Autoregressive Processes on Stiefel and Grassmann Manifolds

2025/09/29 by Jordi-Lluís Figueras, Figueras, Jordi-Lluís, Aron Persson +1
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.24767

Abstract

System identification of autoregressive processes on Stiefel and Grassmann manifolds are presented and studied. We define the system parameters as elements in the orthogonal group and we show that the system can be estimated by averaging over observations. Then we propose an algorithm on how to compute these system parameters using conjugate gradient descent on Stiefel and Grassmann manifolds, respectively.

Citations

• Fisher's Legacy of Directional Statistics, and Beyond to Statistics on Manifolds
• Random orthogonal matrices and the Cayley transform
• Fréchet Analysis Of Variance For Random Objects
• A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric
• Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
• The Geometry of Algorithms with Orthogonality Constraints
• Riemannian center of mass and mollifier smoothing

Related

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• Statistics on the (compact) Stiefel manifold: Theory and Applications
• StiefelGen: A Simple, Model Agnostic Approach for Time Series Data Augmentation over Riemannian Manifolds
• Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds
• Linear Algebra Problems Solved by Using Damped Dynamical Systems on the Stiefel Manifold