Skip to main content
SpringerLink
Log in

Quaternionic multistate Hopfield neural network with extended projection rule

  • Original Article
  • Published:
Artificial Life and Robotics Aims and scope Submit manuscript

Abstract

The aim of this paper is to investigate storing and recalling performances of embedded patterns on associative memory. The associative memory is composed of quaternionic multistate Hopfield neural network. The state of a neuron in the network is described by three kinds of discretized phase with fixed amplitude. These phases are set to discrete values with arbitrary divide size. Hebbian rule and projection rule are used for storing patterns to the network. Recalling performance is evaluated through storing random patterns with changing the divide size of the phases in a neuron. Color images are also embedded and their noise tolerance is explored.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Hirose A (2003) Complex-valued neural networks: theories and applications. World Scientific, Singapore

  2. Nitta T (2009) Complex-valued neural networks: utilizing high-dimensional parameters. Information Science Reference (IGI Global), New York

  3. Jankowski S, Lozowski A, Zurada J (1996) Complex-valued multistate neural associative memory. Neural Netw IEEE Trans 7(6):1491–1496

    Article  Google Scholar 

  4. Muezzinoglu M, Guzelis C, Zurada J (2003) A new design method for the complex-valued multistate hopfield associative memory. Neural Netw IEEE Trans 14(4):891–899

    Article  Google Scholar 

  5. Isokawa T, Nishimura H, Matsui N (2009) An iterative learning scheme for multistate complex-valued and quaternionic hopfield neural networks. In: Proceedings of International Joint Conference on Neural Networks (IJCNN2009), pp 1365–1371

  6. Isokawa T, Nishimura H, Saitoh A, Kamiura N, Matsui N (2008) On the scheme of quaternionic multistate hopfield neural network. In: Proceedings of SCIS and ISIS, Japan Society for Fuzzy Theory and Intelligent Informatics, pp 809–813

  7. Isokawa T, Nishimura H, Matsui N (2013) Quaternionic neural networks for associative memories. In: Hirose A (ed) Complex-valued neural networks: advances and applications. Springer, New York, pp 103–131

  8. Bülow T, Sommer G (2001) Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case. Signal Process IEEE Trans 49(11):2844–2852

    Article  Google Scholar 

  9. Isokawa T, Nishimura H, Kamiura N, Matsui N (2008) Associative memory in quaternionic hopfield neural network. Int J Neural Syst 18(2):135–145

    Article  Google Scholar 

  10. Personnaz L, Guyon I, Dreyfus G (1986) Collective computational properties of neural networks: New learning mechanisms. Phys Rev A 34(5):4217

    Article  MathSciNet  Google Scholar 

  11. Kohonen T (1988) Self-organization and associative memory. Springer, Berlin

  12. Lee DL (2006) Improvements of complex-valued hopfield associative memory by using generalized projection rules. Neural Netw IEEE Trans 17(5):1341–1347

    Article  Google Scholar 

  13. Suzuki Y, Kobayashi M (2014) Complex-valued bipartite auto-associative memory. IEICE Trans Fundam Electron Commun Comput Sci 97(8):1680–1687

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering, University of Hyogo, 2167, Shosha, Himeji, 671-2280, Japan

    Toshifumi Minemoto, Teijiro Isokawa & Nobuyuki Matsui

  2. Graduate School of Applied Informatics, University of Hyogo, Computational Science Center Building 5-7F, 7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo, 650-0047, Japan

    Haruhiko Nishimura

Authors
  1. Toshifumi Minemoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Teijiro Isokawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haruhiko Nishimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nobuyuki Matsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Toshifumi Minemoto.

Additional information

This work was presented in part at the 20th International Symposium on Artificial Life and Robotics, Beppu, Oita, January 21–23, 2015.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Minemoto, T., Isokawa, T., Nishimura, H. et al. Quaternionic multistate Hopfield neural network with extended projection rule. Artif Life Robotics 21, 106–111 (2016). https://doi.org/10.1007/s10015-015-0247-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10015-015-0247-4

Keywords

Search

Navigation