Convergence Analysis for Rectangular Matrix Completion Using Burer-Monteiro Factorization and Gradient Descent
نویسندگان
چکیده
We address the rectangular matrix completion problem by lifting the unknown matrix to a positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over the semidefinite factor using a simple gradient descent scheme. WithO(μr2κ2nmax(μ, log n)) random observations of a n1×n2 μ-incoherent matrix of rank r and condition number κ, where n = max(n1, n2), the algorithm linearly converges to the global optimum with high probability.
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عنوان ژورنال:
- CoRR
دوره abs/1605.07051 شماره
صفحات -
تاریخ انتشار 2016