A multi-valued neuron with a periodic activation function

Abstract

In this paper, a new activation function for the multi-valued neuron (MVN) is presented. The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN has a greater functionality than a sigmoidal or radial basis function neurons, it has a limited capability of learning highly nonlinear functions. A periodic activation function, which is introduced in this paper, makes it possible to learn nonlinearly separable problems and non-threshold multiple-valued functions using a single multi-valued neuron. The MVN's functionality becomes higher and the MVN becomes more efficient in solving various classification problems. A learning algorithm based on the error-correction rule for an MVN with the introduced activation function is also presented.