Higher-Order Grouped Outlier Robust PCA for Spatio-temporal Anomaly Detection

Robust tensor decomposition has been applied in a variety of domains including hyperspectral image restoration, anomaly detection in spatiotemporal traffic data, and event detection in video monitoring. In many of these applications, noise or outliers are commonly modeled as sparse noise. However, in a lot of cases the noise has some inherent structure. In these cases, ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm sparsity is not sufficient to capture the structure of grouped anomalies or non-instantaneous events. In this paper, we introduce a robust tensor decomposition method where the normal part of the tensor is modeled as low-rank and the anomalous part is modeled using latent overlapping group norm. A general notion of grouping is introduced through node- and edge-based grouping using the graph structure corresponding to the underlying spatio-temporal data. The resulting optimization problem is solved using ADMM. The proposed method is evaluated on both simulated and real data for anomaly detection<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>.