Nature of complex number and complex-valued neural networks  

作　　者：Akira HIROSE 

机构地区：[1]Department of Electrical Engineering and Information Systems,The University of Tokyo,7-3-1 Hongo,Bunkyo-ku,Tokyo 113-8656,Japan

出　　处：《Frontiers of Electrical and Electronic Engineering in China》2011年第1期171-180,共10页中国电气与电子工程前沿（英文版）

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

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 features.This viewpoint is essential in general to deal with waves such as electromagnetic wave and lightwave.Then,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 characteristics.This merit is significantly useful not only for waverelated signal processing but also for general processing with frequency-domain treatment through Fourier transform.

关 键 词：electromagnetic wave LIGHTWAVE COHERENCE adaptive processing in sensing and imaging learning logic neural hardware 

分 类 号：O17[理学—数学]