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Pattern Retrieval by Quaternionic Associative Memory with Dual Connections

  • Toshifumi MinemotoEmail author
  • Teijiro Isokawa
  • Masaki Kobayashi
  • Haruhiko Nishimura
  • Nobuyuki Matsui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9949)

Abstract

An associative memory based on Hopfield-type neural network, called Quaternionic Hopfield Associative Memory with Dual Connection (QHAMDC), is presented and analyzed in this paper. The state of a neuron, input, output, and connection weights are encoded by quaternion, a class of hypercomplex number systems with non-commutativity for its multiplications. In QHAMDC, calculation for an internal state of a neuron is conducted by two types of multiplications for neuron’s output and connection weight. This makes robustness of the proposed associative memory for retrieval of patterns. The experimental results show that the performances of retrieving patterns by QHAMDC are superior to those by the previous QHAM.

Notes

Acknowledgment

This study was financially supported by Japan Society for the Promotion of Science (Grant-in-Aids for Scientific Research (C) 16K00337).

References

  1. 1.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79(8), 2554–2558 (1984)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aizenberg, N.N., Ivaskiv, Y.L., Pospelov, D.A.: About one generalization of the threshold function. Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR) 196(6), 1287–1290 (1971)Google Scholar
  3. 3.
    Noest, A.J.: Discrete-state phasor neural networks. Phys. Rev. A 38(4), 2196–2199 (1988)CrossRefGoogle Scholar
  4. 4.
    Aizenberg, N.N., Aizenberg, I.N.: CNN based on multi-valued neuron as a model of associative memory for gray-scale images. In: Proceedings of the 2nd IEEE International Workshop on Cellular Neural Networks and their Applications, pp. 36–41 (1992)Google Scholar
  5. 5.
    Jankowski, S., Lozowski, A., Zurada, J.M.: Complex-valued multistate neural associative memory. IEEE Trans. Neural Netw. 7(6), 1491–1496 (1996)CrossRefGoogle Scholar
  6. 6.
    Aoki, H., Kosugi, Y.: An image storage system using complex-valued associative memories. Proc. Int. Conf. Pattern Recognit. 2, 626–629 (2000)CrossRefGoogle Scholar
  7. 7.
    Müezzinoğlu, M.K., Güzeliş, C., Zurada, J.M.: A new design method for the complex-valued multistate Hopfield associative memory. IEEE Trans. Neural Netw. 14(4), 891–899 (2003)CrossRefGoogle Scholar
  8. 8.
    Lee, D.L.: Improvements of complex-valued Hopfield associative memory by using generalized projection rules. IEEE Trans. Neural Netw. 17(5), 1341–1347 (2006)CrossRefGoogle Scholar
  9. 9.
    Isokawa, T., Nishimura, H., Saitoh, A., Kamiura, N., Matsui, N.: On the scheme of quaternionic multistate Hopfield neural network. In: Proceedings of of Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, pp. 809–813 (2008)Google Scholar
  10. 10.
    Minemoto, T., Isokawa, T., Nishimura, H., Matsui, N.: Quaternionic multistate Hopfield neural network with extended projection rule. Artif. Life Robot. 21(1), 106–111 (2016)CrossRefGoogle Scholar
  11. 11.
    Suzuki, Y., Kobayashi, M.: Complex-valued bipartite auto-associative memory. IEICE Trans. Fund. Electron. Commun. Comput. Sci. 97(8), 1680–1687 (2014)CrossRefGoogle Scholar
  12. 12.
    Minemoto, T., Isokawa, T., Matsui, N., Kobayashi, M., Nishimura, H.: On the performance of quaternionic bidirectional auto-associative memory. In: Proceedings of International Joint Conference on Neural Networks, #15594, 6 pages (2015)Google Scholar
  13. 13.
    Kobayashi, M.: Hybrid quaternionic Hopfield neural network. IEICE Trans. Fund. Electron. Commun. Comput. Sci. 98(7), 1512–1518 (2015)CrossRefGoogle Scholar
  14. 14.
    Bülow, T.: Hypercomplex spectral signal representations for the processing and analysis of images. Ph.D. thesis, Christian-Albrechts-Universität zu Kiel (1999)Google Scholar
  15. 15.
    Bülow, T., Sommer, G.: Hypercomplex signals–a novel extension of the analytic signal to the multidimensional case. IEEE Trans. Signal Process. 49(11), 2844–2852 (2001)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Isokawa, T., Nishimura, H., Matsui, N.: Quaternionic neural networks for associative memories. In: Hirose, A. (ed.) Complex-Valued Neural Networks: Advances and Applications, pp. 103–131. Wiley-IEEE Press (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Toshifumi Minemoto
    • 1
    Email author
  • Teijiro Isokawa
    • 1
  • Masaki Kobayashi
    • 2
  • Haruhiko Nishimura
    • 3
  • Nobuyuki Matsui
    • 1
  1. 1.Graduate School of EngineeringUniversity of HyogoHimejiJapan
  2. 2.Yamanashi UniversityKofuJapan
  3. 3.Graduate School of Applied InformaticsUniversity of HyogoKobeJapan

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