Stability Conditions of Bicomplex-Valued Hopfield Neural Networks-Reference-Cited by-同舟云学术

Stability Conditions of Bicomplex-Valued Hopfield Neural Networks

Published:2021-02-01 Issue:2 Volume:33 Page:552-562
ISSN:0899-7667
Container-title:Neural Computation
language:en
Short-container-title:

Author:

Kobayashi Masaki¹

Affiliation:

1. Mathematical Science Center, University of Yamanashi, Kofu, Yamanashi 400-8511, Japan k-masaki@yamanashi.ac.jp

Abstract

Abstract Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a multistate neural associative memory. However, the stability conditions have been insufficient for the projection rule. In this work, the stability conditions are extended and applied to improvement of the projection rule. The computer simulations suggest improved noise tolerance.

Publisher

MIT Press - Journals

Subject

Cognitive Neuroscience,Arts and Humanities (miscellaneous)

Link

http://direct.mit.edu/neco/article-pdf/33/2/552/1896796/neco_a_01350.pdf

Reference26 articles.

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