Adaptive nearest neighbor classifier

In nearest neighbor classification, one normally uses cross-validation type methods to estimate the optimum value of k, and that estimated value is used for classifying all observations. However, in classification problems, in addition to depending on the training sample, a good choice of k depends on the specific observation to be classified. In this article we propose an adaptive nearest neighbor classification technique, where the value of k is selected depending on the distribution of competing classes in the vicinity of the observation to be classified. Results on some simulated and benchmark examples are presented to show the utility of the proposed method.