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Complex-Valued Neurons with Phase-Dependent Activation Functions

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Artifical Intelligence and Soft Computing (ICAISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6114))

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Abstract

In this paper, we observe two artificial neurons with complex-valued weights. There are a multi-valued neuron and a universal binary neuron. Both neurons have activation functions depending on the argument (phase) of the weighted sum. A multi-valued neuron may learn multiple-valued threshold functions. A universal binary neuron may learn arbitrary (not only linearly-separable) Boolean functions. It is shown that a multi-valued neuron with a periodic activation function may learn non-threshold functions by their projection to the space corresponding to the larger valued logic. A feedforward neural network with multi-valued neurons and its learning are also considered.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University-Texarkana, P.O. Box 5518, Texarkana, TX 75505-5518, USA

    Igor Aizenberg

Authors
  1. Igor Aizenberg
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Editor information

Editors and Affiliations

  1. Department of Artificial Intelligence, Academy of Humanities and Economics, Poland

    Leszek Rutkowski

  2. Academy of Humanities and Economics in Łódź, ul. Rewolucji 1905 nr 64, Łódź, Poland

    Rafał Scherer

  3. Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, PL-30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley Initiative in Soft Computing (BISC), 94720-1776, CA

    Lotfi A. Zadeh

  5. Computational Intelligence Laboratory Department of Electrical and Computer Engineering, University of Louisville, 40292, Louisville, KY

    Jacek M. Zurada

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Aizenberg, I. (2010). Complex-Valued Neurons with Phase-Dependent Activation Functions. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artifical Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13232-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-13232-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13231-5

  • Online ISBN: 978-3-642-13232-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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