广义典型相关分析：一种子空间求交方法
Generalized Canonical Correlation Analysis: A Subspace Intersection Approach
摘要：
广义典型相关分析（GCCA）是数据采掘、机器学习和人工智能中的一个重要工具。它的目的是寻找“共同的”随机变量，这些变量在同一组实体的多个特征表示（视图）之间具有很强的相关性。CCA和GCCA在较小程度上已经从统计和算法的角度进行了研究，但从线性代数的角度来看并不多。本文提供了一个新的代数角度GCCA的基础上（双）线性生成模型，自然捕捉其本质。它表明，从线性代数的角度来看，GCCA是相当于子空间的交集，并提供了条件下，不同的意见，公共子空间是可识别的。提出了一种新的基于子空间交集的GCCA算法，该算法可扩展以处理大规模的GCCA任务。合成以及真实的数据实验，以展示所提出的方法的有效性。
英文摘要：
Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding `common' random variables that are strongly correlated across multiple feature representations (views) of the same set of entities. CCA and to a lesser extent GCCA have been studied from the statistical and algorithmic points of view, but not as much from the standpoint of linear algebra. This paper offers a fresh algebraic perspective of GCCA based on a (bi-)linear generative model that naturally captures its essence. It is shown that from a linear algebra point of view, GCCA is tantamount to subspace intersection; and conditions under which the common subspace of the different views is identifiable are provided. A novel GCCA algorithm is proposed based on subspace intersection, which scales up to handle large GCCA tasks. Synthetic as well as real data experiments are provided to showcase the effectiveness of the proposed approach.
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。
