@conference{10902/39114,
year = {2025},
url = {https://hdl.handle.net/10902/39114},
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.},
organization = {N. Mankovich thanks Homer Durand, Gherardo Varando, Claudio Verdun, and Bernardo Freitas Paulo da Costa for enlightening conversations on flag manifolds and their applications. N. Mankovich and G. Camps-Valls acknowledge support from the project ”Artificial Intelligence for complex systems: Brain, Earth, Climate, Society” funded by the Department of Innovation, Universities, Science, and Digital Society, code: CIPROM/2021/56. This work was also supported by the ELIAS project (HORIZON-CL4-2022-HUMAN-02- 02, Grant No. 101120237), the THINKINGEARTH project (HORIZON-EUSPA-2022-SPACE-02-55, Grant No. 101130544), and the USMILE project (ERC-SyG2019, Grant No. 855187). T. Birdal acknowledges support from the Engineering and Physical Sciences Research Council [grant EP/X011364/1]. T. Birdal was supported by a UKRI Future Leaders Fellowship [grant number MR/Y018818/1] as well as a Royal Society Research Grant RG/R1/241402. The work of I. Santamaria was partly supported under grant PID2022-137099NB-C43 (MADDIE) funded by MICIU/AEI /10.13039/501100011033 and FEDER, UE.},
publisher = {Institute of Electrical and Electronics Engineers, Inc.},
publisher = {IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 2025, 18738-18748},
title = {A flag decomposition for hierarchical datasets},
author = {Mankovich, Nathan and Santamaría Caballero, Luis Ignacio and Camps Valls, Gustau and Birdal, Tolga},
}