The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components, correspondence analysis, multidimensional scaling, canonical correlation, partial least squares). Though the GSVD is ubiquitous, powerful, and flexible, it has very few implementations. Here I introduce the GSVD package for R. The general goal of GSVD is to provide a small set of accessible functions to perform the GSVD and two other related decompositions (generalized eigenvalue decomposition, generalized partial least squares-singular value decomposition). Furthermore, GSVD helps provide a more unified conceptual approach and nomenclature to many techniques. I first introduce the concept of the GSVD, followed by a formal definition of the generalized decompositions. Next I provide some key decisions made during development, and then a number of examples of how to use GSVD to implement various statistical techniques. These examples also illustrate one of the goals of GSVD: how others can (or should) build analysis packages that depend on GSVD. Finally, I discuss the possible future of GSVD.

中文翻译：

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广义特征、奇异值和偏最小二乘分解：GSVD 包

广义奇异值分解（GSVD，又名“SVD 三元组”、“对偶图”方法）提供了一个统一的策略和基础来执行几乎所有最常见的多变量分析（例如，主成分、对应分析、多维标度、典型相关） ，偏最小二乘法）。尽管 GSVD 无处不在、功能强大且灵活，但它的实现却很少。这里我介绍 R 的 GSVD 包。 GSVD 的总体目标是提供一小组可访问的函数来执行 GSVD 和其他两个相关的分解（广义特征值分解、广义偏最小二乘-奇异值分解）。此外，GSVD 有助于为许多技术提供更统一的概念方法和命名法。我首先介绍 GSVD 的概念，然后是广义分解的正式定义。接下来，我提供了在开发过程中做出的一些关键决策，然后提供了一些如何使用 GSVD 实现各种统计技术的示例。这些示例还说明了 GSVD 的目标之一：其他人如何（或应该）构建依赖于 GSVD 的分析包。最后，我讨论了 GSVD 可能的未来。