minimization of the number of misclassified patterns. No matrices are involved whatsoever and the number of projections can be chosen without restrictions. This allows to obtain two-dimensional renderings of data sets with more than three classes such as the 19 class UCI soybean problem. A nonlinear generalization of this procedure based on the hierarchical composition of linear projections is shown to solve the UCI thyroid problem with state of the art recognition rates.