# Interdependency Matters: Graph Alignment for Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2410.08877 · HTML: https://mlsanity.com/paper/2410.08877/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [Impossibility of Partial Recovery in the Graph Alignment Problem](https://mlsanity.com/paper/2102.02685/) (2021)
- [Detecting Multivariate Time Series Anomalies with Zero Known Label](https://mlsanity.com/paper/2208.02108/) (2022)

## Built on by (most cited first, 3 of 3)

- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [InfiGFusion: Graph-on-Logits Distillation via Efficient Gromov-Wasserstein for Model Fusion](https://mlsanity.com/paper/2505.13893/) (2025)
- [Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2610.15250/) (2026)

## Abstract (arXiv)

Anomaly detection in multivariate time series (MTS) is crucial for various applications in data mining and industry. Current industrial methods typically approach anomaly detection as an unsupervised learning task, aiming to identify deviations by estimating the normal distribution in noisy, label-free datasets. These methods increasingly incorporate interdependencies between channels through graph structures to enhance accuracy. However, the role of interdependencies is more critical than previously understood, as shifts in interdependencies between MTS channels from normal to anomalous data are significant. This observation suggests that textitanomalies could be detected by changes in these interdependency graph series. To capitalize on this insight, we introduce MADGA (MTS Anomaly Detection via Graph Alignment), which redefines anomaly detection as a graph alignment (GA) problem that explicitly utilizes interdependencies for anomaly detection. MADGA dynamically transforms subsequences into graphs to capture the evolving interdependencies, and Graph alignment is performed between these graphs, optimizing an alignment plan that minimizes cost, effectively minimizing the distance for normal data and maximizing it for anomalous data. Uniquely, our GA approach involves explicit alignment of both nodes and edges, employing Wasserstein distance for nodes and Gromov-Wasserstein distance for edges. To our knowledge, this is the first application of GA to MTS anomaly detection that explicitly leverages interdependency for this purpose. Extensive experiments on diverse real-world datasets validate the effectiveness of MADGA, demonstrating its capability to detect anomalies and differentiate interdependencies, consistently achieving state-of-the-art across various scenarios.