An algorithm for determining identity of nearest-neighbor and potential function decision rules

Abstract

The nearest-neighbor and potential function decision rules are nonparametric techniques that partition the feature space based on a set of labelled sample points. Determining whether the partitions of the two rules are identical for a given set of points is an interesting problem in computational geometry. Here, a relationship between the two methods in terms of subclasses and composite classes is developed. Considering an exponential potential function, necessary and sufficient conditions for identity of their decision surfaces are obtained. Based on conditions of symmetry, weiohting, and the Voronoi re qion of a point, an algorithm for establishing identity in IR d is introduced.