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

Xuan Vinh Doan(vanxuan***at***math.uwaterloo.ca)
Stephen A Vavasis(vavasis***at***math.uwaterloo.ca)

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.

Keywords: convex programming; nonnegative matrix factorization;rank-one submatrix;nuclear norm

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Data-Mining )


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Entry Submitted: 11/08/2010
Entry Accepted: 11/08/2010
Entry Last Modified: 11/08/2010

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