Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decomposition

TL;DR

This work tackles unsupervised anomaly detection in spatiotemporal data by modeling the observed tensor as a sum of a low-rank normal component and a sparse, spatiotemporally smooth anomaly component. It extends HoRPCA with graph total variation regularizers to enforce temporal persistence and spatial contiguity on the sparse anomalies, and couples this with a proximal-ADMM optimization framework for scalable inference. An anomaly scoring scheme based on local neighborhood likelihoods is proposed, enabling significance-guided detection with calibrated confidence. Empirical results on synthetic data and real-world datasets ( NYC taxi data and server-machine logs) show that the proposed LR-STSS and its variants outperform HoRPCA, with notable gains in real-data anomaly detection when using the likelihood-based scoring. The framework offers a principled way to impute missing values and could be extended to capture higher-order temporal dynamics in spatiotemporal graphs.

Abstract

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. Existing anomaly detection methods focus mainly on point anomalies and cannot deal with temporal and spatial dependencies that arise in spatio-temporal data. Tensor-based anomaly detection methods have been proposed to address this problem. Although existing methods can capture dependencies across different modes, they are primarily supervised and do not account for the specific structure of anomalies. Moreover, these methods focus mainly on extracting anomalous features without providing any statistical confidence. 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 total variation of the tensor with respect to the underlying spatial and temporal graphs quantifies the spatiotemporal smoothness of the anomalies. Once the anomalous features are extracted, we introduce a statistical anomaly scoring framework that accounts for local spatio-temporal dependencies. The proposed framework is evaluated on both synthetic and real data.

Figures (2)

• Figure 1: Ablation study showing the impact of different components of the model. AUC-ROC scores are reported for varying (i) Radius (with $d = 4$ and $g = 100$), (ii) Duration (with $r = 2$, $g = 450$), and (iii) Number of groups of anomalies (with $r = 1$ and $d = 1$). F1 scores are reported for varying (iv) Radius, (v) Duration, and (vi) Number of groups of anomalies with same parameter settings as in AUC-ROC experiments. SNR and amplitude are fixed at 10 and 0.25, respectively. Shaded regions correspond to the $95\%$ confidence intervals calculated over 50 iterations.
• Figure 2: Analysis of robustness against various methods. AUC-ROC scores for (i) varying amplitude (SNR = $10$), (ii) varying SNR ($c = 0.25$) and F1 scores for (iii) varying amplitude (with SNR = $10$) and (iv) varying SNR (with $c = 0.25$) are reported. Radius, duration and number of groups are fixed at 2, 10 and 450 respectively. Shaded regions correspond to 95$\%$ confidence intervals over 50 iterations.

Theorems & Definitions (17)

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