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From Homogeneous Network to Neural Nets with Fractional Derivative Mechanism

  • Zbigniew Gomolka
  • Ewa Dudek-Dyduch
  • Yuriy P. Kondratenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10245)

Abstract

The paper refers to ANNs of the feed-forward type, homogeneous within individual layers. It extends the idea of network modelling and design with the use of calculus of finite differences proposed by Dudek-Dyduch E. and then developed jointly with Tadeusiewicz R. and others. This kind of neural nets was applied mainly to different features extraction i.e. edges, ridges, maxima, extrema and many others that can be defined with the use of classic derivative of any order and their linear combinations. Authors extend this type ANNs modelling by using fractional derivative theory. The formulae for weight distribution functions expressed by means of fractional derivative and its discrete approximation are given. It is also shown that the application of 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 smooth control of a derivative order allows to model the neuron dynamics without direct modification of the source code in IT model. The new approach presented in the paper, universalizes the model of the considered type of ANNs.

Keywords

Fractional Order Fractional Derivative Discrete Approximation Fractional Order Derivative Classic Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The research were conducted in the scientific cooperation between Faculty of Mathematics and Natural Sciences Department of Computer Engineering at University of Rzeszow and AGH University of Science and Technology Cracow, Department of Biomedical Engineering and Automation. The studies were conducted in the laboratory of Computer Graphics and Digital Image Processing at Center for Innovation and Transfer of Natural Sciences and Engineering Knowledge of Rzeszow University. Grants: WMP/GD-11/2016 and AGH-UST 11.120.417.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Zbigniew Gomolka
    • 1
  • Ewa Dudek-Dyduch
    • 2
  • Yuriy P. Kondratenko
    • 3
    • 4
  1. 1.Faculty of Mathematics and Natural Sciences Department of Computer EngineeringUniversity of RzeszowRzeszowPoland
  2. 2.Department of Biomedical Engineering and AutomationAGH University of Science and Technology CracowKrakówPoland
  3. 3.Intelligent Information Systems DepartmentPetro Mohyla Black Sea State UniversityMykolaivUkraine
  4. 4.Cleveland State UniversityClevelandUSA

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