An Optimal Global Nearest Neighbor Metric

Authors:
Keinosuke Fukunaga;Thomas E. Flick
Affiliations:
School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.;Naval Research Laboratory, Washington, DC 20375.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1984

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Abstract

A quadratic metric dAO (X, Y) =[(X - Y)T AO(X - Y)]驴 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.