A Model of Hopfield-Type Quaternion Neural Networks and Its Energy Function

  • Mitsuo Yoshida
  • Yasuaki Kuroe
  • Takehiro Mori
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3316)


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 an extension of complex numbers, have also been proposed. However they are all multilayer quaternion neural networks. This paper proposes a model of recurrent quaternion neural networks, Hopfield-type quaternion neural networks. We investigate dynamics of the proposed model from the point of view of the existence of an energy function and derive its condition.


Neural Network Equilibrium Point Activation Function Energy Function Existence Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mitsuo Yoshida
    • 1
  • Yasuaki Kuroe
    • 2
  • Takehiro Mori
    • 1
  1. 1.Department of Electronics and Information ScienceKyoto Institute of TechnologyKyotoJapan
  2. 2.Center for Information ScienceKyoto Institute of TechnologyKyotoJapan

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