Generalized eigen, singular value, and partial least squares decompositions: The GSVD package

TL;DR

The paper introduces the GSVD package for R, unifying various multivariate analysis techniques through generalized decompositions, enhancing accessibility and conceptual clarity.

Contribution

It provides the first comprehensive implementation of GSVD and related decompositions in R, facilitating diverse multivariate analyses with a unified approach.

Findings

Implemented GSVD, GEV, and GPLSSVD in R

Demonstrated applications across multiple multivariate techniques

Facilitated development of analysis packages using GSVD

Abstract

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.