# Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing

arXiv: https://arxiv.org/abs/1903.04362 · HTML: https://mlsanity.com/paper/1903.04362/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 10 of 10)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applications](https://mlsanity.com/paper/2209.12638/) (2022)
- [Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software](https://mlsanity.com/paper/2402.06019/) (2024)
- [Sum-of-norms regularized Nonnegative Matrix Factorization](https://mlsanity.com/paper/2407.00706/) (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)
- [Maximum-Volume Nonnegative Matrix Factorization](https://mlsanity.com/paper/2602.04795/) (2026)
- [Identification of NMF by choosing maximum-volume basis vectors](https://mlsanity.com/paper/2603.24227/) (2026)
- [PiouCrypt: Decentralized Lattice-based Method for Visual Symmetric Cryptography](https://mlsanity.com/paper/2204.08017/) (2022)
- [Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates](https://mlsanity.com/paper/2503.24075/) (2025)

## Abstract (arXiv)

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume regularizers, and compare them on endmember recovery in hyperspectral unmixing. The NMF algorithms developed in this work are shown to outperform the state-of-the-art volume-regularized NMF methods, and produce meaningful decompositions on real-world hyperspectral images in situations where endmembers are highly mixed (no pure pixels). Furthermore, our extensive numerical experiments show that when the data is highly separable, meaning that there are data points close to the true endmembers, and there are a few endmembers, the regularizer based on the determinant of the Gramian produces the best results in most cases. For data that is less separable and/or contains more endmembers, the regularizer based on the logarithm of the determinant of the Gramian performs best in general.