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A Survey on Canonical Correlation Analysis

机译：规范相关分析调查

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摘要

In recent years, the advances in data collection and statistical analysis promotes canonical correlation analysis (CCA) available for more advanced research. CCA is the main technique for two-set data dimensionality reduction such that the correlation between the pairwise variables in the common subspace is mutually maximized. Over 80-years of developments, a number of CCA models have been proposed according to different machine learning mechanisms. However, the field lacks an insightful review for the state-of-art developments. This survey targets to provide a well-organized overview for CCA and its extensions. Specifically, we first review the CCA theory from the perspective of both model formation and model optimization. The association between two popular solution methods, i.e., eigen value decomposition (EVD) and singular value decomposition (SVD), are discussed. Following that, we present a taxonomy of current progresses and classify them into seven groups: 1) multi-view CCA, 2) probabilistic CCA, 3) deep CCA, 4) kernel CCA, 5) discriminative CCA, 6) sparse CCA and 7) locality preserving CCA. For each group, we demonstrate two or three representative mathematical models, identifying their strengths and limitations. We summarize the representative applications and numerical results of these seven groups in real-world practices, collecting the data sets and open-sources for implementation. In the end, we provide several promising future research directions that can improve the current state of the art.
机译：近年来，数据收集和统计分析的进步促进了可用于更先进的研究的规范相关分析（CCA）。 CCA是用于两组数据维度降低的主要技术，使得公共子空间中的成对变量与彼此相互最大化的相关性。超过80年的发展，根据不同的机器学习机制提出了许多CCA模型。然而，该领域对最先进的发展缺乏洞察力审查。该调查目标提供了CCA及其扩展的良好组织概述。具体而言，我们首先从模型形成和模型优化的角度审查CCA理论。讨论了两个流行的解决方案方法之间的关联，即egen值分解（EVD）和奇异值分解（SVD）。在此之后，我们提出了目前的分类，并将它们分为七组：1）多视图CCA，2）概率CCA，3）深CCA，4）核CCA，5）鉴别性CCA，6）稀疏CCA和7 ）定位保存CCA。对于每组，我们展示了两三个代表性的数学模型，识别它们的优势和局限性。我们总结了这七组在现实世界实践中的代表性应用和数值结果，收集了数据集和开放源以实现实施。最后，我们提供了几个有前途的未来研究方向，可以改善现有的现有技术。

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