A topological approach to the pattern classification in neural networks

The biological intelligence flexibility and its reaction velocity, when an external irritation exists, can be explained as a result of the pattern classification, which should has the premier role in a comparison with the recognition in the sense of finding the most similar prototype. Real neural networks classifies, finding any memorized pattern subset, which represents one or several characteristics of the offered stimulus, and it is not obligatory that the stimulus looks like patterns in the subset. A self-organizing neural network, which is able to classify according to various criteria, is considered in this paper. The proposed model is based on the synergetic Haken-like neural networks, where recognition is reduced to the competition between scalar time-dependent order parameters. It is shown, that some kinds of interconnections between order parameters lead to the vanishing of several fixed stable points, corresponding to patterns in one subset, and to the elliptic variety formation. Each variety consists of fixed stable point continuum and corresponds to the single subset. An arbitrary form of subset formation is considered