Three-Dimensional Quaternionic Hopfield Neural Networks

Abstract

Quaternionic neural networks are extensions of neural networks using quaternion algebra. 3-D and 4-D quaternionic MLPs have been studied. 3-D quaternionic neural networks are useful for handling 3-D objects, such as Euclidean transformation. As for Hopfield neural networks, only 4-D quaternionic Hopfield neural networks (QHNNs) have been studied. In this work, we propose the 3-D QHNNs. Moreover, we define the energy, and prove that it converges.