# Rethinking Non-Negative Matrix Factorization with Implicit Neural Representations

arXiv: https://arxiv.org/abs/2404.04439 · HTML: https://mlsanity.com/paper/2404.04439/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 5 Apr 2024.

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

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Neural Acoustic Fields](https://mlsanity.com/paper/2204.00628/) (2022)
- [Siamese SIREN: Audio Compression with Implicit Neural Representations](https://mlsanity.com/paper/2306.12957/) (2023)
- [Hypernetworks build Implicit Neural Representations of Sounds](https://mlsanity.com/paper/2302.04959/) (2023)
- [Optimizing Short-Time Fourier Transform Parameters via Gradient Descent](https://mlsanity.com/paper/2010.15049/) (2020)
- [A Neural Network Alternative to Non-Negative Audio Models](https://mlsanity.com/paper/1609.03296/) (2016)
- [Point Cloud Audio Processing](https://mlsanity.com/paper/2105.02469/) (2021)
- [Least-squares methods for nonnegative matrix factorization over rational functions](https://mlsanity.com/paper/2209.12579/) (2022)

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

- [Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA](https://mlsanity.com/paper/2507.09091/) (2025)

## Abstract (arXiv)

Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing regularly-sampled data, i.e., data that can be stored in a matrix. For audio, this has led to numerous applications using time-frequency (TF) representations like the Short-Time Fourier Transform. However extending these applications to irregularly-spaced TF representations, like the Constant-Q transform, wavelets, or sinusoidal analysis models, has not been possible since these representations cannot be directly stored in matrix form. In this paper, we formulate NMF in terms of learnable functions (instead of vectors) and show that NMF can be extended to a wider variety of signal classes that need not be regularly sampled.