A complex-valued functional brain connectivity descriptor amenable to Riemannian geometry.
Sign Up to like & getrecommendations! Published in 2020 at "Journal of neural engineering"
DOI: 10.1088/1741-2552/ab8130
Abstract: OBJECTIVE We introduce a novel, phase-based, functional connectivity descriptor that encapsulates not only the synchronization strength between distinct brain regions, but also the time-lag between the involved neural oscillations. The new estimator employs complex-valued measurements… read more here.
Keywords: descriptor; connectivity descriptor; riemannian geometry; geometry ... See more keywords
Revisiting Riemannian geometry-based EEG decoding through approximate joint diagonalization
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Neural Engineering"
DOI: 10.1088/1741-2552/aca4fc
Abstract: Objective. The wider adoption of Riemannian geometry in electroencephalography (EEG) processing is hindered by two factors: (a) it involves the manipulation of complex mathematical formulations and, (b) it leads to computationally demanding tasks. The main… read more here.
Keywords: approximate joint; joint diagonalization; revisiting riemannian; geometry ... See more keywords
Predicting cognitive load with EEG using Riemannian geometry-based features
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Neural Engineering"
DOI: 10.1088/1741-2552/ad680b
Abstract: Objective. We show that electroencephalography (EEG)-based cognitive load (CL) prediction using Riemannian geometry features outperforms existing models. The performance is estimated using Riemannian Procrustes Analysis (RPA) with a test set of subjects unseen during training.… read more here.
Keywords: cognitive load; riemannian geometry; performance; using riemannian ... See more keywords
Multiclass Classification Framework of Motor Imagery EEG by Riemannian Geometry Networks
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Journal of Biomedical and Health Informatics"
DOI: 10.1109/jbhi.2024.3496757
Abstract: In motor imagery (MI) tasks for brain computer interfaces (BCIs), the spatial covariance matrix (SCM) of electroencephalogram (EEG) signals plays a critical role in accurate classification. Given that SCMs are symmetric positive definite (SPD), Riemannian… read more here.
Keywords: classification; riemannian geometry; motor imagery; multiclass classification ... See more keywords
Riemannian geometry-based metrics to measure and reinforce user performance changes during brain-computer interface user training
Sign Up to like & getrecommendations! Published in 2023 at "Frontiers in Computational Neuroscience"
DOI: 10.3389/fncom.2023.1108889
Abstract: Despite growing interest and research into brain-computer interfaces (BCI), their usage remains limited outside of research laboratories. One reason for this is BCI inefficiency, the phenomenon where a significant number of potential users are unable… read more here.
Keywords: user training; user performance; geometry; riemannian geometry ... See more keywords
Transfer Learning Algorithm of P300-EEG Signal Based on XDAWN Spatial Filter and Riemannian Geometry Classifier
Sign Up to like & getrecommendations! Published in 2020 at "Applied Sciences"
DOI: 10.3390/app10051804
Abstract: The electroencephalogram (EEG) signal in the brain–computer interface (BCI) has suffered great cross-subject variability. The BCI system needs to be retrained before each time it is used, which is a waste of resources and time.… read more here.
Keywords: transfer learning; riemannian geometry; spatial filter; geometry ... See more keywords
C-R Immersions and Sub-Riemannian Geometry
Sign Up to like & getrecommendations! Published in 2023 at "Axioms"
DOI: 10.3390/axioms12040329
Abstract: On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form θ, we consider natural ϵ-contractions, i.e., contractions gϵM of the Levi form Gθ, such that the norm… read more here.
Keywords: immersion; geometry; sub riemannian; riemannian geometry ... See more keywords
Decoding Multi-Class Motor Imagery and Motor Execution Tasks Using Riemannian Geometry Algorithms on Large EEG Datasets
Sign Up to like & getrecommendations! Published in 2023 at "Sensors"
DOI: 10.3390/s23115051
Abstract: The use of Riemannian geometry decoding algorithms in classifying electroencephalography-based motor-imagery brain–computer interfaces (BCIs) trials is relatively new and promises to outperform the current state-of-the-art methods by overcoming the noise and nonstationarity of electroencephalography signals.… read more here.
Keywords: geometry; riemannian geometry; motor; motor execution ... See more keywords
Some properties of Riemannian geometry of the tangent bundle of Lie groups
Sign Up to like & getrecommendations! Published in 2019 at "Turkish Journal of Mathematics"
DOI: 10.3906/mat-1812-94
Abstract: We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton,… read more here.
Keywords: geometry tangent; properties riemannian; lie; tangent bundle ... See more keywords
Recent advances in metallic Riemannian geometry: a comprehensive review
Sign Up to like & getrecommendations! Published in 2024 at "Tamkang Journal of Mathematics"
DOI: 10.5556/j.tkjm.56.2025.5405
Abstract: Metallic structures, introduced by V. de Spinadel in 2002, opened a new avenue in differential geometry. Building upon this concept, C. E. Hretcanu and M. Crasmareanu laid the foundation for metallic Riemannian manifolds in 2013.… read more here.
Keywords: riemannian geometry; metallic riemannian; geometry comprehensive; recent advances ... See more keywords