# Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization

arXiv: https://arxiv.org/abs/1401.5649 · HTML: https://mlsanity.com/paper/1401.5649/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2014.

## Built on by (most cited first, 16 of 16)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)
- [Joint Majorization-Minimization for Nonnegative Matrix Factorization with the β-divergence](https://mlsanity.com/paper/2106.15214/) (2021)
- [Majorization-minimization for Sparse Nonnegative Matrix Factorization with the β-divergence](https://mlsanity.com/paper/2207.06316/) (2022)
- [AE-RED: A Hyperspectral Unmixing Framework Powered by Deep Autoencoder and Regularization by Denoising](https://mlsanity.com/paper/2307.00269/) (2023)
- [Adaptive Multi-Order Graph Regularized NMF with Dual Sparsity for Hyperspectral Unmixing](https://mlsanity.com/paper/2503.19258/) (2025)
- [Entropy Minimizing Matrix Factorization](https://mlsanity.com/paper/2103.13487/) (2021)
- [Adversarially-Trained Nonnegative Matrix Factorization](https://mlsanity.com/paper/2104.04757/) (2021)
- [Privacy-preserving Non-negative Matrix Factorization with Outliers](https://mlsanity.com/paper/2211.01451/) (2022)
- [A Second-Order Majorant Algorithm for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2303.17992/) (2023)
- [Feature Weighted Non-negative Matrix Factorization](https://mlsanity.com/paper/2103.13491/) (2021)
- [Deep Nonnegative Matrix Factorization with Beta Divergences](https://mlsanity.com/paper/2309.08249/) (2023)
- [Block Majorization Minimization with Extrapolation and Application to β-NMF](https://mlsanity.com/paper/2401.06646/) (2024)
- [DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2503.03465/) (2025)
- [Deep Nonlinear Hyperspectral Unmixing Using Multi-task Learning](https://mlsanity.com/paper/2402.03398/) (2024)
- [SMILE: A Super-resolution Guided Multi-task Learning Method for Hyperspectral Unmixing](https://mlsanity.com/paper/2509.11093/) (2025)

## Abstract (arXiv)

This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding these nonlinearities. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. This results in a new form of robust nonnegative matrix factorization. The data fidelity term is expressed as a beta-divergence, a continuous family of dissimilarity measures that takes the squared Euclidean distance and the generalized Kullback-Leibler divergence as special cases. The penalized objective is minimized with a block-coordinate descent that involves majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods.