Solving NMF with smoothness and sparsity constraints using PALM

TL;DR

This paper introduces an adaptation of the PALM optimization scheme to effectively solve non-negative matrix factorization problems with additional smoothness and sparsity constraints, enhancing data analysis applications.

Contribution

It presents a novel application of the PALM algorithm to NMF with smoothness and sparsity constraints, addressing a gap in existing optimization methods.

Findings

Successfully incorporates smoothness and sparsity into NMF solutions

Demonstrates improved factorization quality in data analysis tasks

Provides a flexible optimization framework for constrained NMF

Abstract

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.