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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.
Convex Analysis
R. T. Rockafellar · 1970
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Problem 73-14, rank factorization of nonnegative matrices by Berman and Plemmons
L. B. Thomas · 1974
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Nonnegative ranks, decompositions and factorizations of nonnegative matrices
J. Cohen and U. Rothblum · 1993
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Properties of linear approximations of matrices in the spectral norm
K. Ziȩtak · 1993
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Matrix Computations, 3rd Edition
G. H. Golub and C. F. Van Loan · 1996
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T. Hofmann · 1999
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Learning the parts of objects by non-negative matrix factorization
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Rank-sparsity incoherence for matrix decomposition
V. Chandrasekaran, S. Sanghavi, P.A. Parrilo, and A. Willsky · 2009
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Stephen A. Vavasis · 2009
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Using underapproximations for sparse nonnegative matrix factorization
N. Gillis and F. Glineur · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
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Nonnegative matrix factorization via rank-one downdating
Michael Biggs, Ali Ghodsi, and Stephen A. Vavasis · 2008
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B. Recht, M. Fazel, and P. Parrilo · 2010
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