Spatiotemporal Group Anomaly Detection via Graph Total Variation on Tensors

Abstract

Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including urban traffic monitoring. Existing anomaly detection methods mostly focus on point anomalies and cannot deal with temporal and spatial dependencies that arise in spatiotemporal data. Tensor-based anomaly detection methods have been proposed to address this problem. While these methods are able to capture the dependencies across the different modes, they are mostly supervised and do not take the particular nature of anomalies into account. In this paper, we introduce an unsupervised tensor-based anomaly detection method that simultaneously considers the sparse and spatiotemporally smooth nature of anomalies. The anomaly detection problem is formulated as a regularized robust low-rank + sparse tensor decomposition where the spatiotemporal smoothness of the anomalies is quantified by the graph total variation with respect to the underlying spatial and temporal graphs. This minimization ensures that the extracted anomalies are temporally persistent and spatially smooth. The proposed framework is evaluated on both synthetic and real spatiotemporal urban traffic data.