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Finding approximately rank-one submatrices with the nuclear norm and l1 norm

Authors
  • Doan, Xuan Vinh
  • Vavasis, Stephen A.
Type
Preprint
Publication Date
Nov 08, 2010
Submission Date
Nov 08, 2010
Identifiers
arXiv ID: 1011.1839
Source
arXiv
License
Yellow
External links

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.

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