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An Optimal Global Nearest Neighbor Metric
March 1984 (vol. 6 no. 3)
pp. 314-318
Keinosuke Fukunaga, School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
Thomas E. Flick, Naval Research Laboratory, Washington, DC 20375.
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.
Keinosuke Fukunaga, Thomas E. Flick, "An Optimal Global Nearest Neighbor Metric," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 3, pp. 314-318, March 1984, doi:10.1109/TPAMI.1984.4767523
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