# A Variational Autoencoder for Probabilistic Non-Negative Matrix Factorisation

arXiv: https://arxiv.org/abs/1906.05912 · HTML: https://mlsanity.com/paper/1906.05912/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [Differentiable Dictionary Search: Integrating Linear Mixing with Deep Non-Linear Modelling for Audio Source Separation](https://mlsanity.com/paper/2211.15524/) (2022)
- [On the Relation Between Autoencoders and Non-negative Matrix Factorization, and Their Application for Mutational Signature Extraction](https://mlsanity.com/paper/2405.07879/) (2024)
- [Scalable Amortized Variational Inference for Non-Poisson Buy-'Til-You-Die Models](https://mlsanity.com/paper/2608.19022/) (2026)

## Abstract (arXiv)

We introduce and demonstrate the variational autoencoder (VAE) for probabilistic non-negative matrix factorisation (PAE-NMF). We design a network which can perform non-negative matrix factorisation (NMF) and add in aspects of a VAE to make the coefficients of the latent space probabilistic. By restricting the weights in the final layer of the network to be non-negative and using the non-negative Weibull distribution we produce a probabilistic form of NMF which allows us to generate new data and find a probability distribution that effectively links the latent and input variables. We demonstrate the effectiveness of PAE-NMF on three heterogeneous datasets: images, financial time series and genomic.