论文标题
广义规范相关分析：一个子空间交点方法
Generalized Canonical Correlation Analysis: A Subspace Intersection Approach
论文作者
论文摘要
广义规范相关分析（GCCA）是一个重要工具，可在数据挖掘，机器学习和人工智能中找到许多应用。它旨在查找在同一集合实体的多个特征表示（视图）之间密切相关的“常见”随机变量。从统计和算法的角度研究了CCA和较小程度的GCCA，但从线性代数的角度来看并不多。本文基于（双）线性生成模型自然捕获其本质的（双）线性生成模型，提供了GCCA的全新代数观点。结果表明，从线性代数的角度来看，GCCA与子空间交叉点有关系。以及提供可识别不同观点的共同子空间的条件。基于子空间交叉点提出了一种新型的GCCA算法，该算法扩展到处理大型GCCA任务。提供合成和实际数据实验以展示所提出方法的有效性。
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.
