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Neurons’ Transfer Function Modeling with the Use of Fractional Derivative

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Book cover Contemporary Complex Systems and Their Dependability (DepCoS-RELCOMEX 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 761))

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Abstract

The paper presents new approach the idea of artificial neural network (ANN) modelling and design with the use of calculus of finite differences proposed by Dudek-Dyduch [5, 8] and then developed jointly with Tadeusiewicz [5] and others. Previously such neural nets were applied mainly to the extraction of different features i.e. edges, ridges, maxima, extrema and many others that can be defined with the use of a classic derivative of any order and their linear combinations. The author extend this method of ANN modelling by the use of fractional derivative theory for transfer function modelling. Different types of fractional derivatives and their numerical accuracy have been presented. Finally it was shown that the discrete approximation of fractional derivative of some base functions allows for modelling the transfer function of a single neuron for various characteristics. In such an approach, the smooth control of a derivative order allows the neuron dynamics to be modeled without direct modification of the source code in the IT model. The novel approach universalizes the model of the artificial neurons.

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, Department of Computer Engineering, University of Rzeszow, ul. Pigonia 1, 35-959, Rzeszow, Poland

    Zbigniew Gomolka

Authors
  1. Zbigniew Gomolka
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Correspondence to Zbigniew Gomolka .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Wrocław University of Technology, Wrocław, Poland

    Wojciech Zamojski

  2. Department of Computer Engineering, Wrocław University of Technology, Wrocław, Poland

    Jacek Mazurkiewicz

  3. Department of Computer Engineering, Wrocław University of Technology, Wrocław, Poland

    Jarosław Sugier

  4. Department of Computer Engineering, Wrocław University of Technology, Wrocław, Poland

    Tomasz Walkowiak

  5. Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

    Janusz Kacprzyk

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Gomolka, Z. (2019). Neurons’ Transfer Function Modeling with the Use of Fractional Derivative. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) Contemporary Complex Systems and Their Dependability. DepCoS-RELCOMEX 2018. Advances in Intelligent Systems and Computing, vol 761. Springer, Cham. https://doi.org/10.1007/978-3-319-91446-6_21

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