A New Bi-directional Associative Memory

  • Roberto A. Vázquez
  • Humberto Sossa
  • Beatriz A. Garro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4293)


Hebbian hetero-associative learning is inherently asymmetric. Storing a forward association from pattern A to pattern B enables the recalling of pattern B given pattern A. This, in general, does not allow the recalling of pattern A given pattern B. The forward association between A and B will tend to be stronger than the backward association between B and A. In this paper it is described how the dynamical associative model proposed in [10] can be extended to create a bi-directional associative memory where forward association between A and B is equal to backward association between B and A. This implies that storing a forward association, from pattern A to pattern B, would enable the recalling of pattern B given pattern A and the recalling of pattern A given pattern B. We give some formal results that support the functioning of the proposal, and provide some examples were the proposal finds application.


Input Pattern Associative Memory Output Pattern Distorted Version Associative Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Steinbuch, K.: Die Lernmatrix. Kybernetik 1(1), 26–45 (1961)CrossRefGoogle Scholar
  2. 2.
    Anderson, J.A.: A Simple Neural Network Generating an Interactive Memory. Mathematical Biosciences 14, 197–220 (1972)MATHCrossRefGoogle Scholar
  3. 3.
    Kohonen, T.: Correlation Matrix Memories. IEEE Trans. on Computers 21(4), 353–359 (1972)MATHCrossRefGoogle Scholar
  4. 4.
    Hopfield, J.J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings of the National Academy of Sciences 79, 2554–2558 (1982)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Sussner, P.: Generalizing Operations of Binary Auto-Associative Morphological Memories using Fuzzy Set Theory. Journal of mathematical Imaging and Vision 19(2), 81–93 (2003)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ritter, G.X., Urcid, G., Iancu, L.: Reconstruction of Patterns from Noisy Inputs using Morphological Associative Memories. Journal of mathematical Imaging and Vision 19(2), 95–111 (2003)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Sossa, H., Barron, R.: New Associative Model for Pattern Recall in the Presence of Mixed Noise. In: Proceedings of the 5th IASTED International Conference on Signal and Image Processing, SIP 2003, vol. 399, pp. 485–490. Acta Press (2003)Google Scholar
  8. 8.
    Sossa, H., Barrón, R., Vázquez, R.A.: Transforming Fundamental set of Patterns to a Canonical Form to Improve Pattern Recall. In: Lemaître, C., Reyes, C.A., González, J.A. (eds.) IBERAMIA 2004. LNCS (LNAI), vol. 3315, pp. 687–696. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Sossa, H., Barrón, R., Vázquez, R.A.: New Associative Memories for Recall Real-Valued Patterns. In: Sanfeliu, A., Martínez Trinidad, J.F., Carrasco Ochoa, J.A. (eds.) CIARP 2004. LNCS, vol. 3287, pp. 195–202. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Vázquez, R.A., Sossa, H., Barrón, R.: Enhanced Associative Memory Model for Pattern Restoration (submitted, 2006)Google Scholar
  11. 11.
    Vázquez, R.A., Sossa, H.: Associative memories applied to image categorization. In: Martínez-Trinidad, J.F., Carrasco Ochoa, J.A., Kittler, J. (eds.) CIARP 2006. LNCS, vol. 4225, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Ebbinghaus, H.: Memory: A Contribution to Experimental Psychology. Teachers College, Columbia University, New York (1885/1913)Google Scholar
  13. 13.
    Robinson, E.S.: Association Theory Today: An Essay in Systematic Psychology. Century Co., New York (1932)CrossRefGoogle Scholar
  14. 14.
    Asch, S.E., Ebenholtz, S.M.: The Principle of Associative Symmetry. Proceedings of the American Philosophical Society 106, 135–163 (1962)Google Scholar
  15. 15.
    Kohler, W.: Gestalt Psychology. Liveright, New York (1947)Google Scholar
  16. 16.
    Rizzuto, D.S., Kahana, M.J.: Associative Symmetry vs. Independent Association. Neurocomputing 32–33, 973–978 (2000)CrossRefGoogle Scholar
  17. 17.
    Kosko, B.: Bidirectional Associative Memories. IEEE Trans. on Systems, Man and Cybernetic 18(1), 49–60 (1988)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Lee, D.-L., Wang, W.-J.: Improvement of Bidirectional Associative Memories by using Correlation Significance. Electronics Letters 29(8), 688–690 (1993)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Wang, Y.-F., et al.: Guaranteed Recall of all Training Pairs for Bidirectional Associative Memory. IEEE Trans. on Neural Networks 1(6), 559–567 (1991)CrossRefGoogle Scholar
  20. 20.
    Leung, C.S.: Optimum Learnig for Bidirectional Associative Memory in the Sense of Capacity. IEEE Trans. on Systems, Man and Cybernetics 24(5), 791–796 (1994)CrossRefGoogle Scholar
  21. 21.
    Chartier, S., Boukadoum, M.: A Bidirectional Heteroassociative Memory for Binary and Grey Level Patterns. IEEE Trans. on Neural Networks 17(2), 385–396 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roberto A. Vázquez
    • 1
  • Humberto Sossa
    • 1
  • Beatriz A. Garro
    • 1
  1. 1.Centro de Investigación en Computación – IPNCiudad de MéxicoMéxico

Personalised recommendations