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Finding approximately rank-one submatrices with the nuclear norm and $\ell_1$-Norm
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Doan, Xuan Vinh and Vavasis, Stephen (2013) Finding approximately rank-one submatrices with the nuclear norm and $\ell_1$-Norm. SIAM Journal on Optimization, Volume 23 (Number 4). pp. 2502-2540. doi:10.1137/100814251 ISSN 1052-6234.
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Official URL: http://dx.doi.org/10.1137/100814251
Abstract
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the properties of the optimal solutions. We establish conditions under which the optimal solution of the convex formulation has a specific sparse structure. Finally, we show that, under certain hypotheses, with high probability, the approach can recover the rank-one submatrix even when it is corrupted with random noise and inserted as a submatrix into a much larger random noise matrix.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Arts > English and Comparative Literary Studies > Yesu Persaud Centre for Caribbean Studies | ||||
| Journal or Publication Title: | SIAM Journal on Optimization | ||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||
| ISSN: | 1052-6234 | ||||
| Official Date: | 2013 | ||||
| Dates: |
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| Volume: | Volume 23 | ||||
| Number: | Number 4 | ||||
| Page Range: | pp. 2502-2540 | ||||
| DOI: | 10.1137/100814251 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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