Canonical correlation analysis in high dimensions with structured regularization. (June 2023)

• Record Type: Journal Article
• Authors: Tuzhilina, Elena; Tozzi, Leonardo; Hastie, Trevor
• Is Part Of: Statistical modelling. Volume 23:Number 3(2023)
• Page Start: 203
• Page End: 227
• Publication Date: 2023-06
• Subjects: canonical correlation analysis -- Group penalty -- high dimensions -- regularization -- structured data; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X211041033
• Languages: English
• ISSNs: 1471-082X

Abstract

Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes anℓ 2 penalty on the CCA coefficients is widely used in applications with high-dimensional data. One limitation of such regularization is that it ignores any data structure, treating all the features equally, which can be ill-suited for some applications. In this article we introduce several approaches to regularizing CCA that take the underlying data structure into account. In particular, the proposed group regularized canonical correlation analysis (GRCCA) is useful when the variables are correlated in groups. We illustrate some computational strategies to avoid excessive computations with regularized CCA in high dimensions. We demonstrate the application of these methods in our motivating application from neuroscience, as well as in a small simulation example.