# Multiplicative Updates for Convolutional NMF Under β-Divergence

arXiv: https://arxiv.org/abs/1803.05159 · HTML: https://mlsanity.com/paper/1803.05159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2018.

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

- [Multiplicative update rules for accelerating deep learning training and increasing robustness](https://mlsanity.com/paper/2307.07189/) (2023)

## Abstract (arXiv)

In this letter, we generalize the convolutional NMF by taking the β-divergence as the contrast function and present the correct multiplicative updates for its factors in closed form. The new updates unify the β-NMF and the convolutional NMF. We state why almost all of the existing updates are inexact and approximative w.r.t. the convolutional data model. We show that our updates are stable and that their convergence performance is consistent across the most common values of β.