# Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review

arXiv: https://arxiv.org/abs/2205.09933 · HTML: https://mlsanity.com/paper/2205.09933/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 193 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 27 of 27)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization](https://mlsanity.com/paper/1708.02883/) (2017)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Multilayer tensor factorization with applications to recommender systems](https://mlsanity.com/paper/1711.01598/) (2017)
- [Spectral Unmixing via Data-guided Sparsity](https://mlsanity.com/paper/1403.3155/) (2014)
- [Hyperspectral Image Unmixing with Endmember Bundles and Group Sparsity Inducing Mixed Norms](https://mlsanity.com/paper/1805.10232/) (2018)
- [Robust Collaborative Nonnegative Matrix Factorization For Hyperspectral Unmixing (R-CoNMF)](https://mlsanity.com/paper/1506.04870/) (2015)
- [Truncated Cauchy Non-negative Matrix Factorization](https://mlsanity.com/paper/1906.00495/) (2019)
- [Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing](https://mlsanity.com/paper/1903.04362/) (2019)
- [Spectral Unmixing of Hyperspectral Imagery using Multilayer NMF](https://mlsanity.com/paper/1408.2810/) (2014)
- [Deep matrix factorizations](https://mlsanity.com/paper/2010.00380/) (2020)
- [Superpixel Based Graph Laplacian Regularization for Sparse Hyperspectral Unmixing](https://mlsanity.com/paper/2007.14033/) (2020)
- [End-to-end Learning of a Convolutional Neural Network via Deep Tensor Decomposition](https://mlsanity.com/paper/1805.06523/) (2018)
- [Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability](https://mlsanity.com/paper/1811.02413/) (2018)
- [Dual-constrained Deep Semi-Supervised Coupled Factorization Network with Enriched Prior](https://mlsanity.com/paper/2009.03714/) (2020)
- [A Low-rank Tensor Regularization Strategy for Hyperspectral Unmixing](https://mlsanity.com/paper/1803.06355/) (2018)
- [Learning the Hierarchical Parts of Objects by Deep Non-Smooth Nonnegative Matrix Factorization](https://mlsanity.com/paper/1803.07226/) (2018)
- [Deep Approximately Orthogonal Nonnegative Matrix Factorization for Clustering](https://mlsanity.com/paper/1711.07437/) (2017)
- [Robust Hyperspectral Unmixing with Correntropy based Metric](https://mlsanity.com/paper/1305.7311/) (2013)
- [Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models](https://mlsanity.com/paper/1501.05684/) (2015)
- [Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: a Hyperspectral Unmixing Method Dealing with Intra-class Variability](https://mlsanity.com/paper/1702.07630/) (2017)
- [Sparsity Constrained Distributed Unmixing of Hyperspectral Data](https://mlsanity.com/paper/1902.07593/) (2019)
- [Deep Self-representative Concept Factorization Network for Representation Learning](https://mlsanity.com/paper/1912.06444/) (2019)
- [Deep Tensor Factorization for Spatially-Aware Scene Decomposition](https://mlsanity.com/paper/1905.01391/) (2019)

## Built on by (most cited first, 13 of 13)

- [Adaptive Multi-Order Graph Regularized NMF with Dual Sparsity for Hyperspectral Unmixing](https://mlsanity.com/paper/2503.19258/) (2025)
- [Bidirectional recurrent imputation and abundance estimation of LULC classes with MODIS multispectral time series and geo-topographic and climatic data](https://mlsanity.com/paper/2310.07223/) (2023)
- [Learning nonnegative matrix factorizations from compressed data](https://mlsanity.com/paper/2409.04994/) (2024)
- [Neural Network for Blind Unmixing: a novel MatrixConv Unmixing (MCU) Approach](https://mlsanity.com/paper/2503.08745/) (2025)
- [Hyperspectral Image Generation with Unmixing Guided Diffusion Model](https://mlsanity.com/paper/2506.02601/) (2025)
- [Leveraging Convolutional and Graph Networks for an Unsupervised Remote Sensing Labelling Tool](https://mlsanity.com/paper/2508.00506/) (2025)
- [Phase-Locked SNR Band Selection for Weak Mineral Signal Detection in Hyperspectral Imagery](https://mlsanity.com/paper/2508.00539/) (2025)
- [Sparsity and Total Variation Constrained Multilayer Linear Unmixing for Hyperspectral Imagery](https://mlsanity.com/paper/2508.03403/) (2025)
- [Transformer-Guided Content-Adaptive Graph Learning for Hyperspectral Unmixing](https://mlsanity.com/paper/2509.03376/) (2025)
- [WS-Net: Weak-Signal Representation Learning and Gated Abundance Reconstruction for Hyperspectral Unmixing via State-Space and Weak Signal Attention Fusion](https://mlsanity.com/paper/2603.09037/) (2026)
- [Polyhedral Unmixing: Bridging Semantic Segmentation with Hyperspectral Unmixing via Polyhedral-Cone Partitioning](https://mlsanity.com/paper/2603.29438/) (2026)
- [A Deep Equilibrium Network for Hyperspectral Unmixing](https://mlsanity.com/paper/2604.11279/) (2026)
- [Hyperspectral Unmixing Hierarchies](https://mlsanity.com/paper/2604.16969/) (2026)

## Abstract (arXiv)

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in solving this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the article with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.