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Finding the largest low-rank clusters with Ky Fan 2-k-norm and l1-norm
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Doan, Xuan Vinh and Vavasis, Stephen (2016) Finding the largest low-rank clusters with Ky Fan 2-k-norm and l1-norm. SIAM Journal on Optimization, 26 (1). pp. 274-312. doi:10.1137/140962097
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Official URL: http://dx.doi.org/10.1137/140962097
Abstract
We propose a convex optimization formulation with the Ky Fan 2-k-norm and l1-norm to find k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under certain hypotheses, with high probability, the approach can recover rank-one submatrix blocks even when they are corrupted with random noise and inserted into a much larger matrix with other random noise blocks.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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| Library of Congress Subject Headings (LCSH): | Matrices, Gene expression, Computational linguistics | ||||||
| Journal or Publication Title: | SIAM Journal on Optimization | ||||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||||
| ISSN: | 1052-6234 | ||||||
| Official Date: | January 2016 | ||||||
| Dates: |
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| Volume: | 26 | ||||||
| Number: | 1 | ||||||
| Number of Pages: | 39 | ||||||
| Page Range: | pp. 274-312 | ||||||
| DOI: | 10.1137/140962097 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | United States. Air Force. Office of Scientific Research (AFOSR), Natural Sciences and Engineering Research Council of Canada (NSERC), MITACS (Network) |
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