A Variational Autoencoder for Probabilistic Non-Negative Matrix Factorisation
This work provides a probabilistic extension to NMF for researchers in fields like image analysis, finance, and genomics, but it is incremental as it combines existing VAE and NMF techniques.
The authors tackled the problem of making non-negative matrix factorization probabilistic by integrating a variational autoencoder, enabling data generation and linking latent and input variables through probability distributions. They demonstrated the method's effectiveness on image, financial time series, and genomic datasets.
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.