title: An optimal global nearest neighbor metric.
abstract: A quadratic metric dAO (X, Y) =[(X - Y)T AO(X - Y)]¿ is proposed which minimizes the mean-squared error between the nearest neighbor asymptotic risk and the finite sample risk. Under linearity assumptions, a heuristic argument is given which indicates that this metric produces lower mean-squared error than the Euclidean metric. A nonparametric estimate of Ao is developed. If samples appear to come from a Gaussian mixture, an alternative, parametrically directed distance measure is suggested for nearness decisions within a limited region of space. Examples of some two-class Gaussian mixture distributions are included.
authors.affiliation: School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
authors.forename: K
authors.initials: K
authors.lastname: Fukunaga
authors.forename: T E
authors.initials: TE
authors.lastname: Flick