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2018 | OriginalPaper | Buchkapitel

An Efficient Elman Neural Networks Based on Improved Conjugate Gradient Method with Generalized Armijo Search

verfasst von : Mingyue Zhu, Tao Gao, Bingjie Zhang, Qingying Sun, Jian Wang

Erschienen in: Intelligent Computing Theories and Application

Verlag: Springer International Publishing

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Abstract

Elman neural network is a typical class of recurrent network model. Gradient descent method is the popular strategy to train Elman neural networks. However, the gradient descent method is inefficient owing to its linear convergence property. Based on the Generalized Armijo search technique, we propose a novel conjugate gradient method which speeds up the convergence rate in training Elman networks in this paper. A conjugate gradient coefficient is proposed in the algorithm, which constructs conjugate gradient direction with sufficient descent property. Numerical results demonstrate that this method is more stable and efficient than the existing training methods. In addition, simulation shows that, the error function has a monotonically decreasing property and the gradient norm of the corresponding function tends to zero.

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Literatur
1.
Zurück zum Zitat Ooi, S.Y., Tan, S.C., Cheah, W.P.: Experimental Study of Elman Network in Temporal Classification. Springer, Singapore (2017)CrossRef Ooi, S.Y., Tan, S.C., Cheah, W.P.: Experimental Study of Elman Network in Temporal Classification. Springer, Singapore (2017)CrossRef
2.
Zurück zum Zitat Elman, J.L.: Finding structure in time. Cogn. Sci. 14(2), 179–211 (1990)CrossRef Elman, J.L.: Finding structure in time. Cogn. Sci. 14(2), 179–211 (1990)CrossRef
3.
Zurück zum Zitat Ahalt, S.C., Liu, X.M., Wang, D.L.: On temporal generalization of simple recurrent networks. Neural Netw. Official J. Int. Neural Network Soc. 9(7), 1099–1118 (1996)CrossRef Ahalt, S.C., Liu, X.M., Wang, D.L.: On temporal generalization of simple recurrent networks. Neural Netw. Official J. Int. Neural Network Soc. 9(7), 1099–1118 (1996)CrossRef
4.
Zurück zum Zitat Williams, R.J., Zisper, D.: A Learning Algorithm for Continually Running Fully Recurrent Neural Networks. MIT Press 1(2), 270–280 (1989) Williams, R.J., Zisper, D.: A Learning Algorithm for Continually Running Fully Recurrent Neural Networks. MIT Press 1(2), 270–280 (1989)
5.
Zurück zum Zitat Wu, W., Xu, D.P., Li, Z.X.: Convergence of gradient method for Elman networks. Appl. Math. Mech. 29(9), 1231–1238 (2008)MathSciNetCrossRef Wu, W., Xu, D.P., Li, Z.X.: Convergence of gradient method for Elman networks. Appl. Math. Mech. 29(9), 1231–1238 (2008)MathSciNetCrossRef
6.
Zurück zum Zitat Xu, D.P., Li, Z.X., Wu, W.: Convergence of approximated gradient method for Elman network. Neural Network World 18(3), 171–180 (2008) Xu, D.P., Li, Z.X., Wu, W.: Convergence of approximated gradient method for Elman network. Neural Network World 18(3), 171–180 (2008)
7.
Zurück zum Zitat Güntürkün, R.: Using elman recurrent neural networks with conjugate gradient algorithm in determining the anesthetic the amount of anesthetic medicine to be applied. J. Med. Syst. 34(4), 479–484 (2010)CrossRef Güntürkün, R.: Using elman recurrent neural networks with conjugate gradient algorithm in determining the anesthetic the amount of anesthetic medicine to be applied. J. Med. Syst. 34(4), 479–484 (2010)CrossRef
8.
Zurück zum Zitat Wang, J., Wu, W., Zurada, J.M.: Deterministic convergence of conjugate gradient method for feedforward neural networks. Neurocomputing 74(14), 2368–2376 (2011)CrossRef Wang, J., Wu, W., Zurada, J.M.: Deterministic convergence of conjugate gradient method for feedforward neural networks. Neurocomputing 74(14), 2368–2376 (2011)CrossRef
9.
Zurück zum Zitat Wang, J., Zhang, B.J., Sun, Z.Q., Hao, W.X., Sun, Q.Y.: A novel conjugate gradient method with generalized Armijo search for efficient training of feedforward neural networks. Neurocomputing 275, 308–316 (2018)CrossRef Wang, J., Zhang, B.J., Sun, Z.Q., Hao, W.X., Sun, Q.Y.: A novel conjugate gradient method with generalized Armijo search for efficient training of feedforward neural networks. Neurocomputing 275, 308–316 (2018)CrossRef
10.
Zurück zum Zitat Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)MATH Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)MATH
11.
Zurück zum Zitat Hestenes, M.R., Steifel, E.: Method of Conjugate Gradients for Solving Linear Systems. National Bureau of Standards, Washington (1952) Hestenes, M.R., Steifel, E.: Method of Conjugate Gradients for Solving Linear Systems. National Bureau of Standards, Washington (1952)
12.
13.
Zurück zum Zitat Polak, E., Ribiere, G.: Note sur la convergence de methodes de directions conjures. Revue Francaise Information Recherche Operationnelle 16(16), 35–43 (1969)MATH Polak, E., Ribiere, G.: Note sur la convergence de methodes de directions conjures. Revue Francaise Information Recherche Operationnelle 16(16), 35–43 (1969)MATH
14.
Zurück zum Zitat Rivaie, M., Fauzi, M., Mamat, M., Mohd, I.: A new class of nonlinear conjugate gradient coefficients with global convergence properties. AIP Conf. Proc. 1482, 486–491 (2012)CrossRef Rivaie, M., Fauzi, M., Mamat, M., Mohd, I.: A new class of nonlinear conjugate gradient coefficients with global convergence properties. AIP Conf. Proc. 1482, 486–491 (2012)CrossRef
15.
Zurück zum Zitat Sun, Q.Y., Liu, X.H.: Global convergence results of a new three terms conjugate gradient method with generalized Armijo step size rule. Math. Numer. Sin. 26(1), 25–36 (2004)MathSciNet Sun, Q.Y., Liu, X.H.: Global convergence results of a new three terms conjugate gradient method with generalized Armijo step size rule. Math. Numer. Sin. 26(1), 25–36 (2004)MathSciNet
16.
Zurück zum Zitat Dong, X., Yang, X., Huang, Y.: Global convergence of a new conjugate gradient method with Armijo search. J. Henan Normal Univ. 6, 25–29 (2015)MATH Dong, X., Yang, X., Huang, Y.: Global convergence of a new conjugate gradient method with Armijo search. J. Henan Normal Univ. 6, 25–29 (2015)MATH
Metadaten
Titel
An Efficient Elman Neural Networks Based on Improved Conjugate Gradient Method with Generalized Armijo Search
verfasst von
Mingyue Zhu
Tao Gao
Bingjie Zhang
Qingying Sun
Jian Wang
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-95930-6_1

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