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.

• Publication year

  2014

• Venue

  arXiv.org

• Publication date

  2014-01-21

• Fields of study

  Mathematics, Computer Science, Environmental Science

• Identifiers
  DOI 10.1201/b17558-15arXiv 1401.5226
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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