# Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decomposition

arXiv: https://arxiv.org/abs/2510.00460 · HTML: https://mlsanity.com/paper/2510.00460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [Signal Recovery on Graphs: Variation Minimization](https://mlsanity.com/paper/1411.7414/) (2014)
- [Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values](https://mlsanity.com/paper/2401.05800/) (2024)
- [Anomaly Detection in Road Networks Using Sliding-Window Tensor Factorization](https://mlsanity.com/paper/1803.04534/) (2018)

## Abstract (arXiv)

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.