| Paper ID | MLSP-19.2 |
| Paper Title |
Nonnegative Unimodal Matrix Factorization |
| Authors |
Andersen Man Shun Ang, University of Waterloo, Canada; Nicolas Gillis, Arnaud Vandaele, Universite de Mons, Belgium; Hans De Sterck, University of Waterloo, Canada |
| Session | MLSP-19: Non-Negative Matrix Factorization |
| Location | Gather.Town |
| Session Time: | Wednesday, 09 June, 14:00 - 14:45 |
| Presentation Time: | Wednesday, 09 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Machine Learning for Signal Processing: [MLR-MFC] Matrix factorizations/completion |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| 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. |
