Nature of complex number and complex-valued neural networks

作     者：Akira HIROSE 

作者机构：Department of Electrical Engineering and Information SystemsThe University of Tokyo7-3-1 HongoBunkyo-kuTokyo 113-8656Japan 

出 版 物：《Frontiers of Electrical and Electronic Engineering in China》 (中国电气与电子工程前沿（英文版）)

年 卷 期：2011年第6卷第1期

页      面：171-180页

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：supported by the Assistance Grant of the Hoso Bunka Foundation 

主　　题：electromagnetic wave lightwave coherence adaptive processing in sensing and imaging learning logic neural hardware 

摘      要：We discuss the nature of complex number and its effect on complex-valued neural networks(CVNNs).After we review some examples of CVNN applications,we look back at the mathematical history to elucidate the features of complex number,in particular to confirm the importance of the phaseand-amplitude viewpoint for designing and constructing CVNNs to enhance the *** viewpoint is essential in general to deal with waves such as electromagnetic wave and ***,we point out that,although we represent a complex number as an ordered pair of real numbers for example,we can reduce ineffective degree of freedom in learning or self-organization in CVNNs to achieve better generalization *** merit is significantly useful not only for waverelated signal processing but also for general processing with frequency-domain treatment through Fourier transform.