269 citations · 3k across the 82 of their papers we have counts for
15 papers · 1 filter
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…
Provably robust blind source separation of linear-quadratic near-separable mixtures
Christophe Kervazo, Nicolas Gillis, Nicolas Dobigeon
In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two prov…
Matrix-wise -constrained Sparse Nonnegative Least Squares
Nicolas Nadisic, Jeremy E Cohen, Arnaud Vandaele +1
Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most non…
Deep matrix factorizations
Pierre De Handschutter, Nicolas Gillis, Xavier Siebert
Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in lar…
Multiplicative Updates for NMF with -Divergences under Disjoint Equality Constraints
Valentin Leplat, Nicolas Gillis, Jérôme Idier
Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, , as the product of two smaller nonnegative matrices, and . In this pa…
An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization
Le Thi Khanh Hien, Duy Nhat Phan, Nicolas Gillis
In this paper, we introduce TITAN, a novel inerTIal block majorizaTion minimizAtioN framework for non-smooth non-convex optimization problems. To the best of our knowledge, TITAN i…
Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
Le Thi Khanh Hien, Nicolas Gillis
Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between the input data…
Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithms
Maryam Abdolali, Nicolas Gillis
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization.…
Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing
Valentin Leplat, Nicolas Gillis, Cédric Févotte
Many datasets are obtained as a resolution trade-off between two adversarial dimensions; for example between the frequency and the temporal resolutions for the spectrogram of an au…
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…
Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors: A Unified Nonconvex Optimization Perspective
Xiao Fu, Nico Vervliet, Lieven De Lathauwer +2
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly fo…
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…
Accelerating Block Coordinate Descent for Nonnegative Tensor Factorization
Andersen Man Shun Ang, Jeremy E. Cohen, Nicolas Gillis +1
This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an…