Separation Surfaces through Genetic Programming

The aim of this paper is to describe a study for the obtaining, symbolically, of the separation surfaces between clusters of a labelled database. A separation surface is an equation with the form ø; (x)=0, where ø is a function of R n → R. The calculation of function ø is begun by the development of the parametric regression by means of the use of the Genetic Programming. The symbolic regression consists in approximating an unknown function's equation, through knowledge of certain points' coordinates and the value that a function reaches with the same ones. This possibility was propose in [Koza92a] and its advantage in front of the classic statistical regressions is that it is not necessary previously to know the form the function. Once this surface is found, a classifier for the database could be obtained. The technique has been applied to different examples and the results have been very satisfactory.