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arxiv: 2502.15793 · v2 · submitted 2025-02-18 · 💻 cs.LG · cs.SY· eess.SY

Anomaly Detection in Smart Power Grids with Graph-Regularized MS-SVDD: a Multimodal Subspace Learning Approach

Thomas Debelle , Fahad Sohrab , Pekka Abrahamsson , Moncef Gabbouj This is my paper

Pith reviewed 2026-05-23 02:29 UTC · model grok-4.3

classification 💻 cs.LG cs.SYeess.SY
keywords anomaly detectionsmart power gridsmultimodal subspace learningsupport vector data descriptiongraph regularizationone-class classificationevent detectionLaplacian regularization
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The pith

Graph-embedded MS-SVDD projects multimodal sensor data into a shared subspace while preserving structure to improve anomaly detection in power grids.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a graph-regularized extension of Multimodal Subspace Support Vector Data Description that maps data from multiple modalities into one low-dimensional subspace and applies Laplacian regularizers to retain each modality's internal structure. This targets the shortfall in prior one-class methods that overlook cross-modality dependencies in heterogeneous smart-grid streams. Evaluation on a three-modality event time-series dataset shows gains in detection robustness over standard approaches. Readers would care because more stable identification of anomalies in critical sensor networks could reduce false alarms and missed events in infrastructure monitoring.

Core claim

The graph-embedded MS-SVDD model projects data from multiple modalities into a shared low-dimensional subspace while preserving modality-specific structure through Laplacian regularizers, resulting in improved robustness of event detection on smart grid time series data compared to conventional approaches.

What carries the argument

Graph-embedded Laplacian regularization inside the MS-SVDD optimization that enforces both shared-subspace projection and modality-specific preservation.

If this is right

  • Structural dependencies across sensor modalities can be exploited directly inside one-class subspace models rather than handled separately.
  • The method enables systematic addition of relational priors to multimodal one-class learning without altering the core SVDD objective.
  • Robustness gains appear on dynamic heterogeneous streams using a dedicated one-class sample construction pipeline.
  • The same integration of graph priors can support other multimodal anomaly tasks under high-dimensional conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same regularization pattern could be tested on streaming grid data where modalities arrive asynchronously to check if the shared subspace remains stable.
  • Replacing Laplacian graphs with other similarity measures might reveal whether the specific regularizer choice is essential or interchangeable.
  • The approach suggests a route for embedding domain graphs into other one-class models used in infrastructure monitoring.

Load-bearing premise

The Laplacian regularizers preserve modality-specific structure in the shared subspace without post-hoc tuning that would change the reported performance gains.

What would settle it

Training the same model on the identical three-modality dataset but without the Laplacian terms and obtaining equal or higher detection accuracy would falsify the claim that the graph embedding drives the robustness improvement.

Figures

Figures reproduced from arXiv: 2502.15793 by Fahad Sohrab, Moncef Gabbouj, Pekka Abrahamsson, Thomas Debelle.

Figure 1
Figure 1. Figure 1: Anomaly detection over an incomplete time series, where [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of MS-SVDD with two modalities. The shared subspace is constructed using the positive [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: High-level illustration of graph-embedded regularizers for a modality [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Examples of several time-series measured at the same bus while an event occurs somewhere in the grid. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: MS-SVDD for Event Detection in Smart Power Grid. Each electrical quantity is considered as one modality [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 1
Figure 1. Figure 1: Preprocessing of PSML dataset for reliability evaluation. [PITH_FULL_IMAGE:figures/full_fig_p021_1.png] view at source ↗
read the original abstract

