# Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey

arXiv: https://arxiv.org/abs/2405.03615 · HTML: https://mlsanity.com/paper/2405.03615/

## 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 (most cited first, 13 of 13)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization](https://mlsanity.com/paper/1504.01777/) (2015)
- [Clustering by Orthogonal NMF Model and Non-Convex Penalty Optimization](https://mlsanity.com/paper/1906.00570/) (2019)
- [Unsupervised Feature Selection with Adaptive Structure Learning](https://mlsanity.com/paper/1504.00736/) (2015)
- [A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering](https://mlsanity.com/paper/1709.10323/) (2017)
- [HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction](https://mlsanity.com/paper/2101.06827/) (2021)
- [Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering](https://mlsanity.com/paper/2005.09229/) (2020)
- [Self-supervised Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2103.01689/) (2021)
- [Log-based Sparse Nonnegative Matrix Factorization for Data Representation](https://mlsanity.com/paper/2204.10647/) (2022)
- [Approximation Algorithms for Orthogonal Non-negative Matrix Factorization](https://mlsanity.com/paper/2103.01398/) (2021)
- [Matrix tri-factorization over the tropical semiring](https://mlsanity.com/paper/2305.06624/) (2023)

## Built on by (most cited first, 7 of 7)

- [Riemannian Optimization on Relaxed Indicator Matrix Manifold](https://mlsanity.com/paper/2503.20505/) (2025)
- [Optimizing Feature Selection with Genetic Algorithms: A Review of Methods and Applications](https://mlsanity.com/paper/2409.14563/) (2024)
- [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)
- [Identification of NMF by choosing maximum-volume basis vectors](https://mlsanity.com/paper/2603.24227/) (2026)
- [Lee and Seung (2000)'s Algorithms for Non-negative Matrix Factorization: A Supplementary Proof Guide](https://mlsanity.com/paper/2501.11341/) (2025)
- [Discovering Sparse Counterfactual Factors via Latent Adjustment for Survey-based Community Intervention](https://mlsanity.com/paper/2605.04460/) (2026)
- [Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize](https://mlsanity.com/paper/2608.22681/) (2026)

## 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.