#### 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).

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