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The finite sample performance of a nearest neighbor classifier is analyzed for a two-class pattern recognition problem. An exact integral expression is derived for the m-sample risk R,giveii that a reference m-sample of labeled points, drawn independently from Euclidean n-space according to a fixed probability distribution, is available to the classifier. (m-'In) if the class-conditional probability densities have uniformly bounded third derivatives on their probability one support. This analysis thus provides further analytic validation of Bellman's curse of dimensionality. Numerical simulations corloborating the formal results are included, and extensions of the theory discussed. The analysis also contains a novel application of Laplace's asymptotic method of integration to a multidimensional integral where the integrand attains its maximum on a continuum of points.

We (lescribe a page-formatted random-access holographic memory designe(l to store up to 160,000 holograms. The memory consists of 16 vertically spaced locations, each containing 10,000 holograms, which in turn are organized as 10 fractal-multiplexed rows of 1000 angularly-multiplexed holograms. A segmented mirror array is used to enable random access to any of the stored holograms within the access time of a non-mechanical angle scanner such as an acousto-oJ)tic deflector. Using a mechanical scanner with such a mirror array, we demonstrate storage of 10,000 holograms at a single location of the system, as well as simultaneous storage and recall of holograms at 6 locations, including the highest and lowest of the 16 locations.

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