The Why and How of Nonnegative Matrix Factorization
Abstract
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.
Cite
@article{arxiv.1401.5226,
title = {The Why and How of Nonnegative Matrix Factorization},
author = {Nicolas Gillis},
journal= {arXiv preprint arXiv:1401.5226},
year = {2014}
}
Comments
25 pages, 5 figures. Some typos and errors corrected, Section 3.2 reorganized