A Variational Autoencoder for Probabilistic Non-Negative Matrix Factorisation

TL;DR

This paper presents a novel probabilistic non-negative matrix factorisation method using a variational autoencoder, enabling data generation and probabilistic analysis across diverse datasets.

Contribution

It introduces PAE-NMF, integrating VAE with NMF by constraining weights and employing Weibull distribution, a novel approach for probabilistic NMF.

Findings

Effective on images, financial time series, and genomic data

Allows data generation and probabilistic interpretation

Links latent variables with input data effectively

Abstract

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.