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Dynamic Subspace Estimation with Grassmannian Geodesics
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Dynamic Subspace Estimation with Grassmannian Geodesics
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Dynamic subspace estimation, or subspace tracking, is a fundamental problem in statistical signal processing and machine learning. This paper considers a geodesic model for time-varying subspaces. The natural objective function for this model is non-convex. We propose a novel algorithm for minimizing this objective and estimating the parameters of the model from data with Grassmannian-constrained optimization. We show that with this algorithm, the objective is monotonically non-increasing. We demonstrate the performance of this model and our algorithm on synthetic data, video data, and dynamic fMRI data.
Forward citations
Cited by 2 Pith papers
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A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems
A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.
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Geometrically Principled Randomized Optimization for Efficient LLM Training
Randomized Grassmannian subspace updates, combined with Adam-state alignment and residual recovery, produce small evaluation-loss gains over prior low-rank LLM training methods.
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