Fast 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.
fastcca(X, Y, k = min(dim(X), dim(Y)), lambda.x = NULL, lambda.y = NULL)fastcca object
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.
summary statistics of CCA
Results from standard CCA are based on the SVD of \(\Sigma_{xx}^{-\frac{1}{2}} \Sigma_{xy} \Sigma_{yy}^{-\frac{1}{2}}\).
Uses eclairs() and empirical Bayes covariance regularization, and applies speed up of RCCA (Tuzhilina, et al. 2023) to perform CCA on n PCs and instead of p features. Memory usage is \(\mathcal{O}(np)\) instead of \(\mathcal{O}(p^2)\). Computation is \(\mathcal{O}(n^2p)\) instead of \(\mathcal{O}(p^3)\) or \(\mathcal{O}(np^2)\)
Tuzhilina, E., Tozzi, L., & Hastie, T. (2023). Canonical correlation analysis in high dimensions with structured regularization. Statistical modelling, 23(3), 203-227.