Efficient Algorithms for Maximum Covariance Analysis of Datasets with Many Variables and Fewer Realizations: A Revisit

Abstract

Fast and reliable algorithms for maximum covariance analysis (MCA) are investigated. The traditional algorithm based on the direct singular value decomposition (SVD) of a covariance matrix is computationally expensive for large datasets. An alternate algorithm proposed in this study uses the QR factorization technique to reduce the computational burden of the MCA of datasets with many variables and fewer realizations. It is slightly slower but more reliable, as indicated in an example, than an existing alternate algorithm based on the eigenvalue decomposition of a quadruple matrix product. It is faster than another alternate algorithm that uses the principal component analyses of the datasets as the preliminary step of the MCA.