Quaternion neural network with geometrical operators

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.