Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 829692, 27 pages
http://dx.doi.org/10.1155/2010/829692
Research Article

Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks

1Department of Mathematics, Dalian Maritime University, Dalian 116026, China
2Department of Applied Mathematics, Harbin Engineering University, Harbin 150001, China

Received 1 September 2009; Accepted 19 January 2010

Academic Editor: Manuel De La Sen

Copyright © 2010 Huisheng Zhang et al. 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. S. Alonso-Quesada and M. De La Sen, “Robust adaptive control with multiple estimation models for stabilization of a class of non-inversely stable time-varying plants,” Asian Journal of Control, vol. 6, no. 1, pp. 59–73, 2004. View at Google Scholar
  2. P. Zhao and O. P. Malik, “Design of an adaptive PSS based on recurrent adaptive control theory,” IEEE Transactions on Energy Conversion, vol. 24, no. 4, pp. 884–892, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Cortès, “Distributed Kriged Kalman filter for spatial estimation,” IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2816–2827, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. D. R. Wilson and T. R. Martinez, “The general inefficiency of batch training for gradient descent learning,” Neural Networks, vol. 16, no. 10, pp. 1429–1451, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Li, Y. Diao, M. Li, and X. Yin, “Stability analysis of discrete Hopfield neural networks with the nonnegative definite monotone increasing weight function matrix,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 673548, 10 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Q. Zhu and J. Cao, “Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 490515, 20 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. G. M. George and C. Koutsougeras, “Complex domain backpropagation,” IEEE Transactions on Circuits and Systems II, vol. 39, no. 5, pp. 330–334, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. T. Benvenuto and F. Piazza, “On the complex backpropagaton algorithm,” IEEE Transactions on Signal Processing, vol. 40, no. 4, pp. 967–969, 1992. View at Google Scholar
  9. A. Hirose, Complex-Valued Neural Networks, Springer, New York, NY, USA, 2006.
  10. T. Kim and T. Adali, “Fully complex backpropagation for constant envelop signal processing,” in Proceedings of the IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing X, pp. 231–240, Sydney, Australia, December 2000.
  11. A. I. Hanna and D. P. Mandic, “A data-reusing nonlinear gradient descent algorithm for a class of complex-valued neural adaptive filters,” Neural Processing Letters, vol. 17, no. 1, pp. 85–91, 2003. View at Publisher · View at Google Scholar
  12. S. L. Goh and D. P. Mandic, “Stochastic gradient-adaptive complex-valued nonlinear neural adaptive filters with a gradient-adaptive step size,” IEEE Transactions on Neural Networks, vol. 18, no. 5, pp. 1511–1516, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Nitta, “Orthogonality of decision boundaries in complex-valued neural networks,” Neural Computation, vol. 16, no. 1, pp. 73–97, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. S. S. Yang, S. Siu, and C. L. Ho, “Analysis of the initial values in split-complex backpropagation algorithm,” IEEE Transactions on Neural Networks, vol. 19, no. 9, pp. 564–1573, 2008. View at Google Scholar
  15. H. Zhang, W. Wu, F. Liu, and M. Yao, “Boundedness and convergence of online gadient method with penalty for feedforward neural networks,” IEEE Transactions on Neural Networks, vol. 20, no. 6, pp. 1050–1054, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Wu, G. Feng, Z. Li, and Y. Xu, “Deterministic convergence of an online gradient method for BP neural networks,” IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 533–540, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Zhang, C. Zhang, and W. Wu, “Convergence of batch split-complex backpropagation algorithm for complex-valued neural networks,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 329173, 16 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970.