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Large-Scale Convex Minimization with a Low-Rank Constraint
Shai Shalev-Shwartz, Alon Gonen and Ohad Shamir
In: ICML 2011, June 2011, Bellevue, Washington, USA.
AbstractWe address the problem of minimizing a con-
vex function over the space of large matri-
ces with low rank. While this optimization
problem is hard in general, we propose an ef-
cient greedy algorithm and derive its formal
approximation guarantees. Each iteration of
the algorithm involves (approximately) nd-
ing the left and right singular vectors cor-
responding 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 comple-
tion for collaborative ltering and robust low
rank matrix approximation. [Edit]
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