Another Look at the Edited Nearest Neighbor Rule.

摘要

In this paper the authors present a slight modification of Wilson's Edited Nearest Neighbor Rule (1) in the one dimensional case for which it is possible to compute tight bounds on the average asymptotic risk. It is pointed out that the argument used by Wilson to establish his bounds is probably incorrect with the bounds being somewhat optimistic. The rule presented here is not in itself of any great significance since it does not generalize to more than one dimension. The contribution lies in the fact that for this type of rule (which is very similar to Wilson's rule) an exact analysis is possible which permits comparison of the relative merits of various editing schemes. Although no proof is offered, the strong similarities involved give reason to believe that the results concerning the relative efficiencies of the various editing schemes will carry over to higher dimensional problems with the usual version of the nearest neighbor rule. (Author)