  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.
