# On Identifiability of Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1709.00614 · HTML: https://mlsanity.com/paper/1709.00614/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2017.

## Built on by (most cited first, 30 of 34)

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- [Deep Nonnegative Matrix Factorization with Beta Divergences](https://mlsanity.com/paper/2309.08249/) (2023)
- [Nonnegative matrix factorizations and related compositional models: Equivalence, identifiability, and an application on the grain-size analysis of sediments](https://mlsanity.com/paper/2512.22282/) (2025)
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- [Risk budget portfolios with convex Non-negative Matrix Factorization](https://mlsanity.com/paper/2204.02757/) (2022)
- [A Bayesian Perspective for Determinant Minimization Based Robust Structured Matrix Factorizatio](https://mlsanity.com/paper/2302.08416/) (2023)

## Abstract (arXiv)

In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are sufficiently scattered over the nonnegative orthant, while no structural assumption is imposed on the other factor except being full-rank. This is by far the mildest condition under which the latent factors are provably identifiable from the NMF model.