Nonnegative Unimodal Matrix Factorization

Ang, Andersen Man Shun, Gillis, Nicolas, Vandaele, Arnaud and Sterck, Hans De (2021) Nonnegative Unimodal Matrix Factorization. In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 3270-3274 . (doi:10.1109/ICASSP39728.2021.9414631).

Record type: Conference or Workshop Item (Paper)

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.

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More information

Published date: 13 May 2021

Venue - Dates: 2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021, , Virtual, Toronto, Canada, 2021-06-06 - 2021-06-11

Keywords: Fast gradient method, Multi-grid method, Nonnegative matrix factorization, Unimodality

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