Affiliations: Division of Computer Engineering, University of Hyogo,
2167 Shosha, Himeji, 671-2201 Japan | Nanotechnology Group, National Institute of
Information and Communications Technology, 588-2 Iwaoka, Iwaoka-cho, Nishi-ku,
Kobe, 651-2492 Japan | Graduate School of Applied Informatics, University of
Hyogo, 1-3-3 Higashikawasaki-cho, Chuo-ku, Kobe, 650-0044 Japan
Note: [] Corresponding author: Nobuyuki Matsui, Division of Computer
Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo, 671-2201 Japan.
Tel./Fax: +81 792 67 4993; E-mail: matsui@eng.u-hyogo.ac.jp
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.
