Multivariate time series problems widely exist in production and life in the society. Anomaly detection has provided people with a lot of valuable information in financial, hydrological, meteorological fields, and the research areas of earthquake, video surveillance, medicine and others. In order to quickly and efficiently find exceptions in time sequence so that it can be presented in front of people in an intuitive way, we in this study combined the Riemannian manifold with statistical process control charts, based on sliding window, with a description of the covariance matrix as the time sequence, to achieve the multivariate time series of anomaly detection and its visualization. We made MA analog data flow and abnormal electrocardiogram data from MIT-BIH as experimental objects, and verified the anomaly detection method. The results showed that the method was reasonable and effective.
In order to solve the problem that the early onset of paroxysmal atrial fibrillation is very short and difficult to detect, a detection algorithm based on sparse coding of Riemannian manifolds is proposed. The proposed method takes into account that the nonlinear manifold geometry is closer to the real feature space structure, and the computational covariance matrix is used to characterize the heart rate variability (RR interval variation), so that the data is in the Riemannian manifold space. Sparse coding is applied to the manifold, and each covariance matrix is represented as a sparse linear combination of Riemann dictionary atoms. The sparse reconstruction loss is defined by the affine invariant Riemannian metric, and the Riemann dictionary is learned by iterative method. Compared with the existing methods, this method used shorter heart rate variability signal, the calculation was simple and had no dependence on the parameters, and the better prediction accuracy was obtained. The final classification on MIT-BIH AF database resulted in a sensitivity of 99.34%, a specificity of 95.41% and an accuracy of 97.45%. At the same time, a specificity of 95.18% was realized in MIT-BIH NSR database. The high precision paroxysmal atrial fibrillation detection algorithm proposed in this paper has a potential application prospect in the long-term monitoring of wearable devices.
To accurately capture and address the multi-dimensional feature variations in cross-subject motor imagery electroencephalogram (MI-EEG), this paper proposes a time-frequency transform and Riemannian manifold based domain adaptation network (TFRMDANet) in a high-dimensional brain source space. Source imaging technology was employed to reconstruct neural electrical activity and compute regional cortical dipoles, and the multi-subband time-frequency feature data were constructed via wavelet transform. The two-stage multi-branch time–frequency–spatial feature extractor with squeeze-and-excitation (SE) modules was designed to extract local features and cross-scale global features from each subband, and the channel attention and multi-scale feature fusion were introduced simultaneously for feature enhancement. A Riemannian manifold embedding-based structural feature extractor was used to capture high-order discriminative features, while adversarial training promoted domain-invariant feature learning. Experiments on public BCI Competition IV dataset 2a and High-Gamma dataset showed that TFRMDANet achieved classification accuracies of 77.82% and 90.47%, with Kappa values of 0.704 and 0.826, and F1-scores of 0.780 and 0.905, respectively. The results demonstrate that cortical dipoles provide accurate time–frequency representations of MI features, and the unique multi-branch architecture along with its strong time–frequency–spatial–structural feature extraction capability enables effective domain adaptation enhancement in brain source space.