Classification on bounded sets

Three types of verified training algorithms (with a tutor) at the limited infinite sets (based on the theory of separability) are presented. On contrast to two first ones the mathematical motivation of the last one can be a basis of the new theory of cluster analysis without cluster's center search and it is used at the samples without tutor. The estimates on memory usage and recognition time for all types of algorithms, theory modification for parallel calculations are obtained. The problem for optimizing (three minimizing criteria, one maximization criterion) the attribute space, optimal orderable space and description minimization of such sets has been solved. The presented theory explains and proves the fact that one neuron can classify images presented by limited sets. © 2010 Pleiades Publishing, Ltd.