Skipping Fisher's criterion

Abstract

A new version of Fisher's discriminant analysis (FDA) is introduced in this paper. Our algorithm searches also for a reduced space in which patterns can be discriminated. However, no intermediate class separability criterion (such as Fisher's mean distance divided by variance) is used whatsoever. Classification performance is optimized directly. Since no statistical hypothesis are made, the method is of general applicability. Our evolutionary approach for optimization makes the number of projections and classes independent of each other. Even different numbers of projections, not necessarily the means, can be used for each class. As a proof of concept, the UCI thyroid problem (three classes) is solved in one dimension instead of two with state of the art performance and making use of only three of the 21 original features.