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 phase-and-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.
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A part of this invited paper was presented at the International Joint Conference on Neural Networks (IJCNN), 2009, Atlanta.
Akira Hirose received his Ph.D degree in electrical engineering from the University of Tokyo, Tokyo, Japan, in 1991. In 1987, he joined the Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, as a Research Associate, where he was engaged in the research on optical communications and measurement. In 1991, he was appointed as an Instructor at the RCAST. From 1993 to 1995, on leave of absence from the University of Tokyo, he joined the Institute for Neuroinformatics, University of Bonn, Germany. Presently, he is a Professor at the Department of Electrical Engineering and Information Systems, The University of Tokyo, Japan. The main fields of his interest are neural networks and wireless electronics. He has published several books including a monograph Complex-Valued Neural Networks (Springer, 2006) and edited books including Complex-Valued Neural Networks: Theories and Applications (World Scientific, 2003). He received awards such as the 1998 Outstanding Research Award of the Research Foundation for Opto-Science and Technology, the 2000 Inamori Scholars Membership, the 2004 ICONIP Best Paper Award for Theoretical Development, and the 2006 IEEE/INNS WCCI-IJCNN Best Session Presentation Award. He serves as the Chair of the IEICE Neurocomputing Technical Group (2009–2010), a Member of the IEEE Computational Intelligence Society (CIS) Neural Networks Technical Committee (NNTC) (2010–) and Senior Member Program Committee (2010–), a Member of the Steering Committee of IEEE CIS Japan Chapter (2005–), and a Governing Board Member of Japanese Neural Networks Society (JNNS) (2005–) and Asia-Pacific Neural Network Assembly (APNNA) (2007–). He also serves as the Editor-in-Chief Elect of the IEICE Transactions on Electronics (2009–) and an Associate Editor of journals such as the IEEE Transactions on Neural Networks (2009–) and the IEEE Geoscience and Remote Sensing (GRSS) Newsletter.
Dr. Hirose is a Senior Member of the IEEE and the IEICE, and a Member of the JNNS.
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Hirose, A. Nature of complex number and complex-valued neural networks. Front. Electr. Electron. Eng. China 6, 171–180 (2011). https://doi.org/10.1007/s11460-011-0125-3
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DOI: https://doi.org/10.1007/s11460-011-0125-3