Multivariate Time Series Anomaly Detection via Low-Rank and Sparse Decomposition

In the era of data-driven decision-making, multisensor systems acquire complex, high-dimensional streams capturing temporal dynamics, and multivariate time series anomaly detection has become significantly relevant in several application domains. Conventional methods relying on supervised and semi-supervised learning require labeled data, which might not be available in various scenarios. Conversely, noise and outliers present in real-world sensor measurements negatively impact unsupervised methods. Furthermore, several methods rely on black-box architectures, which limit their use in safety-critical applications where interpretability and explainability are often necessary. To address these challenges, we propose a novel unsupervised multivariate time series anomaly detection method that exploits low-rank and sparse (LRS) decomposition combined with spectral detection. More specifically, we use augmented Lagrange multiplier (ALM)-based optimization with eigenvalue soft thresholding for decomposition. Data points are projected onto a low-dimensional subspace, capturing the underlying data structure and enabling robust anomaly detection in noisy multisensor environments. Finally, the effectiveness of the proposed approach is presented via performance comparison to several existing methods using publicly available datasets collecting real-world sensor measurements from testbeds of water treatment systems.