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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Aizenberg, I. (2011). Multi-Valued Neuron with a Periodic Activation Function. In: Complex-Valued Neural Networks with Multi-Valued Neurons. Studies in Computational Intelligence, vol 353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20353-4_5
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DOI: https://doi.org/10.1007/978-3-642-20353-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20352-7
Online ISBN: 978-3-642-20353-4
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