  This paper studies the problem of completing a low-rank matrix from a few of
its random entries with the aid of prior information. We suggest a strategy to
incorporate prior information into the standard matrix completion procedure by
maximizing the correlation between the original signal and the prior
information. We also establish performance guarantees for the proposed method,
which show that with suitable prior information, the proposed procedure can
reduce the sample complexity of the standard matrix completion by a logarithmic
factor. To illustrate the theory, we further analyze an important practical
application where the prior subspace information is available. Both synthetic
and real-world experiments are provided to verify the validity of the theory.
