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 nonconvex optimization.
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1$\begingroup$ Why not find a sparse neighbor and then add a matrix of all epsilons? $\endgroup$– Dustin G. MixonCommented May 28, 2013 at 0:16

$\begingroup$ Theoretically you are right. But practically, I want the nonzero elements to be nonnegligible, as well. $\endgroup$– TahaCommented May 28, 2013 at 0:45

$\begingroup$ You should be more specific in your definition of "dense." $\endgroup$– Dustin G. MixonCommented May 28, 2013 at 0:49
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