Review of Riemannian Distances and Divergences, Applied to SSVEP-based BCI

Chevallier, Sylvain; Kalunga, Emmanuel K.; Barthélemy, Quentin

doi:10.1007/s12021-020-09473-9

Cited by 45 publications

(37 citation statements)

References 51 publications

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“…On the other hand, for a given Riemannian space, a further discretionary element is given by the choice of a distance among the many available ones that can be defined on the space of covariance matrices. Each of these distances has specific properties (Arsigny et al, 2007;Yger, Berar, & Lotte, 2016), and relative task-specific performance level, some performing better in terms of classification accuracy, while others are better in terms of computational efficiency (Chevallier, Kalunga, Barthélemy, & Monacelli, 2021).…”

Section: Effects Of Edge Metrics On Network Propertiesmentioning

confidence: 99%

Principles and open questions in functional brain network reconstruction

Korhonen

Zanin

Papo

2021

Human Brain Mapping

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Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

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Section: Effects Of Edge Metrics On Network Propertiesmentioning

confidence: 99%

Principles and open questions in functional brain network reconstruction

Korhonen

Zanin

Papo

2021

Human Brain Mapping

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“…To manipulate SPD matrices while respecting their intrinsic geometry, we can rely on Riemannian geometry. There are several possible metrics [11] but the Affine Invariant Riemannian Metric (AIRM) is the most natural metric. AIRM distance δ r between two SPD matrices C 1 and C 2 on manifold is defined as:…”

Section: Riemannian Geometry Of Eeg Covariance Matrixmentioning

confidence: 99%

Subspace Oddity - Optimization on Product of Stiefel Manifolds for EEG Data

Yamamoto

Yger

Chevallier

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Dimensionality reduction of high-dimensional electroencephalography (EEG) covariance matrices is crucial for effective utilization of Riemannian geometry in Brain-Computer Interfaces (BCI). In this paper, we propose a novel similaritybased classification method that relies on dimensionality reduction of EEG covariance matrices. Conventionally, the dimension of the original high-dimensional space is reduced by projecting into one low-dimensional space, and the similarity is learned only based on the single space. In contrast, our method, MUltiple SUbspace Mdm Estimation (MUSUME), obtains multiple low-dimensional spaces that enhance class separability by solving the proposed optimization problem, then the similarity is learned in each low-dimensional space. This multiple projection approach encourages finding the space that is more useful for similarity learning. Experimental evaluation with high-dimensionality EEG datasets (128 channels) confirmed that MUSUME proved significant improvement for classification (p < 0.001) and also it showed the potential to beat the existing method relying on only one subspace representation.

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“…On the contrary, the AIRM distance is immune to those drawbacks but its computation is more computationally demanding. Hence, the LogEuclidean distance has been proposed as a trade-off between AIRM and LogEuclidean distances, retaining some interesting properties of the AIRM distance while being faster to compute [28]. Overall, the use of a Riemanning geometry (LogEuclidean or AIRM) leads to a simpler feature extraction step tampering with the need for spatial filtering and a less complex data processing pipeline.…”

Section: Riemannian Geometrymentioning

confidence: 99%

Functional connectivity ensemble method to enhance BCI performance (FUCONE)

Corsi¹,

Chevallier²,

Fallani³

et al. 2021

Preprint

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Functional connectivity is a key approach to investigate oscillatory activities of the brain that provides important insights on the underlying dynamic of neuronal interactions and that is mostly applied for brain activity analysis. Building on the advances in information geometry for brain-computer interface, we propose a novel framework that combines functional connectivity estimators and covariance-based pipelines to classify mental states, such as motor imagery. A Riemannian classifier is trained for each estimator and an ensemble classifier combines the decisions in each feature space. A thorough assessment of the functional connectivity estimators is provided and the best performing pipeline, called FUCONE, is evaluated on different conditions and datasets. Using a meta-analysis to aggregate results across datasets, FUCONE performed significantly better than all state-of-the-art methods. The performance gain is mostly imputable to the improved diversity of the feature spaces, increasing the robustness of the ensemble classifier with respect to the inter-and intrasubject variability.

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Review of Riemannian Distances and Divergences, Applied to SSVEP-based BCI

Cited by 45 publications

References 51 publications

Principles and open questions in functional brain network reconstruction

Principles and open questions in functional brain network reconstruction

Subspace Oddity - Optimization on Product of Stiefel Manifolds for EEG Data

Functional connectivity ensemble method to enhance BCI performance (FUCONE)

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