Subspace oddity - optimization on product of Stiefel manifolds for EEG data

Maria Sayu Yamamoto (1, 2, 3) , Florian Yger (4, 5) , Sylvain Chevallier (1, 2, 3)

1 LISV - Laboratoire d'Ingénierie des Systèmes de Versailles
2 UVSQ - Université de Versailles Saint-Quentin-en-Yvelines
3 Université Paris-Saclay
4 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
5 Université Paris Dauphine-PSL

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.

Mots clés: High-dimensional EEG; Riemannian manifold; optimization; dimensionality reduction; brain-computer interfaces

Domaines: Traitement du signal et de l'image [eess.SP]

Maria Sayu Yamamoto, Florian Yger, Sylvain Chevallier. Subspace oddity - optimization on product of Stiefel manifolds for EEG data. ICASSP, Jun 2021, Toronto, Canada. ⟨hal-03202357v1⟩