2014/01/21 by Nicolas Gillis, Gillis, Nicolas · 3 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Image Retrieval and Classification Techniques #Information Retrieval (cs.IR) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1401.5226
openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.