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 …

Quaternion neural networks: State-of-the-art and research challenges

D García-Retuerta, R Casado-Vara… - … on Intelligent Data …, 2020 - Springer
Abstract Machine Learning has recently emerged as a new paradigm for processing all
types of information. In particular, Artificial Intelligence is attractive to corporations & …

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 …

Stability analysis of quaternion-valued neural networks: decomposition and direct approaches

Y Liu, D Zhang, J Lou, J Lu… - IEEE Transactions on …, 2017 - ieeexplore.ieee.org
In this paper, we investigate the global stability of quaternion-valued neural networks
(QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of …

Constrained quaternion-variable convex optimization: A quaternion-valued recurrent neural network approach

Y Liu, Y Zheng, J Lu, J Cao… - IEEE transactions on …, 2019 - ieeexplore.ieee.org
This paper proposes a quaternion-valued one-layer recurrent neural network approach to
resolve constrained convex function optimization problems with quaternion variables …

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 …

Quaternion convolutional neural networks for end-to-end automatic speech recognition

T Parcollet, Y Zhang, M Morchid, C Trabelsi… - arxiv preprint arxiv …, 2018 - arxiv.org
Recently, the connectionist temporal classification (CTC) model coupled with recurrent
(RNN) or convolutional neural networks (CNN), made it easier to train speech recognition …

Event-triggered quantized quasisynchronization of uncertain quaternion-valued chaotic neural networks with time-varying delay for image encryption

L Liu, M Lei, H Bao - IEEE Transactions on Cybernetics, 2022 - ieeexplore.ieee.org
In this article, a class of quaternion-valued master–slave neural networks (NNs) with time-
varying delay and parameter uncertainties was first established by conducting the extension …