Sketched Column-Based Matrix Approximation With Side Information

In prior work, it was shown that high performance matrix approximation/completion was possible when only a few fully sampled columns were available of a ground truth matrix if there was appropriate side information on the rowspace of the matrix. Several applications from quantum chemistry, magnetic resonance imaging, etc. necessitate structured (versus random) sampling, but do have other domain-specific side information that can be exploited. Herein, it is shown that further complexity reduction is possible, with limited loss in performance, if one only has access to a sketch of the rowspace information. A spectral error bound is derived, which characterizes the needed dimension of the sketched side information. This bound directly considers the accuracy of the row-space information. Numerical results validate the computational efficiency and accuracy offered by the new algorithm.