mlsanityData to 14 Oct 2026

Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey

arXiv 2405.03615 ↗First posted 6 May 2024cs.LGcited by 7

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Abstract (arXiv)

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular and powerful method for dimensionality reduction. Despite its extensive use, there remains a need for a comprehensive analysis of NMF in the context of dimensionality reduction. To address this gap, this paper presents a comprehensive survey of NMF, focusing on its applications in both feature extraction and feature selection. We introduce a classification of dimensionality reduction, enhancing understanding of the underlying concepts. Subsequently, we delve into a thorough summary of diverse NMF approaches used for feature extraction and selection. Furthermore, we discuss the latest research trends and potential future directions of NMF in dimensionality reduction, aiming to highlight areas that need further exploration and development.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 13 of its 169 references that are in the map. First posted on arXiv 6 May 2024.

Builds on

13 of 169 references.

References · 13

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  2. 2015A deep matrix factorization method for learning attribute representationscited by 24
  3. 2018Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorizationcited by 17
  4. 2015Heterogeneous Tensor Decomposition for Clustering via Manifold Optimizationcited by 10
  5. 2019Clustering by Orthogonal NMF Model and Non-Convex Penalty Optimizationcited by 9
  6. 2015Unsupervised Feature Selection with Adaptive Structure Learningcited by 8
  7. 2017A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clusteringcited by 5
  8. 2021HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reductioncited by 5
  9. 2020Two-Dimensional Semi-Nonnegative Matrix Factorization for Clusteringcited by 3
  10. 2021Self-supervised Symmetric Nonnegative Matrix Factorizationcited by 3
  11. 2022Log-based Sparse Nonnegative Matrix Factorization for Data Representationcited by 3
  12. 2021Approximation Algorithms for Orthogonal Non-negative Matrix Factorizationcited by 2
1 more
  1. 2023Matrix tri-factorization over the tropical semiringcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 3.

7 papers.

  1. 2025Riemannian Optimization on Relaxed Indicator Matrix Manifoldcited by 5
  2. 2024Optimizing Feature Selection with Genetic Algorithms: A Review of Methods and Applicationscited by 1
  3. 2025Nonnegative matrix factorizations and related compositional models: Equivalence, identifiability, and an application on the grain-size analysis of sedimentscited by 1
  4. 2026Identification of NMF by choosing maximum-volume basis vectorscited by 1
  5. 2025Lee and Seung (2000)'s Algorithms for Non-negative Matrix Factorization: A Supplementary Proof Guidecited by 0
  6. 2026Discovering Sparse Counterfactual Factors via Latent Adjustment for Survey-based Community Interventioncited by 0
  7. 2026Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySizecited by 0