A Model of Hopfield-Type Quaternion Neural Networks and Its Energy Function
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.
KeywordsNeural Network Equilibrium Point Activation Function Energy Function Existence Condition
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- 1.Kuroe, Y., Hashimoto, N.: On energy function for complex-valued Hopfield-type neural networks. In: Damiani, E., et al. (eds.) KES 2002, pp. 623–627. IOS Press, Amsterdam (2002)Google Scholar
- 2.Kuroe, Y., Yoshida, M., Mori, T.: On activation functions for complex-valued neural networks – existence of energy functions. In: Kaynak, O., et al. (eds.) ICANN/ICONIP 2003. LNCS, vol. 2714, pp. 985–992. Springer, Heidelberg (2003)Google Scholar
- 3.Nitta, T.: A quaternary version of the back-propagation algorithm. In: Proc. IEEE Int. Conf. on Neural Networks, 5th edn., Perth, Australia, pp. 2753–2756 (1995)Google Scholar