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Dynamics of Quaternionic Hopfield Type Neural Networks

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Advances in Computational Intelligence (IWANN 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10305))

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Abstract

In this research paper, a novel ordinary quaternionic hopfield type network is proposed and the associated convergence theorem is proved. Also, a novel structured quaternionic recurrent hopfield network is proposed. It is proved that in the parallel mode of operation, such a network converges to a cycle of length 4.

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References

  1. Jankowski, S., Lazowksi, A., Zurada, J.: Complex-valued multi-state neural associative memory. IEEE Trans. Neural Netw. 7, 1491–1496 (1996)

    Article  Google Scholar 

  2. Muezzinoglu, M.K., Guzelis, 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)

    Article  Google Scholar 

  3. Isokawa, T., Hishimura, H., Saitoh, A., Kmiura, N., Matsui, N.: On the scheme of multistate quaternionic Hopfield neural network. In: Proceedings of Joint 4th International Symposium on Soft Computing Intelligent Systems and 9th International Symposium on advanced Intelligent System (SCIS and ISIS 2008), Nagoya, Japan, pp. 809–813, September 2008

    Google Scholar 

  4. Isokawa, T., Nishimura, H., Matsui, N.: Quaternionic neural networks for associative memories. In: Hirose, A. (ed.) Complex-Valued Neural Networks, pp. 103–131. Wiley-IEEE Press, Hoboken (2013)

    Chapter  Google Scholar 

  5. Valle, M.E., de Castro, F.Z.: Theoretical and computational aspects of quaternionic multivalued Hopfield neural networks. In: Proceedings of the IEEE International Joint Conference on Neural Networks 2016 (IJCNN 2016), Vancouver, Canada, July 2016

    Google Scholar 

  6. Rama Murthy, G., Praveen, D.: Complex-values neural associative memory on the complex hypercube. In: IEEE Conference on Cybernetics and Intelligent Systems, Singapore, pp. 1–3, December 2004

    Google Scholar 

  7. Rama Murthy, G., Kicanaoglu, B., Gabbouj, M.: On the dynamics of a recurrent Hopfield network. In: International Joint Conference on Neural Networks (IJCNN-2015), July 2015

    Google Scholar 

  8. Rama Murthy, G., Anil, R., Dileep, M.: Dynamics of structured complex recurrent Hopfield networks. In: Proceedings of IJCNN-2016, Vancouver, July 2016

    Google Scholar 

  9. Bruck, J., Goodman, J.W.: A generalized convergence theorem for neural networks. IEEE Trans. Inf. Theory 34(5), 1089–1092 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rama Murthy, G., Gabbouj, M.: Existence and synthesis of complex Hopfield type associative memories. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2015. LNCS, vol. 9095, pp. 356–369. Springer, Cham (2015). doi:10.1007/978-3-319-19222-2_30

    Chapter  Google Scholar 

  11. Rama Murthy, G.: Some novel real/complex valued neural network models. In: Advances in Soft Computing, Springer Series, Computational Intelligence, Theory and Applications, Proceedings of 9th Fuzzy days (2006)

    Google Scholar 

  12. Rama Murthy, G., Munugoti, S.D., Rayala, A.: Convolutional associative memory: FIR filter model of synapse. In: Arik, S., Huang, T., Lai, W.K., Liu, Q. (eds.) ICONIP 2015. LNCS, vol. 9491, pp. 356–364. Springer, Cham (2015). doi:10.1007/978-3-319-26555-1_40

    Chapter  Google Scholar 

  13. Bruck, J., Blaum, M.: Neural networks, error-correcting codes, and polynomials over the binary n-cube. IEEE Trans. Inf. Theory 35(5), 976–987 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Raju, S., Rama Murthy, G., Jha, A., Anil, R.: Dynamics of ordinary and recurrent Hopfield networks: novel themes. In: IEEE IACC-2017, January 2017

    Google Scholar 

  15. Rama Murthy, G., Gabbouj, M.: On the design of Hopfield neural networks: synthesis of Hopfield type associative memories. In: Proceedings of IEEE International Joint Conference on Neural Networks (IJCNN 2015), July 2015

    Google Scholar 

  16. Rama Murthy, G.: Optimization of quadratic forms: NP hard problems: neural networks. In: 2013 International Symposium on Computational and Business Intelligence (ISCBI 2013), New Delhi, India, 24–26 August 2013

    Google Scholar 

  17. Rama Murthy, G., Zolnierek, A., Koszalka, L.: Optimal control of time varying linear systems: neural networks. In: 2014 International Symposium on Computational and Business Intelligence (ISCBI 2014), New Delhi, India, 6–7 December 2014

    Google Scholar 

  18. Rama Murthy, G.: Distributed signal processing: neural networks. IEEE Workshop on Computational Intelligence: Theories, Applications and Future Directions, IIT-Kanpur, 14 July 2013

    Google Scholar 

  19. Rama Murthy, G., Nischal, B.: Network, Hopfield-Amari neural: minimization of quadratic forms. In: The 6th International Conference on Soft Computing and Intelligent Systems, Kobe, Japan, 20–24 November 2012

    Google Scholar 

  20. Rama Murthy, G.: Multidimensional Neural Networks Unified Theory. New Age International Publishers, New Delhi (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. International Institute of Information Technology, Hyderabad, India

    Rama Murthy Garimella & Rayala Anil

Authors
  1. Rama Murthy Garimella
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  2. Rayala Anil
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Corresponding author

Correspondence to Rama Murthy Garimella .

Editor information

Editors and Affiliations

  1. Universidad de Granada , Granada, Spain

    Ignacio Rojas

  2. University of Malaga , Malaga, Spain

    Gonzalo Joya

  3. Polytechnic University of Catalonia, Vilanova i la Geltrú, Barcelona, Spain

    Andreu Catala

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Garimella, R.M., Anil, R. (2017). Dynamics of Quaternionic Hopfield Type Neural Networks. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2017. Lecture Notes in Computer Science(), vol 10305. Springer, Cham. https://doi.org/10.1007/978-3-319-59153-7_31

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  • DOI: https://doi.org/10.1007/978-3-319-59153-7_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59152-0

  • Online ISBN: 978-3-319-59153-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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