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，是统计信号处理和机器学习中的基本问题。本文考虑了一个时变子空间的测地线模型。该模型的自然目标函数是非凸的。我们提出了一种新颖的算法，使用Grassmannian限制优化来最小化该目标并从数据中估计模型的参数。我们证明了使用此算法，目标函数单调递减。我们演示了该模型和我们的算法在合成数据、视频数据和动态fMRI数据上的性能。