Despite the fact that the regularisation of multivariate methods is a well-known and widely used statistical procedure, very few studies have considered it from the perspective of analytic matrix decomposition. Here, we introduce a link between one variant of partial least squares (PLS) and canonical correlation analysis (CCA) for multiple groups, as well as two groups covered as a special case. A continuation algorithm based on the implicit function theorem is selected, with particular attention paid to potential non-generic points based on real economic data inputs. Both degenerated crossings and multiple eigenvalues are identified on the paths. The theory of Chebyshev polynomials is applied in order to generate novel insights into the phenomenon simply generalisable to a variety of other techniques.

中文翻译：

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将多元偏最小二乘与规范分析联系起来：一种路径跟踪方法

尽管多元方法的正则化是众所周知且广泛使用的统计程序，但很少有研究从分析矩阵分解的角度来考虑它。在这里，我们介绍了偏最小二乘（PLS）的一个变体与规范相关分析（CCA）之间的多个组之间的链接，以及作为特殊情况涉及的两个组。选择基于隐函数定理的连续算法，并特别注意基于实际经济数据输入的潜在非类属点。在路径上识别退化交叉和多个特征值。应用Chebyshev多项式理论是为了产生对该现象的新颖见解，而该现象可以简单地推广到各种其他技术。