Dynamic Subspace Estimation with Grassmannian Geodesics

TL;DR

This paper introduces a novel geodesic-based model and algorithm for dynamic subspace estimation, effectively tracking time-varying subspaces in data such as videos and fMRI, with proven monotonic convergence.

Contribution

It proposes a new Grassmannian geodesic model and an optimization algorithm for dynamic subspace estimation, addressing non-convexity and demonstrating practical effectiveness.

Findings

Monotonically non-increasing objective function with the proposed algorithm

Effective subspace tracking demonstrated on synthetic, video, and fMRI data

Improved accuracy over existing methods in dynamic environments

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.