ON THE MATHEMATICAL TREATMENT OF SELF-ORGANIZATION: EXTENSION OF SOME CLASSICAL RESULTS

Abstract

Although the basic principles of the self-organizing systems [2,3] are simple, the process behaviour is difficult to be described in mathematical terms. In Kohonen the self-ordering [2,3] phenomena are proved in the simplest cases: one dimensional array of functional units to each of which a scalar-valued input signal X is connected. The topology is simple as well: every unit i has the neighbours i-1, i+1, except at the borders of the array.