# Leveraging Joint-Diagonalization in Transform-Learning NMF

arXiv: https://arxiv.org/abs/2112.05664 · HTML: https://mlsanity.com/paper/2112.05664/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 10 Dec 2021.

## Builds on (most cited first, 5 of 5)

- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2010.01935/) (2020)
- [Beyond Pham's algorithm for joint diagonalization](https://mlsanity.com/paper/1811.11433/) (2018)
- [Nonnegative Matrix Factorization with Transform Learning](https://mlsanity.com/paper/1705.04193/) (2017)
- [A Quasi-Newton algorithm on the orthogonal manifold for NMF with transform learning](https://mlsanity.com/paper/1811.02225/) (2018)

## Abstract (arXiv)

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at learning data representations suited to NMF. In this work, we relate TL-NMF to the classical matrix joint-diagonalization (JD) problem. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach -- termed as JD+NMF -- that estimates the transform through JD, prior to NMF computation. In contrast, we found that when the number of data realizations is limited, not only is JD+NMF no longer equivalent to TL-NMF, but the inherent low-rank constraint of TL-NMF turns out to be an essential ingredient to learn meaningful transforms for NMF.