A modified error-correction learning rule for multilayer neural network with multi-valued neurons

In this paper, we consider a modified error-correction learning rule for the multilayer neural network with multi-valued neurons (MLMVN). MLMVN is a neural network with a standard feedforward organization, but based on the multi-valued neuron (MVN). MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. MLMVN has a derivative-free learning algorithm based on the error-correction learning rule. The discrete k-valued MVN activation function divides a complex plane into k equal sectors. To be able to get more reliable and efficient solutions for various classification problems, it is possible to modify the MLMVN error-correction learning rule in such a way that the learning samples belonging to different classes (clusters) will be concentrated along the bisector of a desired sector (the cluster center) and at the same time will be located as far as possible from each other. Such a modification based on soft margins learning, which is reduced to the minimization of the angular distance between the bisector of a desired sector and a weighted sum, is considered in this paper.