Locally Adaptive Metric Nearest Neighbor Classiication

Nearest neighbor classiication assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions with nite samples due to the curse of dimensionality. Severe bias can be introduced under these conditions when using the nearest neighbor rule. We propose a locally adaptive nearest neighbor classiication method to try to minimize bias. We use a Chi-squared distance analysis to compute a exible metric for producing neighborhoods that are highly adaptive to query locations. Neighborhoods are elongated along less relevant feature dimensions and constricted along most innuential ones. As a result, the class conditional probabilities tend to be smoother in the mod-iied neighborhoods, whereby better classiication performance can be achieved. The eecacy of our method is validated and compared against other techniques using a variety of simulated and real world data.