Neural networks and discriminant functions

The article deals with a geometrical interpretation of the neuron-s models. The interpretation shows some discriminant functions which divides inputs variable-s area into parts with objects in question. The linear discriminant function corresponds to the most of known neuron-s models. A piecewise linear discriminant function corresponds to neural networks, a piecewise polynomial one - to the group method of data handling (GMDH). The neuron-s spline-model is a nonlinear discriminant function which is complicated and to a first approximation can be realized by 3- or 4-layer network of the known neurons.

The workabilities of discriminant functions are demonstrated as an adequate and visual instrument of neuron models -

and neural networks - analysis, of working on theoretical tasks, improvement of synthesis and setting of neural networks -

algorithms.