A computational geometry approach for linear and non linear discriminant analysis

A geometric discriminant criterion is a rule that allows to assign a new observation to preexisting groups. In this paper we propose a new method that works for data sets in two and three dimensions. It is totally data driven, without any model or density function assumptions, unlike usual the parametric approaches. In order to set up the procedure we exploit the geometrical properties of the Voronoi tessellation. The proposed discriminant analysis induces a space partition, that allows to deal efficiently with non linearly separable or non convex population structures. We analize the computational cost of the proposed procedure and the topological conditions concerning the group-conditional density functions that optimize the procedure performance. Because of its geometric properties, the method can be also usefully applied in statistical pattern recognition.