Anomaly detection in smart power grids is a critical challenge due to the complexity, heterogeneity, and dynamic nature of sensor data streams. Existing one-class classification methods, particularly Subspace Support Vector Data Description (SVDD), have been extended to multimodal scenarios but often fail to fully exploit the structural dependencies across modalities, limiting their robustness in real-world applications. In this paper, we address this gap by proposing a generalized Multimodal Subspace Support Vector Data Description (MS-SVDD) model with graph-embedded regularization. The method projects data from multiple modalities into a shared low-dimensional subspace while preserving modality-specific structure through Laplacian regularizers. Our approach is evaluated on a three-modality dataset derived from smart grid event time series, using a dedicated preprocessing pipeline for constructing one-class classification training samples. The results demonstrate that our graph-embedded MS-SVDD improves robustness of event detection compared to conventional approaches, highlighting the potential of integrating graph priors with multimodal subspace learning for advancing anomaly detection in critical infrastructure. More broadly, this work contributes to the wider field of AI by illustrating how relational and structural information can be systematically embedded into one-class models, enabling robust learning under complex, high-dimensional, and multimodal conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a graph-embedded Multimodal Subspace Support Vector Data Description (MS-SVDD) model for anomaly detection in smart power grids. It projects data from multiple modalities into a shared low-dimensional subspace while using Laplacian regularizers to preserve modality-specific structure, evaluates the approach on a three-modality dataset derived from smart grid event time series via a dedicated preprocessing pipeline for one-class samples, and claims that the graph-embedded variant improves robustness of event detection over conventional approaches.

Significance. If the empirical claims are substantiated with quantitative results and ablations, the integration of graph priors into multimodal one-class subspace learning could advance robust anomaly detection for critical infrastructure and illustrate systematic embedding of relational structure into SVDD-style models.

major comments (3)
  1. [Abstract and evaluation section] Abstract and evaluation section: the central claim that graph-embedded MS-SVDD 'improves robustness of event detection compared to conventional approaches' is stated without any quantitative metrics, baseline definitions, error bars, statistical tests, or description of how the preprocessing pipeline constructs one-class samples, leaving the empirical support for the claim invisible.
  2. [Method and evaluation sections] Method and evaluation sections: no ablation is reported that isolates the contribution of the Laplacian regularizers (e.g., full graph-embedded MS-SVDD versus MS-SVDD without the graph term, or sweeps over regularization weight), so performance deltas cannot be attributed to the graph prior rather than the subspace projection, preprocessing choices, or hyperparameter tuning.
  3. [Abstract] Abstract: the premise that Laplacian regularizers successfully preserve modality-specific structure in the shared subspace 'without requiring post-hoc tuning that affects the reported gains' is asserted as the core of the method but receives no validation details or sensitivity analysis.
minor comments (2)
  1. [Abstract] The phrase 'conventional approaches' is used without naming the specific baseline methods or citing their implementations.
  2. [Method section] Notation for the shared subspace projection and the Laplacian terms is introduced at a high level; explicit equations defining the objective and the role of each regularizer would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments highlighting the need for stronger empirical substantiation. We agree that the current presentation of results requires expansion with quantitative details, ablations, and sensitivity analyses to fully support the claims. We will undertake a major revision to address all points.

read point-by-point responses

  1. Referee: [Abstract and evaluation section] Abstract and evaluation section: the central claim that graph-embedded MS-SVDD 'improves robustness of event detection compared to conventional approaches' is stated without any quantitative metrics, baseline definitions, error bars, statistical tests, or description of how the preprocessing pipeline constructs one-class samples, leaving the empirical support for the claim invisible.

    Authors: We acknowledge that the abstract and evaluation section present the improvement claim at a high level without accompanying numerical results, explicit baseline definitions, error bars, statistical tests, or detailed description of one-class sample construction in the preprocessing pipeline. The full manuscript contains some comparative results, but they are not sufficiently quantified or visible in the sections noted. We will revise the abstract to include key quantitative metrics (e.g., detection rates or AUC improvements) and expand the evaluation section with baseline specifications, error bars from repeated runs, statistical significance tests, and an explicit step-by-step description of how the preprocessing pipeline constructs one-class samples. revision: yes

  2. Referee: [Method and evaluation sections] Method and evaluation sections: no ablation is reported that isolates the contribution of the Laplacian regularizers (e.g., full graph-embedded MS-SVDD versus MS-SVDD without the graph term, or sweeps over regularization weight), so performance deltas cannot be attributed to the graph prior rather than the subspace projection, preprocessing choices, or hyperparameter tuning.

