Statistical Modelling 23 (3) (2023), 203–227
Canonical correlation analysis in high dimensions with structured regularization
Elena Tuzhilina,
Department of Statistics,
Stanford University,
Stanford, CA,
USA.
e-mail: elenatuz@stanford.edu
Leonardo Tozzi,
Department of Psychiatry and Behavioral Sciences,
Stanford University,
Stanford, CA,
USA.
Trevor Hastie,
Department of Statistics,
Stanford University,
Stanford, CA,
USA.
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 an L2 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 paper 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.
Keywords:
canonical correlation analysis, Group penalty, high dimensions, regularization, structured data
Downloads:
Code in zipped archive; additional supplementary material; Data on google drive .
back