Multi-Valued Neuron with a Periodic Activation Function

Abstract

In this Chapter, we consider MVN with a periodic activation function. As we have already seen, MVN’s functionality is higher than the one of, for example, sigmoidal neurons. In this Chapter, we will consider how a single MVN may learn nonlinearly separable input/output mappings in that initial n-dimensional space where they are defined. In Section 5.1, we consider a universal binary neuron (UBN), which in fact is the discrete MVN with a periodic activation function for k=2. We show how this neuron may learn non-linearly separable Boolean functions, for example, XOR and Parity n, projecting them into larger valued logic. In Section 5.2, we generalize that approach, which is used in UBN, and introduce a periodic activation function for the discrete MVN. We also consider the learning algorithm for MVN with a periodic activation functions. In Section 5.3, we show how a number of non-linearly separable benchmark classification problems can be solved using a single MVN with a periodic activation function. Concluding remarks are given in Section 5.4.