16 papers
Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization
Nicolas Gillis, Punit Sharma
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some pre…
Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures
Christophe Kervazo, Nicolas Gillis, Nicolas Dobigeon
In this work, we tackle the problem of hyperspectral (HS) unmixing by departing from the usual linear model and focusing on a Linear-Quadratic (LQ) one. The proposed algorithm, ref…
Sparse Separable Nonnegative Matrix Factorization
Nicolas Nadisic, Arnaud Vandaele, Jeremy E. Cohen +1
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…
On a minimum enclosing ball of a collection of linear subspaces
Timothy Marrinan, P. -A. Absil, Nicolas Gillis
This paper concerns the minimax center of a collection of linear subspaces. When the subspaces are -dimensional subspaces of , this can be cast as finding the cent…
Off-diagonal Symmetric Nonnegative Matrix Factorization
François Moutier, Arnaud Vandaele, Nicolas Gillis
Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be p…
A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization
Masoud Ahookhosh, Le Thi Khanh Hien, Nicolas Gillis +1
We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and bl…