Low-rank on Graphs plus Temporally Smooth Sparse Decomposition for Anomaly Detection in Spatiotemporal Data
This work addresses the problem of detecting anomalies in spatiotemporal data for applications like traffic monitoring, but it is incremental as it builds on existing tensor-based methods with added temporal constraints.
The authors tackled anomaly detection in spatiotemporal data by proposing an unsupervised tensor-based method that formulates the problem as a robust low-rank plus sparse decomposition with temporal smoothness regularization, and they evaluated it on synthetic and real urban traffic data, showing improved performance over baselines.
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited for point anomalies in sequence data and cannot deal with temporal and spatial dependencies that arise in spatiotemporal data. In recent years, tensor-based methods have been proposed for anomaly detection to address this problem. These methods rely on conventional tensor decomposition models, not taking the structure of the anomalies into account, and are supervised or semi-supervised. We introduce an unsupervised tensor-based anomaly detection method that takes the sparse and temporally continuous nature of anomalies into account. In particular, the anomaly detection problem is formulated as a robust lowrank + sparse tensor decomposition with a regularization term that minimizes the temporal variation of the sparse part, so that the extracted anomalies are temporally persistent. We also approximate rank minimization with graph total variation minimization to reduce the complexity of the optimization algorithm. The resulting optimization problem is convex, scalable, and is shown to be robust against missing data and noise. The proposed framework is evaluated on both synthetic and real spatiotemporal urban traffic data and compared with baseline methods.