# Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition

Source: [Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition](<https://www.sota2.com/research/paper/690d7ce82828b7cc6937cbd5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-08T05:01:25.623Z

Authors: Giovanni Barbarino, Nicolas Gillis, Subhayan Saha

Published: 2025-11-06T11:36:32.000Z

## Abstract

Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise under a condition referred to as the expanded sufficiently scattered condition which requires the data points to be sufficiently well scattered in the latent simplex generated by the basis vectors.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2511.04291>)

[PDF](<https://arxiv.org/pdf/2511.04291.pdf>)