A broad class of discrete-time hypercomplex-valued Hopfield neural networks

Autor(es)

de Castro, Fidelis Zanetti ^[1] ; Valle, Marcos Eduardo ^[2]

Afiliação do(s) autor(es)

^[1] Fed Inst Educ Sci & Technol Espirito Santo Serra, Rodovia ES-010, Km 6, 5, BR-29173087 Serra, ES - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NEURAL NETWORKS; v. 122, p. 54-67, FEB 2020.
• Citações Web of Science: 1

Resumo

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called B-projection functions. Broadly speaking, a B-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras. (c) 2019 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 19/02278-2 - Morfologia Matemática e Redes Neurais Morfológicas para Dados Multi-valorados
• Beneficiário: Marcos Eduardo Ribeiro Do Valle Mesquita
• Modalidade de apoio: Auxílio à Pesquisa - Regular