# Dynamic Subspace Estimation with Grassmannian Geodesics

arXiv: https://arxiv.org/abs/2303.14851 · HTML: https://mlsanity.com/paper/2303.14851/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)

## Abstract (arXiv)

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.