Asymptotic Properties of Nearest Neighbor Rules Using Edited Data

The convergence properties of a nearest neighbor rule that uses an editing procedure to reduce the number of preclassified samples and to improve the performance of the rule are developed. Editing of the preclassified samples using the three-nearest neighbor rule followed by classification using the single-nearest neighbor rule with the remaining preclassified samples appears to produce a decision procedure whose risk approaches the Bayes´ risk quite closely in many problems with only a few preclassified samples. The asymptotic risk of the nearest neighbor rules and the nearest neighbor rules using edited preclassified samples is calculated for several problems.