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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

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences
Faculty of Social Sciences > Warwick Business School
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:
DateEvent
January 2016Published
25 November 2015Accepted
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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