Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decomposition

Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications, including video surveillance, medical imaging data, and urban traffic monitoring. Tensor-based anomaly detection methods have been proposed to capture the dependencies that arise in spatiotemporal data. However, these methods do not account for the specific structure of anomalies. Moreover, these methods focus primarily on anomaly detection and not scoring, i.e., assigning a probabilistic confidence on the extracted anomalous features. In this paper, we introduce a data-efficient tensor-based anomaly detection method that simultaneously considers the sparse and spatiotemporally smooth nature of anomalies, thus detecting group anomalies. The anomaly detection problem is formulated as a regularized robust low-rank + sparse tensor decomposition where the spatiotemporal contiguity of the anomalies is quantified by the total variation of the tensor with respect to the underlying spatial and temporal graphs. Once the anomalous features are extracted, we introduce a statistical anomaly scoring framework that accounts for local spatiotemporal dependencies. The proposed framework is evaluated on both synthetic and real data. The results show that the proposed approach outperforms existing robust tensor decomposition methods for detecting group anomalies that exhibit temporal and spatial contiguity.