# Generalized Fast Multichannel Nonnegative Matrix Factorization Based on Gaussian Scale Mixtures for Blind Source Separation

arXiv: https://arxiv.org/abs/2205.05330 · HTML: https://mlsanity.com/paper/2205.05330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 61 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 9 of 9)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [A Mixture of Generalized Hyperbolic Distributions](https://mlsanity.com/paper/1305.1036/) (2013)
- [Speech enhancement with variational autoencoders and alpha-stable distributions](https://mlsanity.com/paper/1902.03926/) (2019)
- [FastFCA: A Joint Diagonalization Based Fast Algorithm for Audio Source Separation Using A Full-Rank Spatial Covariance Model](https://mlsanity.com/paper/1805.06572/) (2018)
- [FastFCA-AS: Joint Diagonalization Based Acceleration of Full-Rank Spatial Covariance Analysis for Separating Any Number of Sources](https://mlsanity.com/paper/1805.09498/) (2018)
- [Independent Vector Analysis with more Microphones than Sources](https://mlsanity.com/paper/1905.07880/) (2019)
- [Joint-Diagonalizability-Constrained Multichannel Nonnegative Matrix Factorization Based on Multivariate Complex Sub-Gaussian Distribution](https://mlsanity.com/paper/2007.00416/) (2020)
- [A Joint Diagonalization Based Efficient Approach to Underdetermined Blind Audio Source Separation Using the Multichannel Wiener Filter](https://mlsanity.com/paper/2101.08563/) (2021)
- [The expectation-maximization algorithm for autoregressive models with normal inverse Gaussian innovations](https://mlsanity.com/paper/2111.06565/) (2021)

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

- [Neural Multichannel Distant Speaker Diarization with Heavy-tailed Source Separation Model](https://mlsanity.com/paper/2609.12154/) (2026)

## Abstract (arXiv)

This paper describes heavy-tailed extensions of a state-of-the-art versatile blind source separation method called fast multichannel nonnegative matrix factorization (FastMNMF) from a unified point of view. The common way of deriving such an extension is to replace the multivariate complex Gaussian distribution in the likelihood function with its heavy-tailed generalization, e.g., the multivariate complex Student's t and leptokurtic generalized Gaussian distributions, and tailor-make the corresponding parameter optimization algorithm. Using a wider class of heavy-tailed distributions called a Gaussian scale mixture (GSM), i.e., a mixture of Gaussian distributions whose variances are perturbed by positive random scalars called impulse variables, we propose GSM-FastMNMF and develop an expectationmaximization algorithm that works even when the probability density function of the impulse variables have no analytical expressions. We show that existing heavy-tailed FastMNMF extensions are instances of GSM-FastMNMF and derive a new instance based on the generalized hyperbolic distribution that include the normal-inverse Gaussian, Student's t, and Gaussian distributions as the special cases. Our experiments show that the normalinverse Gaussian FastMNMF outperforms the state-of-the-art FastMNMF extensions and ILRMA model in speech enhancement and separation in terms of the signal-to-distortion ratio.