269 citations · 3k across the 82 of their papers we have counts for
7 papers · 1 filter
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…