# Towards Tuning-Free Minimum-Volume Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2309.13733 · HTML: https://mlsanity.com/paper/2309.13733/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## Builds on (most cited first, 3 of 3)

- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation](https://mlsanity.com/paper/1310.7529/) (2013)

## Built on by (most cited first, 1 of 1)

- [Maximum-Volume Nonnegative Matrix Factorization](https://mlsanity.com/paper/2602.04795/) (2026)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.@ (2019) introduced a minimum-volume NMF for the identifiable recovery of rank-deficient matrices in the presence of noise. The performance of their formulation, however, requires the selection of a tuning parameter whose optimal value depends on the unknown noise level. In this work, we propose an alternative formulation of minimum-volume NMF inspired by the square-root lasso and its tuning-free properties. Our formulation also requires the selection of a tuning parameter, but its optimal value does not depend on the noise level. To fit our NMF model, we propose a majorization-minimization (MM) algorithm that comes with global convergence guarantees. We show empirically that the optimal choice of our tuning parameter is insensitive to the noise level in the data.