Issue No. 03 - March (1984 vol. 6)
Thomas E. Flick , Naval Research Laboratory, Washington, DC 20375.
Keinosuke Fukunaga , School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
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.
Thomas E. Flick, Keinosuke Fukunaga, "An Optimal Global Nearest Neighbor Metric", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 6, no. , pp. 314-318, March 1984, doi:10.1109/TPAMI.1984.4767523