Three-Dimensional Quaternionic Hopfield Neural Networks


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A    No.7    pp.1575-1577
Publication Date: 2017/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.1575
Type of Manuscript: LETTER
Category: Nonlinear Problems
Hopfield neural network,  quaternion,  three-dimension,  rotation,  

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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.