1 code implementation • 17 May 2023 • Christos Kolomvakis, Arnaud Vandaele, Nicolas Gillis
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors.
1 code implementation • 15 May 2023 • Giovanni Seraghiti, Atharva Awari, Arnaud Vandaele, Margherita Porcelli, Nicolas Gillis
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix $X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is an element-wise nonlinear function.
1 code implementation • 22 Nov 2020 • Nicolas Nadisic, Jeremy E Cohen, Arnaud Vandaele, Nicolas Gillis
In this paper, as opposed to most previous works that enforce sparsity column- or row-wise, we first introduce a novel formulation for sparse MNNLS, with a matrix-wise sparsity constraint.
1 code implementation • 13 Jun 2020 • Nicolas Nadisic, Arnaud Vandaele, Jeremy E. Cohen, Nicolas Gillis
We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions.
no code implementations • 2 Oct 2019 • Pierre De Handschutter, Nicolas Gillis, Arnaud Vandaele, Xavier Siebert
Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the basis elements are themselves convex combinations of the data points.
no code implementations • 4 Sep 2015 • Arnaud Vandaele, Nicolas Gillis, Qi Lei, Kai Zhong, Inderjit Dhillon
Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$.
no code implementations • 26 Nov 2014 • Arnaud Vandaele, Nicolas Gillis, François Glineur, Daniel Tuyttens
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an $m$-by-$n$ nonnegative matrix $X$ and a factorization rank $r$, find, if possible, an $m$-by-$r$ nonnegative matrix $W$ and an $r$-by-$n$ nonnegative matrix $H$ such that $X = WH$.