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An Optimal Global Nearest Neighbor Metric

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2 Author(s)
Fukunaga, Keinosuke ; School of Electrical Engineering, Purdue University, West Lafayette, IN 47907. ; Flick, Thomas E.

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.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-6 ,  Issue: 3 )