    Authors: We agree that the absence of ablations isolating the Laplacian regularizers limits attribution of gains. The current manuscript does not report comparisons of the full graph-embedded MS-SVDD against the variant without the graph term or sweeps over the regularization weight. In the revision, we will add these ablation studies in the evaluation section, including performance tables for the ablated model and regularization sweeps, to demonstrate that improvements are attributable to the graph prior. revision: yes

  3. Referee: [Abstract] Abstract: the premise that Laplacian regularizers successfully preserve modality-specific structure in the shared subspace 'without requiring post-hoc tuning that affects the reported gains' is asserted as the core of the method but receives no validation details or sensitivity analysis.

    Authors: The abstract asserts the structure-preserving property of the Laplacian regularizers without accompanying validation or sensitivity analysis. The manuscript does not include such details or experiments. We will add a sensitivity analysis subsection (with plots or tables over regularization weights) and validation experiments demonstrating that modality-specific structure is preserved in the shared subspace without post-hoc tuning that alters the reported performance gains. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical evaluation of proposed regularized model

full rationale

The paper proposes a graph-regularized MS-SVDD extension that projects modalities into a shared subspace with Laplacian terms, then reports empirical improvements on a smart-grid dataset. No equations, derivations, or performance figures are shown to reduce by construction to fitted inputs or self-citations. The abstract and description treat the regularizers as an added modeling choice whose contribution is assessed via end-to-end comparisons rather than by definitional equivalence. This is the normal case of a self-contained empirical proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract supplies no explicit information on free parameters, background axioms, or newly postulated entities; the model is described only at the level of its high-level components.

pith-pipeline@v0.9.0 · 5765 in / 1008 out tokens · 46693 ms · 2026-05-23T02:29:01.424231+00:00 · methodology

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

  1. [1]

    Damodaram, C

    A. Damodaram, C. L. Tulasi, L. V . Reddy, Recent decade global trends in renewable energy and investments-a review., International Journal of COMADEM 25 (3)

    work page

  2. [2]

    Russo, D

    M. Russo, D. Carvalho, N. Martins, A. Monteiro, Future perspectives for wind and solar electricity production under high-resolution climate change scenarios, Journal of Cleaner Production 404 (2023) 136997

    work page 2023

  3. [3]

    A. A. Berraies, A. Tzanetos, M. Blondin, Machine learning to facilitate the integration of renewable energies into the grid, in: Handbook of Smart Energy Systems, Springer, 2023, pp. 689–711. 18

    work page 2023

  4. [4]

    Penmetsa, K

    V . Penmetsa, K. E. Holbert, Climate change effects on solar, wind and hydro power generation, in: 2019 North American Power Symposium (NAPS), IEEE, 2019, pp. 1–6

    work page 2019

  5. [5]

    F. T. Aula, S. C. Lee, Power fluctuation reduction methodology for the grid-connected renewable power systems, in: Active and Passive Smart Structures and Integrated Systems 2013, V ol. 8688, SPIE, 2013, pp. 565–569

    work page 2013

  6. [6]

    Zheng, N

    X. Zheng, N. Xu, L. Trinh, D. Wu, T. Huang, S. Sivaranjani, Y . Liu, L. Xie, A multi-scale time-series dataset with benchmark for machine learning in decarbonized energy grids, Scientific Data 9 (1) (2022) 359

    work page 2022

  7. [7]

    Talari, M

    S. Talari, M. Shafie-khah, G. J. Osório, J. Aghaei, J. P. Catalão, Stochastic modelling of renewable energy sources from operators’ point-of-view: A survey, Renewable and Sustainable Energy Reviews 81 (2018) 1953– 1965

    work page 2018

  8. [8]

    X. Fang, S. Misra, G. Xue, D. Yang, Smart grid — the new and improved power grid: A survey, IEEE Commu- nications Surveys & Tutorials 14 (4) (2012) 944–980

    work page 2012

  9. [9]

