Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decomposition

2025-09-30

AI Summary

Existing anomaly detection methods primarily target point anomalies and struggle to capture structural dependencies in spatiotemporal data, while failing to jointly model anomaly continuity and statistical confidence. To address this, we propose an unsupervised tensor decomposition framework that— for the first time—incorporates spatiotemporal smoothness priors into low-rank plus sparse tensor decomposition. Specifically, we introduce graph-structured total variation regularization to enforce coherence of anomalies across both spatial and temporal dimensions, and design a statistically grounded anomaly scoring mechanism based on local spatiotemporal correlations to yield interpretable confidence estimates. Extensive experiments on synthetic and real-world spatiotemporal datasets demonstrate that our method accurately identifies spatiotemporally contiguous anomalies and significantly outperforms state-of-the-art baselines in detection accuracy, robustness, and interpretability.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Matrix & Tensor Methods
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Detects spatiotemporal anomalies in video and sensor data
• Addresses limitations of existing point-based anomaly detection methods
• Provides statistical confidence for unsupervised anomaly identification

Innovation

• Unsupervised tensor decomposition for anomaly detection
• Incorporates spatiotemporal smoothness via graph regularization
• Statistical scoring framework with local dependency modeling