提出一种新方法，将分层数据转化为保持层级关系的几何表示。
A Flag Decomposition for Hierarchical Datasets
- 用旗流形结构分解分层数据，保留嵌套子空间关系
- 在去噪、聚类和少样本学习任务中表现优于传统方法
- 适合处理具有层次结构的数据，如图像序列或多尺度特征
旗流形编码嵌套子空间序列，在降维、运动平均和子空间聚类等计算机视觉与机器学习任务中具有重要价值。然而，现有应用大多依赖奇异值分解等通用矩阵分解方法提取旗结构。本文提出一种新型基于旗的算法，可将任意分层实值数据分解为保持层级结构的旗表示，采用施蒂费尔坐标系表达。该方法在去噪、聚类及少样本学习等任务中展现出潜力，推动旗流形在复杂数据建模中的应用。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。