A Nonparametric Two-Dimensional Display for Classification

A two-dimensional display whose coordinates are related to the distance to the kth-nearest neighbor of each class is presented. Applications of the display to minimum error, minimum cost, minimax, and Neyman-Pearson type classifier designs are given. The display is shown to present risk information in a manner that easily allows the specification of reject regions. Two methods of error estimation using the display, an error counting technique and a risk averaging method, are detailed. It is shown that the classifiers that result are generalizations of the standard k-NN majority vote classifier. As a result of the properties of the display, classifiers can be readily evaluated and modified. In addition, a condensing algorithm that preserves the nearest neighbor error count of any preclassified data set is described. The display is used to graphically illustrate the distance relationships that are central to the algorithm.