# Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation

arXiv: https://arxiv.org/abs/1310.7529 · HTML: https://mlsanity.com/paper/1310.7529/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2013.

## Built on by (most cited first, 18 of 18)

- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)
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- [Refinement of Hottopixx Method for Nonnegative Matrix Factorization Under Noisy Separability](https://mlsanity.com/paper/2109.02863/) (2021)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [On the Robustness of the Successive Projection Algorithm](https://mlsanity.com/paper/2411.16195/) (2024)
- [Endmember Extraction from Hyperspectral Images Using Self-Dictionary Approach with Linear Programming](https://mlsanity.com/paper/2404.13098/) (2024)
- [Co-Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/2109.00749/) (2021)
- [Towards Tuning-Free Minimum-Volume Nonnegative Matrix Factorization](https://mlsanity.com/paper/2309.13733/) (2023)
- [Coseparable Nonnegative Tensor Factorization With T-CUR Decomposition](https://mlsanity.com/paper/2401.16836/) (2024)
- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)
- [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)
- [fMBN-E: Efficient Unsupervised Network Structure Ensemble and Selection for Clustering](https://mlsanity.com/paper/2107.02071/) (2021)
- [Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence](https://mlsanity.com/paper/2410.07786/) (2024)
- [Hyperspectral Image Data Reduction for Endmember Extraction](https://mlsanity.com/paper/2512.10506/) (2025)
- [Automating Historical Insight Extraction from Large-Scale Newspaper Archives via Neural Topic Modeling](https://mlsanity.com/paper/2512.11635/) (2025)
- [Super-r'esolution non supervis'ee d'images hyperspectrales de t'el'ed'etection utilisant un entrainement enti`erement synth'etique](https://mlsanity.com/paper/2602.02552/) (2026)

## Abstract (arXiv)

In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive projection algorithm (SPA), but takes advantage of the nonnegativity constraint in the decomposition. We prove that SNPA is more robust than SPA and can be applied to a broader class of nonnegative matrices. This is illustrated on some synthetic data sets, and on a real-world hyperspectral image.