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.

One way to analyze and improve the electromagnetic compatibility (EMC) of an electronic system is to sample multiple signals and then locating the electromagnetic interference (EMI) sources. First, each signal is decomposed into sub-signals using wavelet transform in which contains potential interesting EMI components. Then, the cluster algorithm is used to identify EMI sources. However, due to the inconsistency imposed by different sampling time and space, sampling signals belong to the same source may take on diverse patterns, thus deteriorating the clustering accuracy. This paper proposed a feature extraction method based on Stacked Autoencoder (SAE) in order to yield a robust signal representation. An additional robust feature based on Fréchet distance is also proposed. Experimental results demonstrate that the proposed method could significantly promote the clustering performance compared to existing methods.