Adaptive Discriminant and Quasiconformal Kernel Nearest Neighbor Classification

Abstract

Nearest neighbor classification assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions due to the curse-of-dimensionality. Severe bias can be introduced under these conditions when using the nearest neighbor rule. We propose locally adaptive nearest neighbor classification methods to try to minimize bias. We use locally linear support vector machines as well as quasiconformal transformed kernels to estimate an effective metric for producing neighborhoods that are elongated along less discriminant feature dimensions and constricted along most discriminant ones. As a result, the class conditional probabilities can be expected to be approximately constant in the modified neighborhoods, whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other competing techniques using a variety of data sets.