Reference Set Size Reduction for 1-NN Rule Based on Finding Mutually Nearest and Mutually Furthest Pairs of Points

Abstract

Two algorithms for reference set size reduction are presented and tested on an actual data set of a large size. The first one, as most of existing procedures, is based on the consistency idea, which means that all points from the primary reference set are correctly classified by 1-NN rule operating with the reduced set. The second algorithm requires division of the reference set into some subsets and replacing these subsets by their gravity centers. These gravity centers assume the same label as the majority of points of the corresponding subset. This algorithm enables the condensation of the reference set to the desired size, however, the resulting sets do not offer as good classification quality as other existing methods.

As opposed to the first algorithm, the second algorithm does not enable the control of the reduced set size. It is shown that combining both of these algorithms promises as good of a performance while allowing the control of the size of the obtained condensed sets.