Skip to main content
SpringerLink
Log in

Fully Coupled and Feedforward Neural Networks with Complex-Valued Neurons

  • Conference paper
Advances in Intelligent and Distributed Computing

Part of the book series: Studies in Computational Intelligence ((SCI,volume 78))

Summary

This paper discusses neural networks with complex-valued neurons with both discrete and continuous outputs. It reviews existing methods of their applications in fully coupled associative memories. Such memories are able to process multiple gray levels when applied for image de-noising. In addition, when complex-valued neurons are generalized to take a continuum of values, they can be used as substitutes for perceptron networks. Learning of such neurons is demonstrated and described in the context of traditional multilayer feedforward network learning. Such learning is derivative-free and it usually requires reduced network architecture. The notion of a universal binary neuron is also introduced. Selected examples and applications of such networks are also referenced.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. N. Aizenberg, Yu. L. Ivaskiv and D. A. Pospelov: About one generalization of the threshold function. In: Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR), vol.196, no.6, 1971, pp.1287–1290 (in Russian).

    Google Scholar 

  2. N. N. Aizenberg and I. N. Aizenberg: CNN Based on Multi-Valued Neuron as a Model of Associative Memory for Gray-Scale Images. In: Proceedings of the Second IEEE Int. Workshop on Cellular Neural Networks and their Applications, Technical University Munich, Germany, October 14–16, 1992, pp.36–41.

    Chapter  Google Scholar 

  3. I. N. Aizenberg: The Universal Logical Element over the Field of Complex Numbers. In: Kibernetika (Cybernetics and Systems Analysis), no.3, 1991, pp.116–121 (in Russian, journal is translated into English by Consultants Bureau, An Imprint of Springer Verlag New York LLC, Vol. 27, No 3, pp. 467–473).

    Google Scholar 

  4. I. Aizenberg, N. Aizenberg and J. Vandewalle: Multi-valued and universal binary neurons: theory, learning, applications, Kluwer Academic Publishers, Boston/Dordrecht/London, 2000.

    Google Scholar 

  5. I. Aizenberg: Solving the XOR and Parity n Problems Using a Single Universal Binary Neuron. In: Soft Computing, published Online First, June 2007, to appear in a regular hard copy: late 2007.

    Google Scholar 

  6. N. N. Aizenberg and Yu. L. Ivaskiv: Multiple-Valued Threshold Logic, Naukova Dumka Publisher House, Kiev, 1977 (in Russian).

    Google Scholar 

  7. I. Aizenberg and C. Moraga: Multilayer Feedforward Neural Network Based on MultiValued Neurons (MLMVN) and a Backpropagation Learning Algorithm. In: Soft Computing, vol.11, no.2, January 2007, pp. 169–183.

    Article  Google Scholar 

  8. I. Aizenberg, D. Paliy, J. Zurada and J. Astola: Blur Identification by Multilayer Neural Network based on Multi-Valued Neurons. In: IEEE Transactions on Neural Networks, accepted, to appear early 2008.

    Google Scholar 

  9. S. Jankowski, A. Lozowski and J.M. Zurada: Complex-Valued Multistate Neural Associative Memory. In: IEEE Trans. Neural Networks, vol.7, 1996, pp.1491–1496.

    Article  Google Scholar 

  10. H. Aoki and Y. Kosugi: An Image Storage System Using Complex-Valued Associative Memory. In: Proc. of the 15th International Conference on Pattern Recognition, Barcelona, 2000, IEEE Computer Society Press, vol.2, pp.626–629.

    Google Scholar 

  11. M. K. Muezzinoglu, C. Guzelis and J. M. Zurada: A New Design Method for the Complex-Valued Multistate Hopfield Associative Memory. In: IEEE Trans. Neural Networks, vol.14, No.4, 2003, pp.891–899.

    Article  Google Scholar 

  12. H. Aoki, E. Watanabe, A. Nagata and Y. Kosugi: Rotation-Invariant Image Association for Endoscopic Positional Identification Using Complex-Valued Associative Memories. In: J. Mira, A. Prieto (Eds.): Bio-inspired Applications of Connectionism, Lecture Notes in Computer Science, vol.2085, Springer, 2001, pp.369–374.

    Google Scholar 

  13. D. L. Lee: Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule. In: IEEE Transactions on Neural Networks, vol.12, no.2, Mar.2001, pp. 439–443.

