A flag decomposition for hierarchical datasets
File(s)
Author(s)
Mankovich, Nathan
Ignacio, Santamaria
Camps-Valls, Gustau
Birdal, Tolga
Type
Conference Paper
Abstract
Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and subspace clustering, current applications are often restricted to extracting flags using common matrix decomposition methods like the singular value decomposition. Here, we address the need for a general algorithm to factorize and work with hierarchical datasets. In particular, we propose a novel, flag-based method that decomposes arbitrary hierarchical real-valued data into a hierarchy-preserving flag representation in Stiefel coordinates. Our work harnesses the potential of flag manifolds in applications including denoising, clustering, and few-shot learning.
Date Issued
2025-08-13
Date Acceptance
2025-02-26
Citation
2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2025, pp.18738-18748
ISBN
979-8-3315-4364-8
ISSN
2575-7075
Publisher
IEEE
Start Page
18738
End Page
18748
Journal / Book Title
2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
Copyright Statement
Copyright © 2025, IEEE. This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.
Source
The IEEE/CVF Conference on Computer Vision and Pattern Recognition
Publication Status
Published
Start Date
2025-06-11
Finish Date
2025-06-15
Coverage Spatial
Nashville, TN, USA