Summary: A MULTI-VALUED NEURON
WITH A PERIODIC ACTIVATION FUNCTION
Department of Computer Science, Texas A&M University-Texarkana, P.O. Box75505- 5518, Texarkana, TX 75505, U.S.A.
Keywords: Complex-valued neural networks, Derivative-free learning, Pattern recognition, Classification.
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.
The discrete multi-valued neuron (MVN) was
introduced by Aizenberg N. and Aizenberg I.
(1992). This neuron operates with complex-valued
weights. Its inputs and output are located on the unit
circle, and for a discrete MVN they are exactly kth