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Dual‐numbered Hopfield neural networks
Author(s) -
Kobayashi Masaki
Publication year - 2018
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.22524
Subject(s) - hopfield network , artificial neural network , hebbian theory , types of artificial neural networks , dual (grammatical number) , computer science , recurrent neural network , physical neural network , stability (learning theory) , algebra over a field , artificial intelligence , mathematics , pure mathematics , machine learning , art , literature
In recent years, Hopfield neural networks using Clifford algebra have been studied. Clifford algebra is also referred to as geometric algebra, and is useful to deal with geometric objects. There are three kinds of Clifford algebra with degree 2; complex, hyperbolic, and dual‐numbered. Complex‐valued Hopfield neural networks have been studied by many researchers. Several models of hyperbolic Hopfield neural networks have also been proposed. It has been difficult to construct dual‐numbered Hopfield neural networks. In this work, we propose dual‐numbered Hopfield neural networks by modification of hyperbolic Hopfield neural networks with the split activation function. The stability condition and Hebbian learning rule are also provided. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.