A survey on quaternion algebra and geometric algebra applications in engineering and computer science 1995–2020

E Bayro-Corrochano - IEEE Access, 2021 - ieeexplore.ieee.org
Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics,
computer science, and engineering. This review presents a comprehensive study of works …

A survey of quaternion neural networks

T Parcollet, M Morchid, G Linares - Artificial Intelligence Review, 2020 - Springer
Quaternion neural networks have recently received an increasing interest due to noticeable
improvements over real-valued neural networks on real world tasks such as image, speech …

Perspective: Machine learning in experimental solid mechanics

NR Brodnik, C Muir, N Tulshibagwale, J Rossin… - Journal of the …, 2023 - Elsevier
Experimental solid mechanics is at a pivotal point where machine learning (ML) approaches
are rapidly proliferating into the discovery process due to significant advances in data …

Quaternion recurrent neural networks

T Parcollet, M Ravanelli, M Morchid, G Linarès… - arXiv preprint arXiv …, 2018 - arxiv.org
Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due
to their capability to learn short and long-term dependencies between the basic elements of …

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

G Rajchakit, R Sriraman, N Boonsatit… - Advances in difference …, 2021 - Springer
In this study, we investigate the global exponential stability of Clifford-valued neural network
(NN) models with impulsive effects and time-varying delays. By taking impulsive effects into …

Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays

Y Liu, D Zhang, J Lu, J Cao - Information Sciences, 2016 - Elsevier
In this paper, we first propose quaternion-valued neural networks (QVNNs) with unbounded
time-varying delays. Some sufficient conditions on the global μ-stability in the form of both …

New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality

J Xiao, S Wen, X Yang, S Zhong - Neural Networks, 2020 - Elsevier
In this paper, a novel kind of neural networks named fractional-order quaternion-valued
bidirectional associative memory neural networks (FQVBAMNNs) is formulated. On one …

Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties

X Chen, Z Li, Q Song, J Hu, Y Tan - Neural Networks, 2017 - Elsevier
This paper addresses the problem of robust stability for quaternion-valued neural networks
(QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on …

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons

X Yang, C Li, Q Song, J Chen, J Huang - Neural Networks, 2018 - Elsevier
This paper talks about the stability and synchronization problems of fractional-order
quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of …

Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays

Y Liu, D Zhang, J Lu - Nonlinear Dynamics, 2017 - Springer
In this paper, we employ a novel method for solving the problem of the global exponential
stability of quaternion-valued recurrent neural networks (QVNNs) with time-varying delays …