The Why and How of Nonnegative Matrix Factorization

By Nicolas Gillis. arXiv.org, 2014

384 citations recorded by the source corpus.

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.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/634ca7583f9ee4e0c68c9ce278e10227e2c4e819

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

1. Damek Davis
2. Dmitriy Drusvyatskiy

In Media Technology

1. Dmitriy Drusvyatskiy
2. Damek Davis

Citations in the corpus

• Stochastic model-based minimization of weakly convex functions (2018, background): “2] are classical examples, while notable contemporary instances include robust phase retrieval [6, 10], covariance matrix estimation [3, 5], and matrix factorization problems such as NMF [12,13].”