269 citations · 3k across the 82 of their papers we have counts for
8 papers · 1 filter
Multiplicative Updates for Polynomial Root Finding
Nicolas Gillis
Let be a polynomial with real coefficients whose roots have nonnegative real part, where and are polynomials with nonnegative coefficients. In this paper,…
Spectral Unmixing with Multiple Dictionaries
Jeremy E. Cohen, Nicolas Gillis
Spectral unmixing aims at recovering the spectral signatures of materials, called endmembers, mixed in a hyperspectral or multispectral image, along with their abundances. A typica…
Algorithms for Positive Semidefinite Factorization
Arnaud Vandaele, François Glineur, Nicolas Gillis
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an -by- nonnega…
Finding the nearest positive-real system
Nicolas Gillis, Punit Sharma
The notion of positive realness for linear time-invariant (LTI) dynamical systems, equivalent to passivity, is one of the oldest in system and control theory. In this paper, we con…
Low-Rank Matrix Approximation in the Infinity Norm
Nicolas Gillis, Yaroslav Shitov
The low-rank matrix approximation problem with respect to the entry-wise -norm is the following: given a matrix and a factorization rank , find a matrix w…
Computing nearest stable matrix pairs
Nicolas Gillis, Volker Mehrmann, Punit Sharma
In this paper, we study the nearest stable matrix pair problem: given a square matrix pair , minimize the Frobenius norm of such that is a stable…
Dictionary-based Tensor Canonical Polyadic Decomposition
Jérémy E. Cohen, Nicolas Gillis
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one fa…
Introduction to Nonnegative Matrix Factorization
Nicolas Gillis
In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral i…