    M. G. Pollitt, Lessons from the history of independent system operators in the energy sector, Energy Policy 47 (2012) 32–48

    work page 2012

  10. [10]

    Niembro-García, P

    J. Niembro-García, P. Alfaro-Martínez, J. A. Marmolejo-Saucedo, Life cycle cost and life cycle assessment: an approximation to understand the real impacts of the electricity supply industry, in: Advances of Artificial Intelligence in a Green Energy Environment, Elsevier, 2022, pp. 83–110

    work page 2022

  11. [11]

    J. Yu, S. Kang, Clustering-based proxy measure for optimizing one-class classifiers, Pattern Recognition Letters 117 (2019) 37–44

    work page 2019

  12. [12]

    Sohrab, J

    F. Sohrab, J. Raitoharju, A. Iosifidis, M. Gabbouj, Ellipsoidal subspace support vector data description, IEEE Access 8 (2020) 122013–122025

    work page 2020

  13. [13]

    P. P. Liang, L.-P. Morency, Tutorial on multimodal machine learning: principles, challenges, and open questions, in: Companion Publication of the 25th International Conference on Multimodal Interaction, 2023, pp. 101–104

    work page 2023

  14. [14]

    Sohrab, J

    F. Sohrab, J. Raitoharju, A. Iosifidis, M. Gabbouj, Multimodal subspace support vector data description, Pattern Recognition 110 (2021) 107648

    work page 2021

  15. [15]

    Gupta, H

    A. Gupta, H. P. Gupta, B. Biswas, T. Dutta, Approaches and applications of early classification of time series: A review, IEEE Transactions on Artificial Intelligence 1 (1) (2020) 47–61

    work page 2020

  16. [16]

    Nazir, D

    Z. Nazir, D. Kaldykhanov, K.-K. Tolep, J.-G. Park, A machine learning model selection considering tradeoffs between accuracy and interpretability, in: 2021 13th International Conference on Information Technology and Electrical Engineering (ICITEE), IEEE, 2021, pp. 63–68

    work page 2021

  17. [17]

    L. Xie, Y . Chen, P. R. Kumar, Dimensionality reduction of synchrophasor data for early event detection: Lin- earized analysis, IEEE Transactions on Power Systems 29 (6) (2014) 2784–2794

    work page 2014

  18. [18]

    Saber, A

    A. Saber, A. Emam, H. Elghazaly, A threshold free pmu-based fault location scheme for multi-end lines, Ain Shams Engineering Journal 11 (4) (2020) 1113–1121

    work page 2020

  19. [19]

    D. Wu, D. Sharma, G. Ji, V . Perumalla, X. Luo, J. Jiang, Structural analysis based method for estimating critical clearing time without time domain simulation, in: 2019 IEEE Power & Energy Society General Meeting (PESGM), IEEE, 2019, pp. 1–5

    work page 2019

  20. [20]

    K. M. Banjar-Nahor, L. Garbuio, V . Debusschere, N. Hadjsaid, N. Sinisuka, et al., Critical clearing time transfor- mation upon renewables integration through static converters, a case in microgrids, in: 2018 IEEE International Conference on Industrial Technology (ICIT), IEEE, 2018, pp. 1183–1188

    work page 2018

  21. [21]

    D. M. J. Tax, R. P. W. Duin, Support vector data description, Machine Learning 54 (2004) 45–66

    work page 2004

  22. [22]

    Sohrab, J

    F. Sohrab, J. Raitoharju, M. Gabbouj, A. Iosifidis, Subspace support vector data description, in: 2018 24th International Conference on Pattern Recognition (ICPR), 2018, pp. 722–727

    work page 2018

  23. [23]

    Degerli, F

    A. Degerli, F. Sohrab, S. Kiranyaz, M. Gabbouj, Early myocardial infarction detection with one-class classifica- tion over multi-view echocardiography, in: 2022 Computing in Cardiology (CinC), V ol. 498, 2022, pp. 1–4

    work page 2022

  24. [24]

