A Flag Decomposition for Hierarchical Datasets
This work addresses the need for a general algorithm to work with hierarchical datasets, which is significant for computer vision and machine learning applications.
The authors tackled the problem of factorizing hierarchical datasets by proposing a novel flag-based method, enabling hierarchy-preserving flag representation. This method has potential applications in denoising, clustering, and few-shot learning.
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.