title: Models of Hopfield-type quaternion neural networks and their energy functions.
abstract: Recently models of neural networks that can directly deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. Furthermore models of neural networks that can deal with quaternion numbers, which is the extension of complex numbers, have also been proposed. However they are all multilayer quaternion neural networks. This paper proposes models of fully connected recurrent quaternion neural networks, Hopfield-type quaternion neural networks. Since quaternion numbers are non-commutative on multiplication, some different models can be considered. We investigate dynamics of these proposed models from the point of view of the existence of an energy function and derive their conditions for existence.
authors.affiliation: Department of Electronics and Information Science, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan. yoshid7m@ics.dj.kit.ac.jp
authors.forename: Mitsuo
authors.initials: M
authors.lastname: Yoshida
authors.forename: Yasuaki
authors.initials: Y
authors.lastname: Kuroe
authors.forename: Takehiro
authors.initials: T
authors.lastname: Mori
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*