Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A randomized algorithm for principal component analysis   Principal component analysis (PCA) requires the computation of a low-rank
approximation to a matrix containing the data being analyzed. In many
applications of PCA, the best possible accuracy of any rank-deficient
approximation is at most a few digits (measured in the spectral norm, relative
to the spectral norm of the matrix being approximated). In such circumstances,
efficient algorithms have not come with guarantees of good accuracy, unless one
or both dimensions of the matrix being approximated are small. We describe an
efficient algorithm for the low-rank approximation of matrices that produces
accuracy very close to the best possible, for matrices of arbitrary sizes. We
illustrate our theoretical results via several numerical examples.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math