Exact Sparse Nonnegative Least Squares

Nicolas Nadisic (1) , Arnaud Vandaele (1) , Nicolas Gillis (1) , Jérémy E Cohen (2)

1 UMONS - University of Mons [Belgium]
2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio

We propose a novel approach to solve exactly the sparse nonnega-tive least squares problem, under hard 0 sparsity constraints. This approach is based on a dedicated branch-and-bound algorithm. This simple strategy is able to compute the optimal solution even in complicated cases such as noisy or ill-conditioned data, where traditional approaches fail. We also show that our algorithm scales well, despite the combinatorial nature of the problem. We illustrate the advantages of the proposed technique on synthetic data sets, as well as a real-world hyperspectral image.

Mots clés: Branch-and-bound; Sparse coding; Nonnegative least squares

Domaines: Traitement du signal et de l'image [eess.SP]; Mathématiques [math]

Nicolas Nadisic, Arnaud Vandaele, Nicolas Gillis, Jérémy E Cohen. Exact Sparse Nonnegative Least Squares. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing, May 2020, Barcelona, France. pp.5395-5399, ⟨10.1109/ICASSP40776.2020.9053295⟩. ⟨hal-02634895⟩