Abstract

Chaotic Pattern Recognition (PR) is a relatively new sub-field of PR in which a system, which demonstrates chaotic behavior under normal conditions, resonates when it is presented with a pattern that it is trained with. The Adachi Neural Network (AdNN) is a classic neural structure which has been proven to demonstrate the phenomenon of Associative Memory (AM). In their pioneering paper [1,2] , Adachi and his co-authors showed that the AdNN also emanates periodic outputs on being exposed to trained patterns. This was later utilized by Calitoiu et al [4,5] to design systems which possibly possessed PR capabilities. In this paper, we show that the previously reported properties of the AdNN do not adequately describe the dynamics of the system. Rather, although it possesses far more powerful PR and AM properties than was earlier known, it goes through a spectrum of characteristics as one of its crucial parameters, α, changes. As α increases, the AdNN which is first an AM become quasi-chaotic. The system is then distinguished by two phases which really do not have clear boundaries of demarcation. In the former of these phases it is quasi-chaotic for some patterns and periodic for others. In the latter of these, it exhibits properties that have been unknown (or rather, unreported) till now, namely, a PR capability (which even recognizes masked or occluded patterns) in which the network resonates sympathetically for trained patterns while it is quasi-chaotic for untrained patterns. Finally, the system becomes completely periodic. All these results are, to the best of our knowledge, novel.

Keywords

Chaotic NNs Chaotic Pattern Recognition Adachi NN 

References

  1. 1.
    Adachi, M., Aihara, K.: Associative dynamics in a chaotic neural network. Neural Networks 10(1), 83–98 (1997)CrossRefGoogle Scholar
  2. 2.
    Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Physics Letters A 144(6,7), 333–340 (1990)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)MATHGoogle Scholar
  4. 4.
    Calitoiu, D., Oommen, B., Nussbaum, D.: Desynchronzing of chaotic pattern recognition neural network to model inaccurate parception. IEEE Trans. on Systems, Man, and Cybernetics-part B: Cybernetics 37(3), 692–704 (2007)CrossRefGoogle Scholar
  5. 5.
    Calitoiu, D., Oommen, B., Nussbaum, D.: Periodicity and stability issues of a chaotic pattern recognition neural network. Pat. Anal. Applic., 175–188 (October 2007)Google Scholar
  6. 6.
    Fausett, L.: Fundamentals of Neural Networks: Architectures, Algorithms And Applications. Prentice Hall, Upper Saddle River (1994)MATHGoogle Scholar
  7. 7.
    Freeman, W.: Tutorial on neurobiology: from single neurons to brain chaos. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2, 451–482 (1992)CrossRefMATHGoogle Scholar
  8. 8.
    Friedman, M., Kandel, A.: Introduction to Pattern Recognition, Statistical, Structural, Neural and Fuzzy Logic Approaches. World Scientific, Singapore (1999)CrossRefMATHGoogle Scholar
  9. 9.
    Fukunaga, K.: Introduction to Statistical Pattern Recognition. Academic Press, London (1990)MATHGoogle Scholar
  10. 10.
    Qin, K., Oommen, B.J.: The Spectrum of Chaotic Pattern Recognition Properties Obtainable Using Adachi’s Neural Network. Unabridged version of this paper (Submitted for Publication) (Can be made available if required)Google Scholar
  11. 11.
    Ripley, B.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)CrossRefMATHGoogle Scholar
  12. 12.
    Schurman, J.: Pattern Classification, A Unified View of Statistical and Neural Approaches. John Wiley and Sons, New York (1996)Google Scholar
  13. 13.
    Skarda, C., Freeman, W.: How brains make chaos in order to make sense of the world. Behaviorai and Brain Sciences 10(2), 161–195 (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ke Qin
    • 1
  • B. John Oommen
    • 2
  1. 1.School of Computer Science and EngineeringUniversity of Electronic Science & Technology of ChinaChengduChina
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

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