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Low-rank matrix completion is an important problem with extensive real-worldapplications. When observations are uniformly sampled from the underlyingmatrix entries, existing methods all require the matrix to be incoherent. Thispaper provides the first working method for coherent matrix completion underthe standard uniform sampling model. Our approach is based on the weightednuclear norm minimization idea proposed in several recent work, and our keycontribution is a practical method to compute the weighting matrices so thatthe leverage scores become more uniform after weighting. Under suitableconditions, we are able to derive theoretical results, showing theeffectiveness of our approach. Experiments on synthetic data show that ourapproach recovers highly coherent matrices with high precision, whereas thestandard unweighted method fails even on noise-free data.

Adjusting Leverage Scores by Row Weighting: A Practical Approach to Coherent Matrix Completion