269 citations · 3k across the 82 of their papers we have counts for
5 papers · 1 filter
On the Complexity of Robust PCA and -norm Low-Rank Matrix Approximation
Nicolas Gillis, Stephen A. Vavasis
The low-rank matrix approximation problem with respect to the component-wise -norm (-LRA), which is closely related to robust principal component analysis (PCA), ha…
Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization
Arnaud Vandaele, Nicolas Gillis, Qi Lei +2
Given a symmetric nonnegative matrix , symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix , usually with much fewer columns th…
On the Linear Extension Complexity of Regular n-gons
Arnaud Vandaele, Nicolas Gillis, François Glineur
In this paper, we propose new lower and upper bounds on the linear extension complexity of regular -gons. Our bounds are based on the equivalence between the computation of (i)…
Solving the Maximum Clique Problem with Symmetric Rank-One Nonnegative Matrix Approximation
Melisew Tefera Belachew, Nicolas Gillis
Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expres…
Sequential Dimensionality Reduction for Extracting Localized Features
Gabriella Casalino, Nicolas Gillis
Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative ma…