METHODOLOGY  OF  NETWORKS  WITH  SYMMETRICAL TRANSFORMATION  FUNCTIONS  FOR  NEURONS

    The basic methodology of networks with symmetrical transformation functions for neurons (STFN) is presented. Such neural networks (NN) find application in the problems of approximation, pattern recognition, systems (objects) identification, controller designing, noise level lowering for signals in information-measurement systems. The characteristic property of NN structure is the localization of hidden-layer elements in the multidimensional vector space (whose dimension is identical to the input information dimension) and the presence of STFN depending on the (metric) norm of the difference between the hidden-layer element localization vectors and the input signal-vector. The paper presents the applied theory elements for pattern recognition using a network with STFN; NN learning criteria on the basis of a functional regularized with the aid of A.N. Tikhonov’s method; a general form of approximation and interpolation functions (obtained on the basis of those criteria) using Green’s scheme for the inverse problem generated by transformation with a differential operator; a method for regularization parameter selection.