The finite-sample risk of the k-nearest-neighbor classifier under the L/sub p/ metric

Abstract

The finite-sample risk of the k-nearest neighbor classifier that uses an L/sub 2/ distance function is examined. For a family of classification problems with smooth distributions in R/sup n/, the risk can be represented as an asymptotic expansion in inverse powers of the n-th root of the reference-sample size. The leading coefficients of this expansion suggest that the Euclidean or L/sub 2/ distance function minimizes the risk for sufficiently large reference samples.