Universal Binary and Multi-Valued Neurons paradigm: Conception, learning, applications

  • Naum N. Aizenberg
  • Igor N. Aizenberg
Plasticity Phenomena (Maturing, Learning and Memory)
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1240)

Abstract

Futheron development of the Multi-Valued and Universal Binary Neurons conception with basic arithmetic over Complex Numbers Field is presented in this paper. Lot of attention is devoted to Universal Binary Neurons. New high-effective fast convergenced learning algorithm based on Error-correction rule is considered. It is shown that any non-threshold Boolean function can be implemented on the single Universal Binary Neuron. Example for solution of the XOR-problem on the single neuron is considered. Applications of the UBN for solution of the important problems of Image Processing (impulsive noise detection and filtering and edge detection with extraction of the smallest details based on representation of these operations through non-threshold Boolean functions) are also considered.

Keywords

Boolean Function Cellular Neural Network Impulsive Noise Real Number Field Single Impulse 
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.
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References

  1. [1]
    W.S.McCuloch, W.A.Pitts “Logical Caculus of the Ideas Immanent in Nervous Activity”, Bul. Math. Biophys., 5, pp. 115–133 (1943).Google Scholar
  2. [2]
    S.Haykin “Neural Networks. A Comprehensive Foundation”. Macmillan College Publishing Company, New York, 1994.Google Scholar
  3. [3]
    N.N.Aizenberg, Yu.L.Ivaskiv “ Multiple-Valued Threshold Logic”. Kiev: Naukova Dumka Publisher House (1977) (in Russian).Google Scholar
  4. [4]
    N.N.Aizenberg, I.N.Aizenberg “CNN based on Multi-Valued neuron as a model of Associative Memory for Grey-Scale Images”, Proc. of the 2-d International Workshop CNNA-92, Munich, 1992, IEEE Catalog No. 92TH0498-6, pp. 36–41.Google Scholar
  5. [5]
    N.N.Aizenberg, I.N.Aizenberg “Fast Convergenced Learning Algorithms for Multi-Level and Universal Binary Neurons and Solving of the some Image Processing Problems”, Lecture Notes in Computer Science,Ed.-J.Mira,J.Cabestany,A.Prieto,v.686, Shpringer-Verlag, (1993),pp.230–236.Google Scholar
  6. [6]
    Aizenberg N.N., AizenbergI.N., Krivosheev G.A. “Multi-Valued Neurons: Learning, Networks, Application to Image Recognition and Extrapolation of Temporal Series”,“Lect. Notes in Computer Science”,v. 930, (J.Mira, F.Sandoval — Eds.), Shpringer-Verlag, 1995,pp.389–395.Google Scholar
  7. [7]
    G.M.Georgiou and C.Koutsougeras “Complex Domain Backpropagation”, IEEE Trans. CAS-II.Analog and Digital Signal Processing, vol.39, No 5, 1992, pp. 330–334Google Scholar
  8. [8]
    H.Leung, S.Haykin “The Complex Backpropagation Algorithm”, IEEE Trans. on Signal Processing, vol.39, No 9, September, 1991, pp: 2101–2104.Google Scholar
  9. [9]
    N.N.Aizenberg “Spectrum of the Convolution of Discrete Signals in the Arbitrary Basis”, Dokladi Academii Nauk SSSR, vol.247,No 3, pp.551–554, 1978 (in Russian).Google Scholar
  10. [10]
    L.O. Chua and L.Yang, “Cellular neural networks: Theory”, IEEE Trans.Circuits Syst.vol. 35,pp. 1257–1290, Oct. 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Naum N. Aizenberg
    • 1
  • Igor N. Aizenberg
    • 2
  1. 1.Department of Cybernetics of the State University of Uzhgorod (Ukraine)UzhgorodUkraine
  2. 2.Departement Elektrotechniek ESAT/SISTAK.U.LEUVENHeverleeBelgium

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