# Solving NMF with smoothness and sparsity constraints using PALM

arXiv: https://arxiv.org/abs/1910.14576 · HTML: https://mlsanity.com/paper/1910.14576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

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

- [Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimization](https://mlsanity.com/paper/2502.17123/) (2025)

## Abstract (arXiv)

Non-negative matrix factorization is a problem of dimensionality reduction and source separation of data that has been widely used in many fields since it was studied in depth in 1999 by Lee and Seung, including in compression of data, document clustering, processing of audio spectrograms and astronomy. In this work we have adapted a minimization scheme for convex functions with non-differentiable constraints called PALM to solve the NMF problem with solutions that can be smooth and/or sparse, two properties frequently desired.