# A variational autoencoder-based nonnegative matrix factorisation model for deep dictionary learning

arXiv: https://arxiv.org/abs/2301.07272 · HTML: https://mlsanity.com/paper/2301.07272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms](https://mlsanity.com/paper/1610.05683/) (2016)
- [Deep Learning of Part-based Representation of Data Using Sparse Autoencoders with Nonnegativity Constraints](https://mlsanity.com/paper/1601.02733/) (2016)
- [Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms](https://mlsanity.com/paper/1607.00435/) (2016)

## Abstract (arXiv)

Construction of dictionaries using nonnegative matrix factorisation (NMF) has extensive applications in signal processing and machine learning. With the advances in deep learning, training compact and robust dictionaries using deep neural networks, i.e., dictionaries of deep features, has been proposed. In this study, we propose a probabilistic generative model which employs a variational autoencoder (VAE) to perform nonnegative dictionary learning. In contrast to the existing VAE models, we cast the model under a statistical framework with latent variables obeying a Gamma distribution and design a new loss function to guarantee the nonnegative dictionaries. We adopt an acceptance-rejection sampling reparameterization trick to update the latent variables iteratively. We apply the dictionaries learned from VAE-NMF to two signal processing tasks, i.e., enhancement of speech and extraction of muscle synergies. Experimental results demonstrate that VAE-NMF performs better in learning the latent nonnegative dictionaries in comparison with state-of-the-art methods.