Convergence analysis of an augmented algorithm for fully complex-valued neural networks. (September 2015)

• Record Type: Journal Article
• Authors: Xu, Dongpo; Zhang, Huisheng; Mandic, Danilo P.
• Is Part Of: Neural networks. Volume 69(2015:Sep.)
• Page Start: 44
• Page End: 50
• Publication Date: 2015-09
• Subjects: Complex-valued neural networks -- Augmented algorithm -- Unified mean value theorem -- Wirtinger calculus -- Convergence; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2015.05.003
• Languages: English
• ISSNs: 0893-6080

Abstract

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.