Singular spectrum analysis (SSA) is a nonparametric spectral estimation method that decomposes time series signals into interpretable components. With the rise of big time series, the demand for effective and scalable SSA techniques has become increasingly urgent. In this paper, we propose a novel multiway extension of SSA, called higher-order multivariate SSA (HO-MSSA), specifically designed for multivariate and multichannel time series signal analysis via tensor decomposition. HO-MSSA utilizes time-delay embedding and tensor singular value decomposition to transform multichannel time series signals into trajectory tensors, which are then decomposed into elementary components in the Fourier domain, rather than the time domain as in traditional SSA methods. These components are grouped into disjoint subsets using spectral clustering, enabling the reconstruction of the underlying source signals. Experimental results demonstrate that HO-MSSA outperforms state-of-the-art SSA methods in various biomedical applications, including electromyography (EMG), electrocardiography (ECG), and electroencephalogram (EEG) signals. • A novel tensor-based multivariate singular spectrum analysis is introduced. • A new time embedding technique embeds time series into a higher dimension. • Tensor SVD is used to factorize the trajectory tensor of time series. • Spectral clustering detects and groups the underlying time series components.

This paper introduces TenSOFO, a novel tensor-based method specifically designed for blind source separation (BSS). Ten-SOFO presents a new efficient alternating direction method of multipliers framework, allowing for simultaneous decomposition of two symmetric third-order tensors under the individual differences in scaling (INDSCAL) format. By establishing a fundamental link between joint INDSCAL decomposition and BSS using second and fourth order statistics, TenSOFO proves to be effective for BSS. The performance of TenSOFO is evaluated in both joint INDSCAL decomposition and BSS tasks, showcasing its remarkable accuracy and potential applications.

In this paper, we investigate the problem of convolutive blind source separation (BSS) via tensor decomposition. A fundamental link between convolutive BSS and block-term decomposition (BTD) is established, forming the basis for our novel tensor-based convolutive BSS method, namely TCBSS. Specifically, the proposed method offers a new effective approach for factorizing tensors under the BTD format where the loading factors are constrained to be identical. By leveraging second-order statistics of data observations, we construct a third-order tensor by stacking covariance matrices at different time lags, and then, apply TCBSS to identify the mixing process. Experimental results demonstrate the robust performance of TCBSS in addressing both BTD and convolutive BSS tasks, particularly when dealing with electromyography (EMG) signal decomposition.

International audience

We propose to apply the Gaussian Mixture Model (GMM) to surface electromyography (sEMG) signals in order to detect the muscular activation (MA) onset, timing off and intervals. First, classical time and frequency features are extracted from the sEMG signals, beside the Teager-Kaiser energy operator (TKEO) is evaluated and added as a new feature which enhances the detection performance. All the obtained features are then used as the input for the GMM to conduct the binary clustering. Finally, a decision theory is applied in order to declare sEMG activation timing of human skeletal museles during movement. Accuracy and precision of the algorithm are assessed by using a set of synthetic simulated sEMG signals and real ones. A comparison with two previously published techniques is conducted: wavelet transform-based method and double threshold-based method. Our experimental results prove that the proposed GMM-based algorithm is able to accurately reveal the MA timing with performance beyond that of the state-of-the-art methods. Moreover, this proposed algorithm is automatic and user-independent.