title: Convergence analysis of fully complex backpropagation algorithm based on Wirtinger calculus.
abstract: This paper considers the fully complex backpropagation algorithm (FCBPA) for training the fully complex-valued neural networks. We prove both the weak convergence and strong convergence of FCBPA under mild conditions. The decreasing monotonicity of the error functions during the training process is also obtained. The derivation and analysis of the algorithm are under the framework of Wirtinger calculus, which greatly reduces the description complexity. The theoretical results are substantiated by a simulation example.
authors.affiliation: Department of Mathematics, Dalian Maritime University, Dalian, 116026 People's Republic of China ; Research Center of Information and Control, Dalian University of Technology, Dalian, 116024 People's Republic of China.
authors.forename: Huisheng
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Research Center of Information and Control, Dalian University of Technology, Dalian, 116024 People's Republic of China.
authors.forename: Xiaodong
authors.initials: X
authors.lastname: Liu
authors.affiliation: College of Science, Harbin Engineering University, Harbin, 150001 People's Republic of China.
authors.forename: Dongpo
authors.initials: D
authors.lastname: Xu
authors.affiliation: Department of Mathematics, Dalian Maritime University, Dalian, 116026 People's Republic of China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Zhang
keywords: Complex-valued neural networks; Convergence; Fully complex backpropagation algorithm; Wirtinger calculus