Nature of complex number and complex-valued neural networks

doi:10.1007/s11460-011-0125-3

Front Elect Electr Eng Chin

2011, Vol. 6

Issue (1) : 171-180 https://doi.org/10.1007/s11460-011-0125-3

RESEARCH ARTICLE

Nature of complex number and complex-valued neural networks

Akira HIROSE^1,2(

)

1. A part of this invited paper was presented at the International Joint Conference on Neural Networks (IJCNN), 2009, Atlanta.; 2. Department of Electrical Engineering and Information Systems, The University of Tokyo,7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

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Abstract

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.

Keywords electromagnetic wave lightwave coherence adaptive processing in sensing and imaging learning logic neural hardware

Corresponding Author(s): HIROSE Akira,Email:ahirose@eis.t.u-tokyo.ac.jp

Issue Date: 05 March 2011

Cite this article:

Akira HIROSE. Nature of complex number and complex-valued neural networks[J]. Front Elect Electr Eng Chin, 2011, 6(1): 171-180.

URL:

https://academic.hep.com.cn/fee/EN/10.1007/s11460-011-0125-3
https://academic.hep.com.cn/fee/EN/Y2011/V6/I1/171

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