Quaternion neural network with geometrical operators

Authors:
Nobuyuki Matsui;Teijiro Isokawa;Hiromi Kusamichi;Ferdinand Peper;Haruhiko Nishimura
Affiliations:
(Correspd. Tel./Fax: +81 792 67 4993/ E-mail: matsui@eng.u-hyogo.ac.jp) Division of Computer Engineering, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan;Division of Computer Engineering, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan;Division of Computer Engineering, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan;Division of Computer Engineering, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan and Nanotechnology Group, National Institute of Information and Communications Technology, 588-2 Iwaoka, ...;Graduate School of Applied Informatics, University of Hyogo, 1-3-3 Higashikawasaki-cho, Chuo-ku, Kobe, 650-0044 Japan
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Engineering applications of Computational Intelligence
Year:
2004

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Abstract

Quaternion neural networks are models in which computations of the neurons are based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in three-dimensional space, as well as in color space for an image compression problem, whereas real-valued BP algorithms fail. The quaternion neural network also performs superior in terms of convergence speed to a real-valued neural network with respect to the 3-bit parity check problem, as simulations show.