Skip to main content

A Generalised Entropy Based Associative Model

  • Conference paper
Neural Information Processing (ICONIP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4984))

Included in the following conference series:

  • 1220 Accesses

Abstract

In this paper, a generalised entropy based associative memory model will be proposed and applied to memory retrievals with analogue embedded vectors instead of the binary ones in order to compare with the conventional autoassociative model with a quadratic Lyapunov functionals. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the autocorrelation dynamics as a special case. From numerical results, it will be found that the presently proposed novel approach realizes the larger memory capacity even for the analogue memory retrievals in comparison with the autocorrelation model based on dynamics such as associatron according to the higher-order correlation involved in the proposed dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, J.A.: A Simple Neural Network Generating Interactive Memory. Mathematical Biosciences 14, 197–220 (1972)

    Article  MATH  Google Scholar 

  2. Kohonen, T.: Correlation Matrix Memories. IEEE Transaction on Computers C-21, 353–359 (1972)

    Google Scholar 

  3. Nakano, K.: Associatron-a Model of Associative Memory. IEEE Trans. SMC-2, 381–388 (1972)

    Google Scholar 

  4. Amari, S.: Neural Theory of Association and Concept Formation. Biological Cybernetics 26, 175–185 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  5. Amit, D.J., Gutfreund, H., Sompolinsky, H.: Storing Infinite Numbers of Patternsin a Spin-glass Model of Neural Networks. Physical Review Letters 55, 1530–1533 (1985)

    Article  Google Scholar 

  6. Gardner, E.: Structure of Metastable States in the Hopfield Model. Journal of Physics A19, L1047–L1052 (1986)

    Google Scholar 

  7. Kohonen, T., Ruohonen, M.M.: Representation of Associated Pairs by Matrix Operators. IEEE Transaction C-22, 701–702 (1973)

    Google Scholar 

  8. Amari, S., Maginu, K.: Statistical Neurodynamics of Associative Memory. Neural Networks 1, 63–73 (1988)

    Article  Google Scholar 

  9. Morita, M.: Neural Networks. Associative Memory with Nonmonotone Dynamics 6, 115–126 (1993)

    Google Scholar 

  10. Yanai, H.-F., Amari, S.: Auto-associative Memory with Two-stage Dynamics of non-monotonic neurons. IEEE Transactions on Neural Networks 7, 803–815 (1996)

    Article  Google Scholar 

  11. Shiino, M., Fukai, T.: Self-consistent Signal-to-noise Analysis of the Statistical Behaviour of Analogu Neural Networks and Enhancement of the Storage Capacity. Phys. Rev. E48, 867 (1993)

    Google Scholar 

  12. Kanter, I., Sompolinski, H.: Associative Recall of Memory without Errors. Phys. Rev. A 35, 380–392 (1987)

    Article  Google Scholar 

  13. Personnaz, L., Guyon, I., Dreyfus, D.: Information Storage and Retrieval in Spin-Glass like Neural Networks. J. Phys(Paris) Lett. 46, L-359 (1985)

    Google Scholar 

  14. Nakagawa, M.: Chaos and Fractals in Engineering, p. 944. World Scientific Inc., Singapore (1999)

    Google Scholar 

  15. Nakagawa, M.: Autoassociation Model based on Entropy Functionals. In: Proc. of NOLTA 2006, pp. 627–630 (2006)

    Google Scholar 

  16. Nakagawa, M.: Entropy based Associative Model. IEICE Trans. Fundamentals EA-89(4), 895–901 (2006)

    Article  Google Scholar 

  17. Fuchs, A., Haken, H.: Pattern Recognition and Associative Memory as Dynamical Processes in a Synergetic System I. Biological Cybernetics 60, 17–22 (1988)

    MATH  MathSciNet  Google Scholar 

  18. Fuchs, A., Haken, H.: Pattern Recognition and Associative Memory as Dynamical Processes in a Synergetic System II. Biological Cybernetics 60, 107–109 (1988)

    Article  MathSciNet  Google Scholar 

  19. Fuchs, A., Haken, H.: Dynamic Patterns in Complex Systems. In: Kelso, J.A.S., Mandell, A.J., Shlesinger, M.F. (eds.), World Scientific, Singapore (1988)

    Google Scholar 

  20. Haken, H.: Synergetic Computers and Cognition. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  21. Nakagawa, M.: A study of Association Model based on Synergetics. In: Proceedings of International Joint Conference on Neural Networks 1993 NAGOYA, JAPAN, pp. 2367–2370 (1993)

    Google Scholar 

  22. Nakagawa, M.: A Synergetic Neural Network. IEICE Fundamentals E78-A, 412–423 (1995)

    Google Scholar 

  23. Nakagawa, M.: A Synergetic Neural Network with Crosscorrelation Dynamics. IEICE Fundamentals E80-A, 881–893 (1997)

    Google Scholar 

  24. Nakagawa, M.: A Circularly Connected Synergetic Neural Networks. IEICE Fundamentals E83-A, 881–893 (2000)

    Google Scholar 

  25. Nakagawa, M.: Entropy based Associative Model. In: Proceedings of ICONIP 2006, pp. 397–406. Springer, Heidelberg (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Masumi Ishikawa Kenji Doya Hiroyuki Miyamoto Takeshi Yamakawa

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nakagawa, M. (2008). A Generalised Entropy Based Associative Model. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69158-7_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69158-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69154-9

  • Online ISBN: 978-3-540-69158-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics