  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).
