Nonlinear discriminant adaptive nearest neighbor classifiers

Nearest neighbor classifiers are one of most common techniques for classification and ATR applications. Hastie and Tibshirani propose a discriminant adaptive nearest neighbor (DANN) rule for computing a distance metric locally so that posterior probabilities tend to be homogeneous in the modified neighborhoods. The idea is to enlongate or constrict the neighborhood along the direction that is parallel or perpendicular to the decision boundary between two classes. DANN morphs a neighborhood in a linear fashion. In this paper, we extend it to the nonlinear case using the kernel trick. We demonstrate the efficacy of our kernel DANN in the context of ATR applications using a number of data sets.