Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Why and How of Nonnegative Matrix Factorization   Nonnegative matrix factorization (NMF) has become a widely used tool for the
analysis of high-dimensional data as it automatically extracts sparse and
meaningful features from a set of nonnegative data vectors. We first illustrate
this property of NMF on three applications, in image processing, text mining
and hyperspectral imaging --this is the why. Then we address the problem of
solving NMF, which is NP-hard in general. We review some standard NMF
algorithms, and also present a recent subclass of NMF problems, referred to as
near-separable NMF, that can be solved efficiently (that is, in polynomial
time), even in the presence of noise --this is the how. Finally, we briefly
describe some problems in mathematics and computer science closely related to
NMF via the nonnegative rank.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat