Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provably

  title={Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provably},
  author={Dohyung Park and Anastasios Kyrillidis and Constantine Caramanis and Sujay Sanghavi},
A rank-r matrix X ∈ Rm×n can be written as a product UV >, where U ∈ Rm×r and V ∈ Rn×r. One could exploit this observation in optimization: e.g., consider the minimization of a convex function f(X) over rank-r matrices, where the set of rank-r matrices is modeled via the factorization UV >. Though such parameterization reduces the number of variables, and is more computationally efficient (of particular interest is the case r min{m,n}), it comes at a cost: f(UV >) becomes a non-convex function… CONTINUE READING
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