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

TL;DR

This paper presents an unsupervised tensor-based anomaly detection method for spatiotemporal data that models anomalies as sparse, temporally persistent components, improving robustness and scalability over existing approaches.

Contribution

It introduces a novel low-rank plus sparse tensor decomposition framework with temporal regularization and graph total variation approximation, addressing limitations of prior tensor methods.

Findings

Effective detection of persistent anomalies in urban traffic data

Robustness against missing data and noise demonstrated

Outperforms baseline methods in experiments

Abstract

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.