Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 829692, 27 pages
doi:10.1155/2010/829692
Convergence of an online split-complex gradient algorithm for complex-valued neural networks
Huisheng Zhang1
, Dongpo Xu2
and Zhiping Wang1
1Department of Mathematics, Dalian Maritime University, Dalian 116026, China
2Department of Applied Mathematics, Harbin Engineering University, Harbin 150001, China
Abstract
The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings.