Abstract
This paper presents a limited-memory BFGS (L-BFGS) based learning algorithm for complex-valued neural networks (CVNNs) with phase-amplitude-type activation functions, which can be applied to deal with coherent signals effectively. The performance of the proposed L-BFGS algorithm is compared with traditional complex-valued stochastic gradient descent method on the tasks of wave-related signal processing with various degrees of coherence. The experimental results demonstrate that both faster convergence speed and smaller training errors are achieved by our algorithm. Furthermore, the phase outputs of the CVNNs trained by this algorithm are more stable when white Gaussian noises are added to the input signals.
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References
Nitta, T.: Local minima in hierarchical structures of complex-valued neural networks. Neural Netw. 43, 1–7 (2013)
Mandic, D., Goh, V.S.L.: Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. Wiley, New York (2009)
Ding, T., Hirose, A.: Fading channel prediction based on combination of complex-valued neural networks and chirp Z-transform. IEEE Trans. Neural Netw. Learn. Syst. 25, 1686–1695 (2014)
Sivachitra, M., Vijayachitra, S.: A metacognitive fully complex valued functional link network for solving real valued classification problems. Appl. Soft. Comput. 33, 328–336 (2015)
Baruch, I.S., Quintana, V.A., Reynaud, E.P.: Complex-valued neural network topology and learning applied for identification and control of nonlinear systems. Neurocomputing 233, 104–115 (2017)
Hara, T., Hirose, A.: Plastic mine detecting radar system using complex-valued self-organizing map that deals with multiple-frequency interferometric images. Neural Netw. 17, 1201–1210 (2004)
Al-Nuaimi, A.Y.H., Amin, M.F., Murase, K.: Enhancing MP3 encoding by utilizing a predictive complex-valued neural network. In: 25th International Joint Conference on Neural Networks, pp. 1–6. IEEE, Brisbane (2012)
Georgiou, G.M., Koutsougeras, C.: Complex domain backpropagation. IEEE Trans. Circ. Syst. II. 39, 330–334 (1992)
Hirose, A., Yoshida, S.: Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence. IEEE Trans. Neural Netw. Learn. Syst. 23, 541–551 (2012)
Hirose, A., Yoshida, S.: Relationship between phase and amplitude generalization errors in complex- and real-valued feedforward neural network. Neural Comput. Appl. 22, 1357–1366 (2013)
Huang, T., Li, C., Yu, W.: Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback. Nonlinearity 22, 569–584 (2009)
Zhang, H., Xu, D., Zhang, Y.: Boundedness and convergence of split-complex back-propagation algorithm with momentum and penalty. Neural Process. Lett. 39, 297–307 (2014)
Amin, M.F., Murase, K.: Single-layered complex-valued neural network for real-valued classification problems. Neurocomputing 72, 945–955 (2009)
Huang, T., Li, C., Duan, S.: Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans. Neural Netw. Learn. Syst. 23, 866–875 (2012)
Popa, C.A.: Quasi-newton learning methods for complex-valued neural networks. In: 28th International Joint Conference on Neural Networks, pp. 1-8. IEEE, Killarney (2015)
Ren, Y.Y., Xu, Y.X., Bao, J.: The study of learning algorithm the BP neural network based on extended BFGS method. In: 2010 International Conference on Computer. Mechatronics, Control and Electronic Engineering, pp. 208–211. IEEE, ChangChun (2010)
Byrd, R.H., Nocedal, J., Schnabel, R.B.: Representations of quasi-newton matrices and their use in limited memory mehods. Math. Program. 63, 129–156 (1994)
Hirose, A., Eckmiller, R.: Behavior control of coherent-type neural networks by carrier-frequency modulation. IEEE Trans. Neural Netw. 7, 1032–1034 (1996)
Hirose, A.: Complex-Valued Neural Networks. Springer, Berlin Heidelberg (2006)
Zhang, L., Zhou, W., Li, D.: Global convergence of a modified fletcher-reeves conjugate gradient method with armijo-type line search. Num. Math. 104, 561–572 (2006)
Fletcher, R.: Practical Methods of Optimization. Wiley, NewYork (1980)
Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China under Grant nos. 61273122 and 61005047, and the Qing Lan Project of Jiangsu Province. This publication was made possible by NPRP grant: NPRP 8-274-2-107 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the author[s].
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Wu, R., Huang, H., Huang, T. (2017). Learning of Phase-Amplitude-Type Complex-Valued Neural Networks with Application to Signal Coherence. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, ES. (eds) Neural Information Processing. ICONIP 2017. Lecture Notes in Computer Science(), vol 10634. Springer, Cham. https://doi.org/10.1007/978-3-319-70087-8_10
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