mlsanityData to 14 Oct 2026

The Why and How of Nonnegative Matrix Factorization

arXiv 1401.5226 ↗First posted 21 Jan 2014stat.ML cs.IR cs.LGcited by 34

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Abstract (arXiv)

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.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Jan 2014.

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Citing papers per year: 2021: 12; 2022: 6; 2023: 4; 2024: 8; 2025: 3; 2026: 1.

34 papers.

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  1. 2021Citizen Participation and Machine Learning for a Better Democracycited by 14
  2. 2022Factorizer: A Scalable Interpretable Approach to Context Modeling for Medical Image Segmentationcited by 12
  3. 2021Probabilistic Simplex Component Analysiscited by 8
  4. 2023A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorizationcited by 6
  5. 2023Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approachcited by 5
  6. 2021Sensing Cox Processes via Posterior Sampling and Positive Basescited by 4
  7. 2021Analysis of Legal Documents via Non-negative Matrix Factorization Methodscited by 3
  8. 2024Identifiable Shared Component Analysis of Unpaired Multimodal Mixturescited by 3
  9. 2021Non-negative matrix factorization algorithms generally improve topic model fitscited by 2
  10. 2021A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizationscited by 2
  11. 2022A Fast Scale-Invariant Algorithm for Non-negative Least Squares with Non-negative Datacited by 2
  12. 2022Separable Quaternion Matrix Factorization for Polarization Imagescited by 2
22 more
  1. 2022Concept-based Explanations using Non-negative Concept Activation Vectors and Decision Tree for CNN Modelscited by 2
  2. 2024Privacy-Preserving Distributed Nonnegative Matrix Factorizationcited by 2
  3. 2021Analysis of the robustness of NMF algorithmscited by 1
  4. 2022Supporting peace negotiations in the Yemen war through machine learningcited by 1
  5. 2023Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matricescited by 1
  6. 2023Stratified-NMF for Heterogeneous Datacited by 1
  7. 2024Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognitioncited by 1
  8. 2024GSVD-NMF: Recovering Missing Features in Non-negative Matrix Factorizationcited by 1
  9. 2024Hybrid Ensemble Deep Graph Temporal Clustering for Spatiotemporal Datacited by 1
  10. 2024TACO: Training-free Sound Prompted Segmentation via Semantically Constrained Audio-visual CO-factorizationcited by 1
  11. 2025Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)cited by 1
  12. 2025Bolster Hallucination Detection via Prompt-Guided Data Augmentationcited by 1
  13. 2021Time series forecasting from partial observations via Non-negative Matrix Factorizationcited by 0
  14. 2021A Comprehensive Review on Non-Neural Networks Collaborative Filtering Recommendation Systemscited by 0
  15. 2021Multi-Channel Automatic Music Transcription Using Tensor Algebracited by 0
  16. 2021Convex Latent Effect Logit Model via Sparse and Low-rank Decompositioncited by 0
  17. 2021Machine Learning for Mediation in Armed Conflictscited by 0
  18. 2022Crime Hot-Spot Modeling via Topic Modeling and Relative Density Estimationcited by 0
  19. 2024Efficient algorithms for regularized Poisson Non-negative Matrix Factorizationcited by 0
  20. 2024Learning nonnegative matrix factorizations from compressed datacited by 0
  21. 2025Testing Hypotheses of Covariate Effects on Topics of Discoursecited by 0
  22. 2026Scalable Minimum-Volume Simplex Estimation with Non-asymptotic Analysiscited by 0