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Enhanced Gradient Descent Algorithms for Quaternion-Valued Neural Networks

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Soft Computing Applications (SOFA 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 634))

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Abstract

This paper proposes enhanced gradient descent learning algorithms for quaternion-valued feedforward neural networks. The quickprop, resilient backpropagation, delta-bar-delta, and SuperSAB algorithms are the most known such enhanced algorithms for the real- and complex-valued neural networks. They gave superior performances than the gradient descent algorithm, so it is natural to extend these learning methods to quaternion-valued neural networks, also. The quaternion variants of these four algorithms are presented, which are then used to learn various time series prediction applications. Experimental results show an important improvement in performance over the quaternion gradient descent.

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References

  1. Arena, P., Fortuna, L., Muscato, G., Xibilia, M.: Multilayer perceptrons to approximate quaternion valued functions. Neural Netw. 10(2), 335–342 (1997)

    Article  Google Scholar 

  2. Arena, P., Fortuna, L., Muscato, G., Xibilia, M.: Neural Networks in Multidimensional Domains Fundamentals and New Trends in Modelling and Control. Lecture Notes in Control and Information Sciences, vol. 234. Springer, London (1998)

    Book  MATH  Google Scholar 

  3. Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Inc., New York (1995)

    MATH  Google Scholar 

  4. Buchholz, S., Le Bihan, N.: Polarized signal classification by complex and quaternionic multi-layer perceptrons. Int. J. Neural Syst. 18(2), 75–85 (2008)

    Article  Google Scholar 

  5. Che Ujang, B., Took, C., Mandic, D.: Split quaternion nonlinear adaptive filtering. Neural Netw. 23(3), 426–434 (2010)

    Article  Google Scholar 

  6. Che Ujang, B., Took, C., Mandic, D.: Quaternion-valued nonlinear adaptive filtering. IEEE Trans. Neural Netw. 22(8), 1193–1206 (2011)

    Article  Google Scholar 

  7. Fahlman, S.: An empirical study of learning speed in backpropagation networks. Technical report 1800, Carnegie Mellon University, January 1988. http://repository.cmu.edu/compsci/1800

  8. Isokawa, T., Kusakabe, T., Matsui, N., Peper, F.: Quaternion neural network and its application. In: Palade, V., Howlett, R., Jai, L. (eds.) Knowledge-Based Intelligent Information and Engineering Systems. Lecture Notes in Computer Science, vol. 2774, pp. 318–324. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Jacobs, R.: Increased rates of convergence through learning rate adaptation. Neural Netw. 1(4), 295–307 (1988)

    Article  Google Scholar 

  10. Jahanchahi, C., Took, C., Mandic, D.: On HR calculus, quaternion valued stochastic gradient, and adaptive three dimensional wind forecasting. In: International Joint Conference on Neural Networks (IJCNN), pp. 1–5. IEEE, July 2010

    Google Scholar 

  11. Kusamichi, H., Isokawa, T., Matsui, N., Ogawa, Y., Maeda, K.: A new scheme for color night vision by quaternion neural network. In: International Conference on Autonomous Robots and Agents, pp. 101–106, December 2004

    Google Scholar 

  12. Mandic, D., Chambers, J.: Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability. Wiley, New York (2001)

    Book  Google Scholar 

  13. Popa, C.A.: Enhanced gradient descent algorithms for complex-valued neural networks. In: International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 272–279. IEEE, September 2014

    Google Scholar 

  14. Riedmiller, M.: Advanced supervised learning in multi-layer perceptrons - from backpropagation to adaptive learning algorithms. Comput. Stand. Interfaces 16(3), 265–278 (1994)

    Article  Google Scholar 

  15. Riedmiller, M., Braun, H.: A direct adaptive method for faster backpropagation learning: the RPROP algorithm. In: IEEE International Conference on Neural Networks, vol. 1, pp. 586–591. IEEE, March 1993

    Google Scholar 

  16. Tollenaere, T.: Supersab: fast adaptive back propagation with good scaling properties. Neural Netw. 3(5), 561–573 (1990)

    Article  Google Scholar 

  17. Took, C., Mandic, D.: The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans. Signal Process. 57(4), 1316–1327 (2009)

    Article  MathSciNet  Google Scholar 

  18. Took, C., Mandic, D.: Quaternion-valued stochastic gradient-based adaptive IIR filtering. IEEE Trans. Signal Process. 58(7), 3895–3901 (2010)

    Article  MathSciNet  Google Scholar 

  19. Took, C., Mandic, D.: A quaternion widely linear adaptive filter. IEEE Trans. Signal Process. 58(8), 4427–4431 (2010)

    Article  MathSciNet  Google Scholar 

  20. Took, C., Mandic, D., Aihara, K.: Quaternion-valued short term forecasting of wind profile. In: International Joint Conference on Neural Networks (IJCNN), pp. 1–6. IEEE, July 2010

    Google Scholar 

  21. Took, C., Strbac, G., Aihara, K., Mandic, D.: Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters. Renew. Energy 36(6), 1754–1760 (2011)

    Article  Google Scholar 

  22. Xia, Y., Jahanchahi, C., Mandic, D.: Quaternion-valued echo state networks. IEEE Trans. Neural Netw. Learn. Syst. 26(4), 663–673 (2015)

    Article  MathSciNet  Google Scholar 

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Correspondence to Călin-Adrian Popa .

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Popa, CA. (2018). Enhanced Gradient Descent Algorithms for Quaternion-Valued Neural Networks. In: Balas, V., Jain, L., Balas, M. (eds) Soft Computing Applications. SOFA 2016. Advances in Intelligent Systems and Computing, vol 634. Springer, Cham. https://doi.org/10.1007/978-3-319-62524-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-62524-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62523-2

  • Online ISBN: 978-3-319-62524-9

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