Quaternion Neural Network with Geometrical Operators

Nobuyuki Matsui, Teijiro Isokawa, Hiromi Kusamichi, Ferdinand Peper*, and Haruhiko Nishimura**
* Nanotechnology Group, National Institute of Information and Communications Technology
** Graduate School of Applied Informatics, University of Hyogo

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.

Journal of Intelligent & Fuzzy Systems, vol.15, no.3-4, pp.149-164 (2004).