Nonnegative Unimodal Matrix Factorization
Andersen Man Shun Ang, Nicolas Gillis, Arnaud Vandaele, Hans De Sterck
Abstract
We introduce a new Nonnegative Matrix Factorization (NMF) model called Nonnegative Unimodal Matrix Factorization (NuMF), which adds on top of NMF the unimodal condition on the columns of the basis matrix. NuMF finds applications for example in analytical chemistry. We propose a simple but naive brute-force heuristics strategy based on accelerated projected gradient. It is then improved by using multi-grid for which we prove that the restriction operator preserves the unimodality. We also present two preliminary results regarding the uniqueness of the solution, that is, the identifiability, of NuMF. Empirical results on synthetic and real datasets confirm the effectiveness of the algorithm and illustrate the theoretical results on NuMF.
BibTeX
@inproceedings{icassp2021_nonnegativeunimo,
title = {Nonnegative Unimodal Matrix Factorization},
author = {Andersen Man Shun Ang and Nicolas Gillis and Arnaud Vandaele and Hans De Sterck},
booktitle = {ICASSP 2021},
year = {2021}
}