基于标准角保持特性的压缩子空间学习
Compressed Subspace Learning Based on Canonical Angle Preserving Property
摘要：
子空间联合（UoS）是一种描述数据底层低维结构的流行模型。UoS结构的精细细节可以用子空间之间的正则角（也称为主角）来描述，这是相对子空间位置的众所周知的表征。本文证明了具有Johnson-Lindenstrauss（JL）性质的随机投影以压倒性的概率近似保持子空间之间的标准角。这一结果表明，随机投影近似地保持了UoS结构。受这一结果的启发，我们提出了一个压缩子空间学习（CSL）的框架，它能够从数据的UoS结构中提取有用的信息，大大降低了维度。我们证明了CSL在各种子空间相关的任务，如子空间可视化，主动子空间检测，子空间聚类的有效性。
英文摘要：
Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this paper, we prove that random projection with the so-called Johnson-Lindenstrauss (JL) property approximately preserves canonical angles between subspaces with overwhelming probability. This result indicates that random projection approximately preserves the UoS structure. Inspired by this result, we propose a framework of Compressed Subspace Learning (CSL), which enables to extract useful information from the UoS structure of data in a greatly reduced dimension. We demonstrate the effectiveness of CSL in various subspace-related tasks such as subspace visualization, active subspace detection, and subspace clustering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
