We explore the problems of classification of composite object (images, speech signals) with low number of models per class. We study the question of improving recognition performance for medium-sized database (thousands of classes). The key issue of fast approximate nearest-neighbor methods widely applied in this task is their heuristic nature. It is possible to strongly prove their efficiency by using the theory of algorithms only for simple similarity measures and artificially generated tasks. On the contrary, in this paper we propose an alternative, statistically optimal greedy algorithm. At each step of this algorithm joint density (likelihood) of distances to previously checked models is estimated for each class. The next model to check is selected from the class with the maximal likelihood. The latter is estimated based on the asymptotic properties of the Kullback-Leibler information discrimination and mathematical model of piecewise-regular object with distribution of each regular segment of exponential type. Experimental results in face recognition for FERET dataset prove that the proposed method is much more effective than not only brute force and the baseline (directed enumeration method) but also approximate nearest neighbor methods from FLANN and NonMetricSpaceLib libraries (randomized kd-tree, composite index, perm-sort).
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