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Computational Intelligence and Neuroscience
Volume 2017, Article ID 4894278, 6 pages
https://doi.org/10.1155/2017/4894278
Research Article

Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules

Mathematical Science Center, University of Yamanashi, Takeda 4-3-11, Kofu, Yamanashi 400-8511, Japan

Correspondence should be addressed to Masaki Kobayashi; pj.ca.ihsanamay@ikasam-k

Received 12 April 2016; Accepted 6 March 2017; Published 3 May 2017

Academic Editor: Silvia Conforto

Copyright © 2017 Masaki Kobayashi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Hirose, Complex-Valued Neural Networks: Theories and Applications, World Scientific Publishing, River Edge, NJ, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. Hirose, “Complex-valued neural networks,” in Series on Studies in Computational Intelligence, Springer, 2nd edition, 2012. View at Google Scholar
  3. A. Hirose, “Complex-valued neural networks: advances and applications,” in The IEEE Press Series on Computational Intelligence, Wiley-IEEE Press, 2013. View at Google Scholar
  4. T. Nitta, “Complex-valued neural networks: Utilizing high-dimensional parameters,” Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters, pp. 1–479, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Arena, L. Fortuna, G. Muscato, and M. G. Xibilia, Neural Networks in Multidimensional Domains: Fundamentals and New Trends in Modelling and Control, vol. 234 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Nakano and A. Hirose, “Improvement of plastic landmine visualization performance by use of ring-CSOM and frequency-domain local correlation,” IEICE Transactions on Electronics, vol. E92-C, no. 1, pp. 102–108, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. T. Hara and A. Hirose, “Plastic mine detecting radar system using complex-valued self-organizing map that deals with multiple-frequency interferometric images,” Neural Networks, vol. 17, no. 8-9, pp. 1201–1210, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Onojima, Y. Arima, and A. Hirose, “Millimeter-wave security imaging using complex-valued self-organizing map for visualization of moving targets,” Neurocomputing, vol. 134, pp. 247–253, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Jankowski, A. Lozowski, and J. M. Zurada, “Complex-valued multistate neural associative memory,” IEEE Transactions on Neural Networks, vol. 7, no. 6, pp. 1491–1496, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. T. Minemoto, T. Isokawa, H. Nishimura, and N. Matsui, “Quaternionic multistate Hopfield neural network with extended projection rule,” Artificial Life and Robotics, vol. 21, no. 1, pp. 106–111, 2016. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Kobayashi, “Hyperbolic hopfield neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 2, pp. 335–341, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Kitahara and M. Kobayashi, “Projection rule for rotor hopfield neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 7, pp. 1298–1307, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. P. Zheng, “Threshold complex-valued neural associative memory,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 9, pp. 1714–1718, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. M. E. Acevedo-Mosqueda, C. Yanez-Marquez, and M. A. Acevedo-Mosqueda, “Bidirectional associative memories: Different approaches,” ACM Computing Surveys (CSUR), vol. 45, no. 2, pp. 18:1–18:30, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Aoki, M. R. Azimi-Sadjadi, and Y. Kosugi, “Image association using a complex-valued associative memory model, IEICE Transactions on Fundamentals of Electronics,” Communications and Computer Sciences, vol. E83-A, no. 9, pp. 1824–1832, 2000. View at Google Scholar
  16. G. Tanaka and K. Aihara, “Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction,” IEEE Transactions on Neural Networks, vol. 20, no. 9, pp. 1463–1473, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. M. K. Müezzinoglu, C. Güzeliş, and J. M. Zurada, “A new design method for the complex-valued multistate hopfield associative memory,” IEEE Transactions on Neural Networks, vol. 14, no. 4, pp. 891–899, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Kobayashi, “Gradient Descent Learning Rule for Complex-valued Associative Memories with Large Constant Terms,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 11, no. 3, pp. 357–363, 2016. View at Google Scholar
  19. D. L. Lee, “Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule,” IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 439–443, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Kitahara and M. Kobayashi, “Projection rule for complex-valued associative memory with large constant terms,” Nonlinear Theory and Its Applications, IEICE, vol. 3, no. 3, pp. 426–435, 2012. View at Publisher · View at Google Scholar
  21. M. Kobayashi, “Attractors accompanied with a training pattern of multivalued hopfield neural networks,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 10, no. 2, pp. 195–200, 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Donq-Liang and W. Wen-June, “A multivalued bidirectional associative memory operating on a complex domain,” Neural Networks, vol. 11, no. 9, pp. 1623–1635, 1998. View at Publisher · View at Google Scholar · View at Scopus
  23. D.-L. Lee, “Improvements of complex-valued Hopfield associative memory by using generalized projection rules,” IEEE Transactions on Neural Networks, vol. 17, no. 5, pp. 1341–1347, 2006. View at Publisher · View at Google Scholar · View at Scopus