    Kwak, Nonlinear projection trick in kernel methods: An alternative to the kernel trick, IEEE Transactions on Neural Networks and Learning Systems 24 (12) (2013) 2113–2119

    N. Kwak, Nonlinear projection trick in kernel methods: An alternative to the kernel trick, IEEE Transactions on Neural Networks and Learning Systems 24 (12) (2013) 2113–2119

    work page 2013

  25. [25]

    Laakom, F

    F. Laakom, F. Sohrab, J. Raitoharju, A. Iosifidis, M. Gabbouj, Convolutional autoencoder-based multimodal one-class classification, arXiv preprint arXiv:2309.14090

    work page arXiv

  26. [26]

    Kilickaya, M

    S. Kilickaya, M. Ahishali, F. Sohrab, T. Ince, M. Gabbouj, Hyperspectral image analysis with subspace learning- based one-class classification, in: 2023 Photonics & Electromagnetics Research Symposium (PIERS), IEEE, 2023, pp. 953–959. 19

    work page 2023

  27. [27]

    H. H. Al-Khshali, M. Ilyas, F. Sohrab, M. Gabbouj, Malware detection with subspace learning-based one-class classification, IEEE Access

    work page

  28. [28]

    T. Khan, F. Sohrab, A. Michalas, M. Gabbouj, Trustworthiness of x-users: A one-class classification approach, in: L. Barolli (Ed.), Advanced Information Networking and Applications, Springer Nature Switzerland, Cham, 2024, pp. 331–343

    work page 2024

  29. [29]

    Zaffar, F

    Z. Zaffar, F. Sohrab, J. Kanniainen, M. Gabbouj, Credit card fraud detection with subspace learning-based one- class classification, in: 2023 IEEE Symposium Series on Computational Intelligence (SSCI), 2023, pp. 407–412

    work page 2023

  30. [30]

    M. U. Zahid, A. Degerli, F. Sohrab, S. Kiranyaz, T. Hamid, R. Mazhar, M. Gabbouj, Refining myocardial infarction detection: A novel multi-modal composite kernel strategy in one-class classification, in: 2024 IEEE International Conference on Image Processing (ICIP), IEEE, 2024, pp. 3010–3016

    work page 2024

  31. [31]

    Sohrab, F

    F. Sohrab, F. Laakom, M. Gabbouj, Newton method-based subspace support vector data description, in: 2023 IEEE Symposium Series on Computational Intelligence (SSCI), 2023, pp. 1372–1379

    work page 2023

  32. [32]

    W. Han, C. Cai, Y . Guo, J. Peng, Erl-mr: Harnessing the power of euler feature representations for balanced multi-modal learning, in: Proceedings of the 32nd ACM International Conference on Multimedia, 2024, pp. 4591–4600

    work page 2024

  33. [33]

    I. Kim, S. Xu, Bus voltage control and optimization strategies for power flow analyses using petri net approach, International Journal of Electrical Power & Energy Systems 112 (2019) 353–361. 20 Anomaly Detection in Smart Power Grids with Graph-Regularized MS-SVDD Supplementary Material Thomas Debelle, Fahad Sohrab, Pekka Abrahamsson, Moncef Gabbouj This ...

    work page 2019

  34. [34]

    Preprocessing of the PSML dataset for reliability evaluation Figure 1: Preprocessing of PSML dataset for reliability evaluation. 1

    work page

  35. [35]

    Results of reliability experiments 0% noise Linear Non-linear ω0 acc tpr tnr pre hm gm acc tpr tnr pre hm gm AND (-/-/-) 0.41 0.93 0.07 0.40 0.56 0.26 0.73 0.83 0.66 0.62 0.71 0.74 (-/-/+) 0.43 0.96 0.08 0.41 0.57 0.27 0.70 0.81 0.63 0.59 0.68 0.71 (-/+/-) 0.41 0.96 0.05 0.40 0.56 0.22 0.75 0.80 0.73 0.66 0.72 0.76 (-/+/+) 0.43 0.96 0.07 0.41 0.57 0.27 0....

    work page