Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization   The linearly constrained matrix rank minimization problem is widely
applicable in many fields such as control, signal processing and system
identification. The tightest convex relaxation of this problem is the linearly
constrained nuclear norm minimization. Although the latter can be cast as a
semidefinite programming problem, such an approach is computationally expensive
to solve when the matrices are large. In this paper, we propose fixed point and
Bregman iterative algorithms for solving the nuclear norm minimization problem
and prove convergence of the first of these algorithms. By using a homotopy
approach together with an approximate singular value decomposition procedure,
we get a very fast, robust and powerful algorithm, which we call FPCA (Fixed
Point Continuation with Approximate SVD), that can solve very large matrix rank
minimization problems. Our numerical results on randomly generated and real
matrix completion problems demonstrate that this algorithm is much faster and
provides much better recoverability than semidefinite programming solvers such
as SDPT3. For example, our algorithm can recover 1000 x 1000 matrices of rank
50 with a relative error of 1e-5 in about 3 minutes by sampling only 20 percent
of the elements. We know of no other method that achieves as good
recoverability. Numerical experiments on online recommendation, DNA microarray
data set and image inpainting problems demonstrate the effectiveness of our
algorithms.

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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th