# Nonnegative Matrix Factorization with Transform Learning

arXiv: https://arxiv.org/abs/1705.04193 · HTML: https://mlsanity.com/paper/1705.04193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2017.

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

- [Leveraging Joint-Diagonalization in Transform-Learning NMF](https://mlsanity.com/paper/2112.05664/) (2021)

## Abstract (arXiv)

Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn a short-time orthogonal transform together with the factorization. To this end, we formulate a regularized optimization problem reminiscent of conventional NMF, yet with the transform as additional unknown parameters, and design a novel block-descent algorithm enabling to find stationary points of this objective function. The proposed joint transform learning and factorization approach is tested for two audio signal processing experiments, illustrating its conceptual and practical benefits.