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Feed-Forward Neural Networks Using Hermite Polynomial Activation Functions

  • Gerasimos G. Rigatos
  • Spyros G. Tzafestas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3955)

Abstract

In this paper feed-forward neural networks are introduced where hidden units employ orthogonal Hermite polynomials for their activation functions. The proposed neural networks have some interesting properties: (i) the basis functions are invariant under the Fourier transform, subject only to a change of scale, and (ii) the basis functions are the eigenstates of the quantum harmonic oscillator, and stem from the solution of Schrödinger’s diffusion equation. The proposed neural networks demonstrate the particle-wave nature of information and can be used in nonparametric estimation. Possible applications of neural networks with Hermite basis functions include system modelling and image processing.

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References

  1. 1.
    Cohen-Tannoudji, C., Diu, D., Laloë, F.: Mécanique Quantique I, Hermann (1998)Google Scholar
  2. 2.
    Strauss, W.A.: Partial Differential Equations: An Introduction. J. Wiley, Chichester (1992)zbMATHGoogle Scholar
  3. 3.
    Kosko, B.: Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence. Prentice Hall, Englewood Cliffs (1992)zbMATHGoogle Scholar
  4. 4.
    Ventura, D., Martinez, T.: Quantum Associative Memory. Information Sciences 24, 273–296 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Perus, M.: Multi-level Synergetic Computation in Brain. Nonlinear Phenomena in Complex Systems 4, 157–193 (2001)MathSciNetGoogle Scholar
  6. 6.
    Rigatos, G.G., Tzafestas, S.G.: Parallelization of a fuzzy control algorithm using quantum computation. IEEE Transactions on Fuzzy Systems 10, 451–460 (2002)CrossRefGoogle Scholar
  7. 7.
    Rigatos, G.G., Tzafestas, S.G.: Fuzzy learning compatible with quantum mechanics postulates. In: Computational Intelligence and Natural Computation, CINC 2003, North Carolina (2003)Google Scholar
  8. 8.
    Refregier, A.: Shapelets - I. A method for image analysis. Mon. Not. R. Astron. Soc. 338, 35–47 (2003)CrossRefGoogle Scholar
  9. 9.
    Haykin, S.: Neural Networks: A Comprehensive Foundation. McMillan (1994)Google Scholar
  10. 10.
    Ma, L., Khorasani, K.K.: Constructive Feedforward Neural Networks Using Hermite Polynomial Activation Functions. IEEE Transactions on Neural Networks 16, 821–833 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gerasimos G. Rigatos
    • 1
  • Spyros G. Tzafestas
    • 2
  1. 1.Industrial Systems Institute, Unit of Industrial AutomationRion PatrasGreece
  2. 2.Dept. of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece

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