Efficient Dimensionality Reduction for Canonical Correlation Analysis
  We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input matrices, and then applies any CCA algorithm to the new pair of matrices. The algorithm computes an approximate CCA to the original pair of matrices with provable guarantees, while requiring asymptotically less operations than the state-of-the-art exact algorithms. 
Haim Avron, Christos Boutsidis, Sivan Toledo and Anastasios Zouzias
cs.DS math.NA