Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI
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 manifol...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/7/1570 |
| _version_ | 1797607491220013056 |
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| author | Zhen Peng Hongyi Li Di Zhao Chengwei Pan |
| author_facet | Zhen Peng Hongyi Li Di Zhao Chengwei Pan |
| author_sort | Zhen Peng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T05:30:41Z |
| format | Article |
| id | doaj.art-65197cafa8fe47a0b8c5d1b6fe8739a8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:41Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-65197cafa8fe47a0b8c5d1b6fe8739a82023-11-17T17:07:31ZengMDPI AGMathematics2227-73902023-03-01117157010.3390/math11071570Reducing the Dimensionality of SPD Matrices with Neural Networks in BCIZhen Peng0Hongyi Li1Di Zhao2Chengwei Pan3School of Mathematical Science, Beihang University, Beijing 100191, ChinaSchool of Mathematical Science, Beihang University, Beijing 100191, ChinaSchool of Mathematical Science, Beihang University, Beijing 100191, ChinaInstitute of Artificial Intelligence, Beihang University, Beijing 100191, ChinaIn 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.https://www.mdpi.com/2227-7390/11/7/1570brain–computer interfaceRiemannian geometrySPD manifoldsnon-linear dimensionality reductionneural networks |
| spellingShingle | Zhen Peng Hongyi Li Di Zhao Chengwei Pan Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI Mathematics brain–computer interface Riemannian geometry SPD manifolds non-linear dimensionality reduction neural networks |
| title | Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI |
| title_full | Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI |
| title_fullStr | Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI |
| title_full_unstemmed | Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI |
| title_short | Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI |
| title_sort | reducing the dimensionality of spd matrices with neural networks in bci |
| topic | brain–computer interface Riemannian geometry SPD manifolds non-linear dimensionality reduction neural networks |
| url | https://www.mdpi.com/2227-7390/11/7/1570 |
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