Canonical Correlation Analysis in high dimensions with structured regularization

TL;DR

This paper introduces structured regularization methods for canonical correlation analysis (CCA) that incorporate data structure, such as group correlations, improving analysis in high-dimensional settings, with applications demonstrated in neuroscience.

Contribution

It proposes new regularization approaches for CCA that account for data structure, specifically group correlations, enhancing performance in high-dimensional data analysis.

Findings

GRCCA effectively captures group-based correlations.

Structured regularization improves CCA performance in high dimensions.

Applications demonstrate relevance in neuroscience data analysis.

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 $\ell_2$ 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 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.