Search Results for author: Arnaud Vandaele

Found 7 papers, 4 papers with code

Algorithms for Boolean Matrix Factorization using Integer Programming

1 code implementation17 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.

Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function

1 code implementation15 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.

Matrix-wise $\ell_0$-constrained Sparse Nonnegative Least Squares

1 code implementation22 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.

Sparse Separable Nonnegative Matrix Factorization

1 code implementation13 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.

blind source separation

Near-Convex Archetypal Analysis

no code implementations2 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.

Dimensionality Reduction

Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

no code implementations4 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 $A \approx HH^T$.

Clustering

Heuristics for Exact Nonnegative Matrix Factorization

no code implementations26 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 $X = WH$.

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