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arXiv · 2303.14851

Dynamic Subspace Estimation with Grassmannian Geodesics

Cameron J. Blocker·Haroon Raja·Jeffrey A. Fessler·Laura Balzano
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Abstract

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.

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Cameron J. Blocker, Haroon Raja, Jeffrey A. Fessler, Laura Balzano. 2023-03-26. Dynamic Subspace Estimation with Grassmannian Geodesics. https://arxiv.org/abs/2303.14851

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