269 citations · 3k across the 82 of their papers we have counts for
87 papers
Computing the Nonnegative Low-Rank Leading Eigenmatrix and its Applications to Markov Grids and Metzler Operators
Nicolas Gillis, Carmela Scalone
We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm…
Algorithms for Boolean Matrix Factorization using Integer Programming
Christos Kolomvakis, Arnaud Vandaele, Nicolas Gillis
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses stand…
Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function
Giovanni Seraghiti, Atharva Awari, Arnaud Vandaele +2
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix , find a low-rank matrix such that , wh…
Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation
Hazan Daglayan, Simon Vary, Valentin Leplat +2
We propose to use low-rank matrix approximation using the component-wise L1-norm for direct imaging of exoplanets. Exoplanet detection by direct imaging is a challenging task for t…
Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach
Neelam Choudhary, Nicolas Gillis, Punit Sharma
In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a general…
Least-squares methods for nonnegative matrix factorization over rational functions
Cécile Hautecoeur, Lieven De Lathauwer, Nicolas Gillis +1
Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in N…
Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applications
Olivier Vu Thanh, Nicolas Gillis, Fabian Lecron
In this paper, we propose a new low-rank matrix factorization model dubbed bounded simplex-structured matrix factorization (BSSMF). Given an input matrix and a factorization ra…
Revisiting data augmentation for subspace clustering
Maryam Abdolali, Nicolas Gillis
Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-ar…
A consistent and flexible framework for deep matrix factorizations
Pierre De Handschutter, Nicolas Gillis
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of fea…
Partial Identifiability for Nonnegative Matrix Factorization
Nicolas Gillis, Róbert Rajkó
Given a nonnegative matrix factorization, , and a factorization rank, , Exact nonnegative matrix factorization (Exact NMF) decomposes as the product of two nonnegative ma…
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…
Structured Nonnegative Matrix Factorization for Traffic Flow Estimation of Large Cloud Networks
Syed Muhammad Atif, Nicolas Gillis, Sameer Qazi +1
Network traffic matrix estimation is an ill-posed linear inverse problem: it requires to estimate the unobservable origin destination traffic flows, X, given the observable link tr…
Smoothed Separable Nonnegative Matrix Factorization
Nicolas Nadisic, Nicolas Gillis, Christophe Kervazo
Given a set of data points belonging to the convex hull of a set of vertices, a key problem in linear algebra, signal processing, data analysis and machine learning is to estimate…
Block Alternating Bregman Majorization Minimization with Extrapolation
Le Thi Khanh Hien, Duy Nhat Phan, Nicolas Gillis +2
In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous…
Conic-Optimization Based Algorithms for Nonnegative Matrix Factorization
Valentin Leplat, Yurii Nesterov, Nicolas Gillis +1
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix and a factorization rank , compute two nonnegative matrices, with columns…
On the non-symmetric semidefinite Procrustes problem
Mohit Kumar Baghel, Nicolas Gillis, Punit Sharma
In this paper, we consider the non-symmetric positive semidefinite Procrustes (NSPSDP) problem: Given two matrices , find the matrix $A \in \mathbb{R}^{n,…
Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems
Mohit Kumar Baghel, Nicolas Gillis, Punit Sharma
In this paper, we find necessary and sufficient conditions to identify pairs of matrices and for which there exists such that is positive sem…
A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization
Le Thi Khanh Hien, Duy Nhat Phan, Nicolas Gillis
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock comp…
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…