Redefining nearest neighbor classification in high-dimensional settings

In this work, a novel nearest neighbor approach is presented. The main idea is to redefine the distance metric in order to include only a subset of relevant variables, assuming that they are of equal importance for the classification model. Three different distance measures are redefined: the traditional squared Euclidean, the Manhattan, and the Chebyshev. These modifications are designed to improve classification performance in high-dimensional applications, in which the concept of distance becomes blurry, i.e., all training points become uniformly distant from each other. Additionally, the inclusion of noisy variables leads to a loss of predictive performance if the main patterns are contained in just a few variables, since they are equally weighted. Experimental results on low- and high-dimensional datasets demonstrate the importance of these modifications, leading to superior average performance in terms of Area Under the Curve (AUC) compared with the traditional k nearest neighbor approach.