Stiefel Manifold

The Stiefel manifold is a mathematical space representing the set of all orthonormal matrices, crucial for various applications requiring orthogonal constraints, such as machine learning and signal processing. Current research focuses on developing efficient optimization algorithms on this manifold, particularly exploring retraction-free methods and decentralized approaches to reduce computational costs and improve scalability for large-scale problems. These advancements are significant because they enable the application of manifold-based optimization techniques to increasingly complex datasets and distributed computing environments, improving the performance of algorithms in diverse fields like time series analysis and meta-learning.

Papers

October 27, 2024

Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds
Tiangang Cui, Alex Gorodetsky
Posterior Sampling Matrix Completion Hamiltonian Monte Carlo Low Rank Matrix Low Rank Matrix Completion Stiefel Manifold

July 25, 2024

Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, P. -A. Absil, Nina Miolane
General Bound Generalized Geodesic Single Parent Family Riemannian Metric Geodesic Distance Stiefel Manifold

May 19, 2024

Global Convergence of Decentralized Retraction-Free Optimization on the Stiefel Manifold
Youbang Sun, Shixiang Chen, Alfredo Garcia, Shahin Shahrampour
Global Convergence Decentralized Optimization Gradient Update Orthogonality Constraint Decentralized Nonconvex Stiefel Manifold Retraction Based Method

May 2, 2024

Optimization without Retraction on the Random Generalized Stiefel Manifold
Simon Vary, Pierre Ablin, Bin Gao, P.-A. Absil
Optimization Purpose Covariance Matrix Riemannian Optimization Orthogonality Constraint Stiefel Manifold Generalized Eigenvalue Problem Retraction Based Method

February 29, 2024

StiefelGen: A Simple, Model Agnostic Approach for Time Series Data Augmentation over Riemannian Manifolds
Prasad Cheema, Mahito Sugiyama
Data Augmentation Time Series Model Agnostic Riemannian Manifold Noise Injection Stiefel Manifold

February 28, 2024

FORML: A Riemannian Hessian-free Method for Meta-learning on Stiefel Manifolds
Hadi Tabealhojeh, Soumava Kumar Roy, Peyman Adibi, Hossein Karshenas
Meta Learning Gradient Based Meta Learning Riemannian Geometry Approach Hessian Free Riemannian Graph Stiefel Manifold

September 19, 2023

$O(k)$-Equivariant Dimensionality Reduction on Stiefel Manifolds
Andrew Lee, Harlin Lee, Jose A. Perea, Nikolas Schonsheck, Madeleine Weinstein
Dimensionality Reduction Principal Component Analysis Grassmann Manifold Equivariant Generative Stiefel Manifold

August 21, 2023

Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifold
Jun Chen, Haishan Ye, Mengmeng Wang, Tianxin Huang, Guang Dai, Ivor W. Tsang, Yong Liu
Riemannian Gradient Riemannian Optimization Conjugate Gradient Stiefel Manifold Decentralized Riemannian

July 31, 2023

Semi-Supervised Laplacian Learning on Stiefel Manifolds
Chester Holtz, Pengwen Chen, Alexander Cloninger, Chung-Kuan Cheng, Gal Mishne
Semi Supervised Learning Semi Supervised Graph Laplacian Laplacian Matrix Laplacian Learning Stiefel Manifold

March 31, 2023

Decentralized Weakly Convex Optimization Over the Stiefel Manifold
Jinxin Wang, Jiang Hu, Shixiang Chen, Zengde Deng, Anthony Man-Cho So
Non Smooth Decentralized Nonconvex Proximal Operator Finite Sum Optimization Stiefel Manifold Decentralized Riemannian

December 30, 2021

Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function
Lei Wang, Xin Liu
Global Convergence Lagrangian System Decentralized Optimization Decentralized Algorithm Stiefel Manifold Augmented Lagrangian