Sparse Separable Nonnegative Matrix Factorization - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Sparse Separable Nonnegative Matrix Factorization

Résumé

We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity requires that the columns of the second NMF factor are sparse. We call this variant sparse separable NMF (SSNMF), which we prove to be NP-complete, as opposed to separable NMF which can be solved in polynomial time. The main motivation to consider this new model is to handle underdetermined blind source separation problems, such as multispectral image unmixing. We introduce an algorithm to solve SSNMF, based on the successive nonnegative projection algorithm (SNPA, an effective algorithm for separable NMF), and an exact sparse nonnegative least squares solver. We prove that, in noiseless settings and under mild assumptions, our algorithm recovers the true underlying sources. This is illustrated by experiments on synthetic data sets and the unmixing of a multispectral image.

Dates et versions

hal-02869490 , version 1 (16-06-2020)

Identifiants

Citer

Nicolas Nadisic, Arnaud Vandaele, Jérémy E Cohen, Nicolas Gillis. Sparse Separable Nonnegative Matrix Factorization. ECML PKDD 2020 - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, Sep 2020, Ghent, Belgium. pp.1-20. ⟨hal-02869490⟩
158 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More