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.

翻译：动态子空间估计（或称子空间跟踪）是统计信号处理与机器学习领域的基础问题。本文针对时变子空间提出了一种测地线模型。该模型的自然目标函数具有非凸性。我们提出了一种新颖算法，通过格拉斯曼约束优化方法最小化该目标函数并从数据中估计模型参数。证明表明，该算法能保证目标函数单调非增。我们通过合成数据、视频数据及动态fMRI数据验证了所提模型与算法的性能。