    Article  Google Scholar 

  14. D. L. Lee: Complex-valued Neural Associative Memories: Learning Algorithm and Network Stability. In: A. Hirose (Ed.): Complex-Valued Neural Networks: Theories and Applications, World Scientific, 2004.

    Google Scholar 

  15. H. Aoki: Applications of Complex-Valued Neural Networks for Image Processing. In: A. Hirose Ed.): Complex-Valued Neural Networks: Theories and Applications, World Scientific, 2004.

    Google Scholar 

  16. T. Miyajima and K. Yamanaka: Phasor models and their applications to communications. In: A. Hirose Ed.): Complex-Valued Neural Networks: Theories and Applications, World Scientific, 2004.

    Google Scholar 

  17. H. Aoki: A complex-valued neuron to transform gray level images to phase information. In: L. Wang J. C Rajapakse, K. Fukushima, S.-Y. Lee and Xin Yao (Eds.): Proceedings of the 9th International Conference on Neural information Processing (ICONIP’2002), 2002, vol.3, pp.1084–1088.

    Google Scholar 

  18. I. Aizenberg, E. Myasnikova, M. Samsonova M. and J. Reinitz: Temporal Classification of Drosophila Segmentation Gene Expression Patterns by the Multi-Valued Neural Recognition Method. In: Mathematical Biosciences, vol.176 (1), 2002, pp.145–159.

    Article  MATH  MathSciNet  Google Scholar 

  19. I. Aizenberg, P. Ruusuvuori, O. Yli-Harja and J. Astola: Multilayer neural network based on multi-valued neurons (MLMVN) applied to classification of microarray gene expression data. In: Proc. 4th TICSP Workshop on Computational Systems Biology (WCSB 2006), Tampere University of Technology, Finland, June, 2006, pp.27–30.

    Google Scholar 

  20. I. Aizenberg and J. M. Zurada: Solving Selected Classification Problems in Bioinformat-ics Using Multilayer Neural Network based on Multi-Valued Neurons (MLMVN). In: Proceedings of 13th International Conference on Artificial Neural Networks (ICANN-2007) (accepted), to appear: September 2007.

    Google Scholar 

  21. I. Aizenberg I. and C. Moraga: The Genetic Code as a Function of Multiple-Valued Logic Over the Field of Complex Numbers and its Learning using Multilayer Neural Network Based on Multi-Valued Neuron. In: Multiple-Valued Logic and Soft Computing, accepted, to appear: late 2007.

    Google Scholar 

  22. I. Aizenberg and C. Butakoff: Image Processing Using Cellular Neural Networks Based on Multi-Valued and Universal Binary Neurons. In: Journal of VLSI Signal Processing Systems for Signal, Image and Video Technology, vol.32, no.1–2, 2002, pp.169–188.

    MATH  Google Scholar 

  23. D. E. Rumelhart and J. L. McClelland: Parallel distributed processing: explorations in the microstructure of cognition. MIT Press, Cambridge, 1986.

    Google Scholar 

  24. J. M. Zurada: Introduction to Artificial Neural Systems, West Publishing Company, St. Paul, Minnesota, 1992.

    Google Scholar 

  25. J. M. Zurada: Neural Networks: Binary Monotonic and Multiple-Valued. In: Proc. of the 30th IEEE International Symposium on Multiple-Valued Logic, Portland, Oregon, May 23–25, 2000, pp.67–74

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Louisville, Louisville, Kentucky, 20208, USA

    Jacek M. Zurada

  2. Texas A&M University-Texarkana, N. Robison Rd., 5518, 2600, Texarkana, Texas, 75505, USA

    Igor Aizenberg

Authors
  1. Jacek M. Zurada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Igor Aizenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacek M. Zurada .

Editor information

Editors and Affiliations

  1. Software Engineering Department Faculty of Automatics, Computers and Electronics, University of Craiova, Bvd. Decebal, Nr. 107, Craiova, RO, 200440, Romania

    Costin Badica

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warsaw, 01-447, Poland

    Marcin Paprzycki

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zurada, J.M., Aizenberg, I. (2008). Fully Coupled and Feedforward Neural Networks with Complex-Valued Neurons. In: Badica, C., Paprzycki, M. (eds) Advances in Intelligent and Distributed Computing. Studies in Computational Intelligence, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74930-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74930-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74929-5

  • Online ISBN: 978-3-540-74930-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation