title: Convergence analysis of an augmented algorithm for fully complex-valued neural networks.
abstract: This paper presents an augmented algorithm for fully complex-valued neural network based on Wirtinger calculus, which simplifies the derivation of the algorithm and eliminates the Schwarz symmetry restriction on the activation functions. A unified mean value theorem is first established for general functions of complex variables, covering the analytic functions, non-analytic functions and real-valued functions. Based on so introduced theorem, convergence results of the augmented algorithm are obtained under mild conditions. Simulations are provided to support the analysis.
authors.affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China; College of Science, Harbin Engineering University, Harbin 150001, China. Electronic address: dongpoxu@gmail.com.
authors.forename: Dongpo
authors.initials: D
authors.lastname: Xu
authors.affiliation: Department of Mathematics, Dalian Maritime University, Dalian 116026, China. Electronic address: zhhuisheng@163.com.
authors.forename: Huisheng
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ London, UK. Electronic address: d.mandic@imperial.ac.uk.
authors.forename: Danilo P
authors.initials: DP
authors.lastname: Mandic
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D016571:Neural Networks, Computer
keywords: Augmented algorithm; Complex-valued neural networks; Convergence; Unified mean value theorem; Wirtinger calculus