Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection

Yilin Liu, Hongchao Zhang, Ahmad Taha, Taylor T Johnson, Meiyi Ma
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:79840-79854, 2026.

Abstract

Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach. Our code is available at https://github.com/AICPS-Lab/Spectral-Energy-Shifts-in-GAD.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-liu26gb, title = {Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection}, author = {Liu, Yilin and Zhang, Hongchao and Taha, Ahmad and Johnson, Taylor T and Ma, Meiyi}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {79840--79854}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/liu26gb/liu26gb.pdf}, url = {https://proceedings.mlr.press/v306/liu26gb.html}, abstract = {Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach. Our code is available at https://github.com/AICPS-Lab/Spectral-Energy-Shifts-in-GAD.} }
Endnote
%0 Conference Paper %T Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection %A Yilin Liu %A Hongchao Zhang %A Ahmad Taha %A Taylor T Johnson %A Meiyi Ma %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-liu26gb %I PMLR %P 79840--79854 %U https://proceedings.mlr.press/v306/liu26gb.html %V 306 %X Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach. Our code is available at https://github.com/AICPS-Lab/Spectral-Energy-Shifts-in-GAD.
APA
Liu, Y., Zhang, H., Taha, A., Johnson, T.T. & Ma, M.. (2026). Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:79840-79854 Available from https://proceedings.mlr.press/v306/liu26gb.html.

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