Abstract Canonical correlation analysis (CCA) is a very useful tool for measuring the linear relationship between two multidimensional variables. However, it often fails to extract meaningful features in high-dimensional settings. This motivates the sparse CCA problem, in which l1 constraints are applied to the canonical vectors. Although some sparse CCA solvers exist in the literature, we found that none of them is efficient. We propose a fast two-stage semi-smooth Newton augmented Lagrangian method ( tSSNALM ) to solve sparse CCA problems, and we provide convergence analysis. Numerical comparisons between our approach and a number of state-of-the-art solvers, on simulated data sets, are presented to demonstrate its efficiency. To the best of our knowledge, this is the first time that duality has been integrated with a semi-smooth Newton method for solving sparse CCA.

中文翻译：

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tSSNALM：一种用于稀疏 CCA 的快速两阶段半光滑牛顿增广拉格朗日方法

摘要 典型相关分析（CCA）是一种非常有用的测量两个多维变量之间线性关系的工具。然而，它往往无法在高维设置中提取有意义的特征。这引发了稀疏 CCA 问题，其中 l1 约束应用于规范向量。尽管文献中存在一些稀疏的 CCA 求解器，但我们发现它们都不是有效的。我们提出了一种快速两阶段半光滑牛顿增广拉格朗日方法 (tSSNALM) 来解决稀疏 CCA 问题，并提供收敛分析。我们的方法与许多最先进的求解器在模拟数据集上进行了数值比较，以证明其效率。据我们所知，