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

2010/11/08 by Xuan Vinh Doan, Doan, Xuan Vinh, Stephen A. Vavasis +1 · 1 citation
Mathematics · #65F30 #90C25 #FOS: Mathematics #G.1.3 #G.1.6 #H.3.3 #Optimization and Control (math.OC) #acm:65F30 #acm:90C25 #math.OC #msc:65F30 #msc:90C25

paper · pdf · doi:10.48550/arxiv.1011.1839

Submitted to SIAM J. Optimization

arxiv created 2010/11/08 · arxiv updated 2010/11/09

Abstract

We propose a convex optimization formulation with the nuclear norm and ℓ₁-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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