Min-Max Grassmannian Optimization for Online Subspace Tracking
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918423613669376 |
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| author | Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi |
| author_facet | Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi |
| contents | This paper discusses robustness guarantees for online tracking of time-varying subspaces from noisy data. Building on recent work in optimization over a Grassmannian manifold, we introduce a new approach for robust subspace tracking by modeling data uncertainty in a Grassmannian ball. The robust subspace tracking problem is cast into a min-max optimization framework, for which we derive a closed-form solution for the worst-case subspace, enabling a geometric robustness adjustment that is both analytically tractable and computationally efficient, unlike iterative convex relaxations. The resulting algorithm, GeRoST (Geometrically Robust Subspace Tracking), is validated on two case studies: tracking a linear time-varying system and online foreground-background separation in video. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Min-Max Grassmannian Optimization for Online Subspace Tracking Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi Systems and Control Optimization and Control This paper discusses robustness guarantees for online tracking of time-varying subspaces from noisy data. Building on recent work in optimization over a Grassmannian manifold, we introduce a new approach for robust subspace tracking by modeling data uncertainty in a Grassmannian ball. The robust subspace tracking problem is cast into a min-max optimization framework, for which we derive a closed-form solution for the worst-case subspace, enabling a geometric robustness adjustment that is both analytically tractable and computationally efficient, unlike iterative convex relaxations. The resulting algorithm, GeRoST (Geometrically Robust Subspace Tracking), is validated on two case studies: tracking a linear time-varying system and online foreground-background separation in video. |
| title | Min-Max Grassmannian Optimization for Online Subspace Tracking |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2604.00825 |