Canonical correlation analysis that is scalable to high dimensional data. Uses covariance shrinkage and algorithmic speed ups to be linear time in p when p > n.
cca(X, Y, k = min(dim(X), dim(Y)), lambda.x = NULL, lambda.y = NULL)statistics summarizing CCA
first matrix (n x p1)
first matrix (n x p2)
number of canonical components to return
optional shrinkage parameter for estimating covariance of X. If NULL, estimate from data.
optional shrinkage parameter for estimating covariance of Y. If NULL, estimate from data.
Results from standard CCA are based on the SVD of \(\Sigma_{xx}^{-\frac{1}{2}} \Sigma_{xy} \Sigma_{yy}^{-\frac{1}{2}}\).
Avoids computation of \(\Sigma_{xx}^{-\frac{1}{2}}\) by using eclairs. Avoids cov(X,Y) by framing this as a matrix product that can be distributed. Uses low rank SVD. Other regularized CCA adds lambda to covariance like Ridge. Here it is a mixture