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Introduction to Nonnegative Matrix Factorization

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abstract

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions, complexity, algorithms, and its link with extended formulations of polyhedra. In order to put NMF into perspective, the more general problem class of constrained low-rank matrix approximation problems is first briefly introduced.

fields

cs.LG 1

years

2026 1

verdicts

CONDITIONAL 1

representative citing papers

An Exterior Method for Nonnegative Matrix Factorization

cs.LG · 2026-05-19 · conditional · novelty 7.0

eNMF is a new exterior-point algorithm for NMF that initializes from unconstrained factorization, applies a rotation to reach the nonnegative boundary, and empirically outperforms 81 baseline combinations on real and synthetic data.

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  • An Exterior Method for Nonnegative Matrix Factorization cs.LG · 2026-05-19 · conditional · none · ref 36 · internal anchor

    eNMF is a new exterior-point algorithm for NMF that initializes from unconstrained factorization, applies a rotation to reach the nonnegative boundary, and empirically outperforms 81 baseline combinations on real and synthetic data.