Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI

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.

Research on Relation Classification Tasks Based on Cybersecurity Text

“…The use of natural language processing technology can help cybersecurity experts quickly and accurately process and analyze large amounts of cybersecurity data and textual information, thereby better understanding and applying cybersecurity knowledge. Therefore, scholars attempted to leverage natural language processing techniques, including named entity recognition [1], relation extraction [2], and attribute extraction [3]; as well as mathematical representation methods, including quantization [4], dimensionality reduction [5], and interpolation [6,7]; as means of identifying, analyzing, defending against, and mitigating various cybersecurity attacks.…”