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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper gives a new convex relaxation for sparse matrix factorization. They show the new relaxation has better denoising performance and lower statistical dimension compared to traditional l_1 or trace norms. However, the new convex relaxation is hard to compute. The paper also involves many potential applications, experiments on denosing performance and application to predict drug-target interactions.