Improved estimation of canonical vectors in canonical correlation analysis

Canonical Correlation Analysis (CCA) is a multidimensional algorithm for two datasets that finds linear transformations, called canonical vectors, that maximize the correlation between the transformed datasets. However, in the low-sample high-dimension regime these canonical vector estimates are extremely inaccurate. We use insights from random matrix theory to propose a new algorithm that can reliably estimate canonical vectors in the sample deficient regime. Through numerical simulations we showcase that our new algorithm is robust to both limited training data and overestimating the dimension of the signal subspaces.