Nearest neighbor classification expects the class conditional prob(cid:173) abilities to be locally constant, and suffers from bias in high di(cid:173) mensions We propose a locally adaptive form of nearest neighbor classification to try to finesse this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective met(cid:173) ric for computing neighborhoods. We determine the local decision boundaries from centroid information, and then shrink neighbor(cid:173) hoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighborhood-based classifier can be employed, using the modified neighborhoods. We also propose a method for global dimension reduction, that combines local dimension information.

Our goal is to predict the class membership of an observation with predictor vector Xo Nearest neighbor classification is a simple and appealing approach to this problem.

Our goal is to predict the class membership of an observation with predictor vector Xo Nearest neighbor classification is a simple and appealing approach to this problem.

Nearest neighbor classification expects the class conditional probabilities tobe locally constant, and suffers from bias in high dimensions Wepropose a locally adaptive form of nearest neighbor classification to try to finesse this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric forcomputing neighborhoods. We determine the local decision boundaries from centroid information, and then shrink neighborhoods indirections orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighborhood-based classifier can be employed, using the modified neighborhoods. We also propose a method for global dimension reduction, that combines local dimension information.