Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: CUR Decompositions, Approximations, and Perturbations   This article discusses a useful tool in dimensionality reduction and low-rank
matrix approximation called the CUR decomposition. Various viewpoints of this
method in the literature are synergized and are compared and contrasted;
included in this is a new characterization of exact CUR decompositions. A novel
perturbation analysis is performed on CUR approximations of noisy versions of
low-rank matrices, which compares them with the putative CUR decomposition of
the underlying low-rank part. Additionally, we give new column and row sampling
results which allow one to conclude that a CUR decomposition of a low-rank
matrix is attained with high probability. We then illustrate the stability of
these sampling methods under the perturbations studied before, and provide
numerical illustrations of the methods and bounds discussed.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys