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JMLR
2012

High-Rank Matrix Completion

12 years 2 months ago
High-Rank Matrix Completion
This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full rank. Since the columns belong to a union of subspaces, this problem may also be viewed as a missing-data version of the subspace clustering problem. Let X be an n×N matrix whose (complete) columns lie in a union of at most k subspaces, each of rank ≤ r < n, and assume N ≫ kn. The main result of the paper shows that under mild assumptions each column of X can be perfectly recovered with high probability from an incomplete version so long as at least CrN log2 (n) entries of X are observed uniformly at random, with C > 1 a constant depending on the usual incoherence conditions, the geometrical arrangement of subspaces, and the distribution of columns over the sub...
Brian Eriksson, Laura Balzano, Robert Nowak
Added 27 Sep 2012
Updated 27 Sep 2012
Type Journal
Year 2012
Where JMLR
Authors Brian Eriksson, Laura Balzano, Robert Nowak
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