Relation, Transition and Comparison Between the Adaptive Nearest Neighbor Rule and the Hypersphere Classifier

The Adaptive Nearest Neighbor (ANN) rule and the Hyper- sphere Classifier (HC) are two very simple and relatively new variants of the classical nearest neighbor (1NN) rule. Even if they share a simi- lar formulation—they correct the query-to-prototype distance by taking into account the distance of the prototype to the nearest one from other classes—their relation has never been investigated. The main goal of this paper is studying this relation and providing an exhaustive perfor- mance comparison of both methods, highlighting occasions when their performances differ as well as identifying cases in which their application is advisable or leads to poorer results. Moreover, we propose a smooth transition between the two classifiers by studying the use of several con- vex combinations of their penalized distances. Experiments show that a combination is particularly helpful when both ANN and HC are worse than 1NN.