- Finding approximately rank-one submatrices with the nuclear norm and l1 norm Xuan Vinh Doan(vanxuanmath.uwaterloo.ca) Stephen A Vavasis(vavasismath.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 ) Citation: Download: [PDF]Entry Submitted: 11/08/2010Entry Accepted: 11/08/2010Entry Last Modified: 11/08/2010Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.