Abstract
In this paper, conjugate gradient algorithms for complex-valued feedforward neural networks are proposed. Since these algorithms yielded better training results for the real-valued case, an extension to the complex-valued case is a natural option to enhance the performance of the complex backpropagation algorithm. The full deduction of the classical variants of the conjugate gradient algorithm is presented, and the resulting training methods are exemplified on synthetic and real-world applications. The experimental results show a significant improvement over the complex gradient descent algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amin, M., Savitha, R., Amin, M., Murase, K.: Complex-valued functional link network design by orthogonal least squares method for function approximation problems. In: International Joint Conference on Neural Networks (IJCNN), pp. 1489–1496. IEEE, July 2011
Arena, P., Fortuna, L., Re, R., Xibilia, M.: Multilayer perceptrons to approximate complex valued functions. Int. J. Neural Syst. 6(4), 435–446 (1995)
Beale, E.: A derivation of conjugate gradients. In: Lootsma, F.A. (ed.) Numerical Methods for Nonlinear Optimization, pp. 39–43. Academic Press, London (1972)
Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press Inc., New York (1995)
Buchholz, S., Sommer, G.: On clifford neurons and clifford multi-layer perceptrons. Neural Netw. 21(7), 925–935 (2008)
Charalambous, C.: Conjugate gradient algorithm for efficient training of artificial neural networks. IEEE Proc. G Circ. Devices Syst. 139(3), 301–310 (1992)
Dai, Y., Yuan, Y.: A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10(1), 177–182 (1999)
Gilbert, J., Nocedal, J.: Global convergence properties of conjugate gradient methods for optimization. SIAM J. Optim. 2(1), 21–42 (1992)
Goh, S., Mandic, D.: A complex-valued rtrl algorithm for recurrent neural networks. Neural Comput. 16(12), 2699–2713 (2004)
Goh, S., Mandic, D.: Nonlinear adaptive prediction of complex-valued signals by complex-valued prnn. IEEE Trans. Signal Process. 53(5), 1827–1836 (2005)
Goh, S., Mandic, D.: Stochastic gradient-adaptive complex-valued nonlinear neural adaptive filters with a gradient-adaptive step size. IEEE Trans. Neural Netw. 18(5), 1511–1516 (2007)
Hestenes, M., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl Bur. Stan. 49(6), 409–436 (1952)
Hirose, A.: Complex-Valued Neural Networks: Advances and Applications. Wiley, New York (2013)
Huang, G.B., Li, M.B., Chen, L., Siew, C.K.: Incremental extreme learning machine with fully complex hidden nodes. Neurocomputing 71(4–6), 576–583 (2008)
Johansson, E., Dowla, F., Goodman, D.: Backpropagation learning for multilayer feed-forward neural networks using the conjugate gradient method. Int. J. Neural Syst. 2(4), 291–301 (1991)
Luenberger, D., Ye, Y.: Linear and Nonlinear Programming. International Series in Operations Research & Management Science, vol. 116. Springer, US (2008)
Narendra, K., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1(1), 4–27 (1990)
Polak, E., Ribiere, G.: Note sur la convergence de méthodes de directions conjuguées. Rev. Fr. d’Informatique et de Rech. Opérationnelle 3(16), 35–43 (1969)
Powell, M.: Restart procedures for the conjugate gradient method. Math. Program. 12(1), 241–254 (1977)
Reeves, C., Fletcher, R.: Function minimization by conjugate gradients. Comput. J. 7(2), 149–154 (1964)
Savitha, R., Suresh, S., Sundararajan, N.: A fully complex-valued radial basis function network and its learning algorithm. Int. J. Neural Syst. 19(4), 253–267 (2009)
Savitha, R., Suresh, S., Sundararajan, N.: A self-regulated learning in fully complex-valued radial basis function networks. In: International Joint Conference on Neural Networks (IJCNN), pp. 1–8. IEEE, July 2010
Savitha, R., Suresh, S., Sundararajan, N.: A meta-cognitive learning algorithm for a fully complex-valued relaxation network. Neural Netw. 32, 209–218 (2012)
Widrow, B., McCool, J., Ball, M.: The complex lms algorithm. Proc. IEEE 63(4), 719–720 (1975)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Popa, CA. (2015). Conjugate Gradient Algorithms for Complex-Valued Neural Networks. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9490. Springer, Cham. https://doi.org/10.1007/978-3-319-26535-3_47
Download citation
DOI: https://doi.org/10.1007/978-3-319-26535-3_47
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26534-6
Online ISBN: 978-3-319-26535-3
eBook Packages: Computer ScienceComputer Science (R0)