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I have a matrix $X \in \mathbb{R}^{m\times n}$ and I want to estimate it with a dense matrix $Y^{m\times n}$ such that $Y$ is still close to $X$ in some distance measure. Is this doable in a computationally efficient way? While the sparse estimation is commonly used, but all my efforts for a regularization based solution ended up in non-convex optimization.

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Why not find a sparse neighbor and then add a matrix of all epsilons? –  Dustin G. Mixon May 28 '13 at 0:16
Theoretically you are right. But practically, I want the non-zero elements to be non-negligible, as well. –  Taha May 28 '13 at 0:45
You should be more specific in your definition of "dense." –  Dustin G. Mixon May 28 '13 at 0:49

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