mlsanityData to 7 Oct 2026

On Identifiability of Nonnegative Matrix Factorization

arXiv 1709.00614 ↗First posted 2 Sep 2017cs.LG stat.MLcited by 34

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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.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Sep 2017.

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Citing papers per year: 2021: 5; 2022: 10; 2023: 7; 2024: 2; 2025: 8; 2026: 2.

34 papers.

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  1. 2021Provably End-to-end Label-Noise Learning without Anchor Pointscited by 97
  2. 2025Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Modelscited by 67
  3. 2024Non-negative Contrastive Learningcited by 18
  4. 2021Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Modelscited by 14
  5. 2022Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiabilitycited by 14
  6. 2023Deep Learning From Crowdsourced Labels: Coupled Cross-entropy Minimization, Identifiability, and Regularizationcited by 12
  7. 2023Interpretable Meta-Learning of Physical Systemscited by 11
  8. 2023Clustered Embedding Learning for Recommender Systemscited by 8
  9. 2021Crowdsourcing via Annotator Co-occurrence Imputation and Provable Symmetric Nonnegative Matrix Factorizationcited by 6
  10. 2022Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixingcited by 6
  11. 2022Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sourcescited by 6
  12. 2022Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applicationscited by 5
22 more
  1. 2023Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approachcited by 5
  2. 2022Majorization-minimization for Sparse Nonnegative Matrix Factorization with the β-divergencecited by 4
  3. 2025Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiabilitycited by 4
  4. 2021Recovery of Joint Probability Distribution from one-way marginals: Low rank Tensors and Random Projectionscited by 3
  5. 2022Correlative Information Maximization Based Biologically Plausible Neural Networks for Correlated Source Separationcited by 3
  6. 2024Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Softwarecited by 3
  7. 2022Provable Subspace Identification Under Post-Nonlinear Mixturescited by 2
  8. 2025Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layercited by 2
  9. 2022Semi-Supervised Convolutive NMF for Automatic Piano Transcriptioncited by 1
  10. 2022Joint Probability Estimation Using Tensor Decomposition and Dictionariescited by 1
  11. 2023Estimating Joint Probability Distribution With Low-Rank Tensor Decomposition, Radon Transforms and Dictionariescited by 1
  12. 2023Deep Nonnegative Matrix Factorization with Beta Divergencescited by 1
  13. 2025Identifiability of Nonnegative Tucker Decompositions -- Part I: Theorycited by 1
  14. 2025Nonnegative matrix factorizations and related compositional models: Equivalence, identifiability, and an application on the grain-size analysis of sedimentscited by 1
  15. 2026Maximum-Volume Nonnegative Matrix Factorizationcited by 1
  16. 2021Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problemcited by 0
  17. 2022Risk budget portfolios with convex Non-negative Matrix Factorizationcited by 0
  18. 2023A Bayesian Perspective for Determinant Minimization Based Robust Structured Matrix Factorizatiocited by 0
  19. 2025Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimizationcited by 0
  20. 2025A Tractable Two-Step Linear Mixing Model Solved with Second-Order Optimization for Spectral Unmixing under Variabilitycited by 0
  21. 2025Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Conditioncited by 0
  22. 2026Identifying Latent Actions and Dynamics from Offline Data via Demonstrator Diversitycited by 0