Matrix Completion with Prior Subspace Information via Maximizing Correlation
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This paper studies the problem of completing a low-rank matrix from a few random entries with the help of prior subspace information. Assuming that we have access to the column and row subspaces of the desired matrix, a new approach is proposed to incorporate the prior subspace information into the vanilla matrix completion program. Apart from promoting low-rank property, the proposed approach maximizes the correlation between the desired matrix and the matrix constructed by prior subspace information. The theoretical guarantee is established for the proposed method, which shows that with suitable prior information, the proposed approach can reduce the sample size of matrix completion by a logarithmic factor.
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