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CORR
2011
Springer

Large-Scale Convex Minimization with a Low-Rank Constraint

7 years 9 months ago
Large-Scale Convex Minimization with a Low-Rank Constraint
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left and right singular vectors corresponding to the largest singular value of a certain matrix, which can be calculated in linear time. This leads to an algorithm which can scale to large matrices arising in several applications such as matrix completion for collaborative filtering and robust low rank matrix approximation.
Shai Shalev-Shwartz, Alon Gonen, Ohad Shamir
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors Shai Shalev-Shwartz, Alon Gonen, Ohad Shamir
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