Multiplicative Updates for Convolutional NMF Under $β$-Divergence
This work addresses a technical issue in signal processing and machine learning for researchers, but it is incremental as it builds on existing NMF methods.
The authors tackled the problem of inexact updates in convolutional non-negative matrix factorization (NMF) by generalizing it with β-divergence and presenting correct multiplicative updates in closed form, resulting in stable and consistent convergence performance across common β values.
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 $β$.