Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI

Zhen Peng, Hongyi Li, Di Zhao () and Chengwei Pan ()
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Zhen Peng: School of Mathematical Science, Beihang University, Beijing 100191, China
Hongyi Li: School of Mathematical Science, Beihang University, Beijing 100191, China
Di Zhao: School of Mathematical Science, Beihang University, Beijing 100191, China
Chengwei Pan: Institute of Artificial Intelligence, Beihang University, Beijing 100191, China

Mathematics, 2023, vol. 11, issue 7, 1-18

Abstract: In brain–computer interface (BCI)-based motor imagery, the symmetric positive definite (SPD) covariance matrices of electroencephalogram (EEG) signals with discriminative information features lie on a Riemannian manifold, which is currently attracting increasing attention. Under a Riemannian manifold perspective, we propose a non-linear dimensionality reduction algorithm based on neural networks to construct a more discriminative low-dimensional SPD manifold. To this end, we design a novel non-linear shrinkage layer to modify the extreme eigenvalues of the SPD matrix properly, then combine the traditional bilinear mapping to non-linearly reduce the dimensionality of SPD matrices from manifold to manifold. Further, we build the SPD manifold network on a Siamese architecture which can learn the similarity metric from the data. Subsequently, the effective signal classification method named minimum distance to Riemannian mean (MDRM) can be implemented directly on the low-dimensional manifold. Finally, a regularization layer is proposed to perform subject-to-subject transfer by exploiting the geometric relationships of multi-subject. Numerical experiments for synthetic data and EEG signal datasets indicate the effectiveness of the proposed manifold network.

Keywords: brain–computer interface; Riemannian geometry; SPD manifolds; non-linear dimensionality reduction; neural networks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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