Min-Max Grassmannian Optimization for Online Subspace Tracking
This work addresses robustness in subspace tracking for applications like video analysis and system identification, though it appears incremental as it builds on existing Grassmannian optimization methods.
The paper tackles robust online tracking of time-varying subspaces from noisy data by introducing a min-max optimization framework on a Grassmannian manifold, resulting in the GeRoST algorithm that achieves computational efficiency and is validated on linear system tracking and video foreground-background separation.
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.