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.
@article{arxiv.2303.14851,
title = {Dynamic Subspace Estimation with Grassmannian Geodesics},
author = {Cameron J. Blocker and Haroon Raja and Jeffrey A. Fessler and Laura Balzano},
journal= {arXiv preprint arXiv:2303.14851},
year = {2023}
}