# Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF

arXiv: https://arxiv.org/abs/1907.02404 · HTML: https://mlsanity.com/paper/1907.02404/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

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

- [Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiability](https://mlsanity.com/paper/2202.09638/) (2022)
- [Self-supervised Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2103.01689/) (2021)
- [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)
- [Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory](https://mlsanity.com/paper/2505.12713/) (2025)
- [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)
- [GSVD-NMF: Recovering Missing Features in Non-negative Matrix Factorization](https://mlsanity.com/paper/2408.08260/) (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)
- [Maximum Discrepancy Generative Regularization and Non-Negative Matrix Factorization for Single Channel Source Separation](https://mlsanity.com/paper/2404.15296/) (2024)
- [On the Connection Between Non-negative Matrix Factorization and Latent Dirichlet Allocation](https://mlsanity.com/paper/2405.20542/) (2024)
- [Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimization](https://mlsanity.com/paper/2502.17123/) (2025)
- [Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition](https://mlsanity.com/paper/2511.04291/) (2025)
- [Hyperspectral Image Data Reduction for Endmember Extraction](https://mlsanity.com/paper/2512.10506/) (2025)

## Abstract (arXiv)

Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of the sources. To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito β-divergences is a standard and state-of-the-art technique that uses the time-frequency representation of the signal. We present a new NMF model better suited for this task. It is based on the minimization of β-divergences along with a penalty term that promotes the columns of the dictionary matrix to have a small volume. Under some mild assumptions and in noiseless conditions, we prove that this model is provably able to identify the sources. In order to solve this problem, we propose multiplicative updates whose derivations are based on the standard majorization-minimization framework. We show on several numerical experiments that our new model is able to obtain more interpretable results than standard NMF models. Moreover, we show that it is able to recover the sources even when the number of sources present into the mixed signal is overestimated. In fact, our model automatically sets sources to zero in this situation, hence performs model order selection automatically.