Nonparametric learning of decision regions via the genetic algorithm

A method for nonparametric (distribution-free) learning of complex decision regions in n-dimensional pattern space is introduced. Arbitrary n-dimensional decision regions are approximated by the union of a finite number of basic shapes. The primary examples introduced in this paper are parallelepipeds and ellipsoids. By explicitly parameterizing these shapes, the decision region can be determined by estimating the parameters associated with each shape. A structural random search type algorithm called the genetic algorithm is applied to estimate these parameters. Two complex decision regions are examined in detail. One is linearly inseparable, nonconvex and disconnected. The other one is linearly inseparable, nonconvex and connected. The scheme is highly resilient to misclassification errors. The number of parameters to be estimated only grows linearly with the dimension of the pattern space for simple version of the scheme.