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Neural Computation

February 2021, Vol. 33, No. 2, Pages 552-562
(doi: 10.1162/neco_a_01350)
© 2021 Massachusetts Institute of Technology
Stability Conditions of Bicomplex-Valued Hopfield Neural Networks
Article PDF (489.28 KB)
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.