Nearest neighbor classi cation 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 classi cation method to try to minimize bias. We use a Chisquared 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 in uential ones. As a result, the class conditional probabilities tend to be smoother in the modi ed neighborhoods, whereby better classi cation performance can be achieved. The e cacy of our method is validated and compared against other techniques using a variety of simulated and real world data.
In REF adaptive nearest neighbor classification in high-dimensional spaces was studied.
Locally Adaptive Metric Nearest Neighbor Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Science