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Anomaly detection in spatiotemporal data is a challenging problem encounteredin a variety of applications including hyperspectral imaging, videosurveillance, and urban traffic monitoring. Existing anomaly detection methodsare most suited for point anomalies in sequence data and cannot deal withtemporal and spatial dependencies that arise in spatiotemporal data. In recentyears, tensor-based methods have been proposed for anomaly detection to addressthis problem. These methods rely on conventional tensor decomposition models,not taking the structure of the anomalies into account, and are supervised orsemi-supervised. We introduce an unsupervised tensor-based anomaly detectionmethod that takes the sparse and temporally continuous nature of anomalies intoaccount. In particular, the anomaly detection problem is formulated as a robustlowrank + sparse tensor decomposition with a regularization term that minimizesthe temporal variation of the sparse part, so that the extracted anomalies aretemporally persistent. We also approximate rank minimization with graph totalvariation minimization to reduce the complexity of the optimization algorithm.The resulting optimization problem is convex, scalable, and is shown to berobust against missing data and noise. The proposed framework is evaluated onboth synthetic and real spatiotemporal urban traffic data and compared withbaseline methods.

Low-rank on Graphs plus Temporally Smooth Sparse Decomposition for Anomaly Detection in Spatiotemporal Data