Introducing quaternion multi-valued neural networks with numerical examples

This paper introduces a new quaternion multi-valued neural network architecture and demonstrates its potential with numerical examples of multi-channel prediction and classification. A variety of real-valued learning structures have been introduced in prior literature; an important example is the multilayer perceptron neural network, which forms the underlying basis for modern deep learning architectures. However, in multidimensional information processing problems, real-valued learning structures perform suboptimally due to distortion of inter-channel relationships. A natural way to represent multidimensional data is using quaternions, a four-dimensional associative normed division algebra over the real numbers that allows for the multiplication and division of points in three-dimensional space. This paper introduces quaternion multi-valued neural networks, which perform nonlinear operations on the three-dimensional phase of quaternion data points. As shown with two numerical examples, the proposed quaternion multi-valued neural network outperforms existing learning structures, particularly in cases where limited training data is available.