Nearest Neighbor Algorithms for Pattern Classification

Abstract

A solution of the discrimination problem is considered by means of the minimum distance classifier, commonly referred to as the nearest neighbor (NN) rule. The NN rule is nonparametric, or distribution free, in the sense that it does not depend on any assumptions about the underlying statistics for its application. The k-NN rule is a procedure that assigns an observation vector z to a category F if most of the k nearby observations x sub i are elements of F. The condensed nearest neighbor (CNN) rule may be used to reduce the size of the training set required categorize The Bayes risk serves merely as a reference-the limit of excellence beyond which it is not possible to go. The NN rule is bounded below by the Bayes risk and above by twice the Bayes risk.