54 citations · 128 across the 18 of their papers we have counts for
23 papers
The ReLU Matrix Decomposition: NP-Hardness, Ill-Posedness, and ReLU-Rank
Giovanni Seraghiti, Arnaud Vandaele, Nicolas Gillis
The ReLU Matrix Decomposition (RMD) approximates a sparse, nonnegative m-by-n matrix X by max(0, WH), where W is an m-by-r matrix, H is an r-by-n matrix, and r is the rank of the d…
Strong NP-Hardness of Rank-2 Nonnegative Matrix Factorization
Arnaud Vandaele
Nonnegative matrix factorization (NMF) approximates a nonnegative matrix by the product of two nonnegative matrices with a prescribed inner dimension~. The existence of an exact…
Nonlinear Tensor Decomposition for Pattern Discovery
Atharva Awari, Geert Roelof van der Ploeg, Arnaud Vandaele +2
The CANDECOMP/PARAFAC (CP) decomposition is widely used for revealing the underlying patterns from multiway data (also referred to as a higher-order tensor). When the data is clipp…
Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection
Alexandra Dache, Manon Rustin, Arnaud Vandaele +1
Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of diff…
On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization
Nicolas Gillis, Subhayan Saha, Stefano Sicilia +1
Given a nonnegative matrix , a factorization rank and {a positive integer }, entrywise power matrix factorization (EPMF) looks for a low-rank matrix such that $X =…
Manifold-based Algorithms for the Hadamard Decomposition
Nicolas Gillis, Subhayan Saha, Stefano Sicilia +1
Given a matrix , and two ranks and , the Hadamard decomposition (HD) looks for two low-rank matrices, of rank and of rank , both of the same si…
Computing Lower Bounds on the Nonnegative Rank via Non-Convex Optimization Solvers
Timothy Baeckelant, Arnaud Vandaele, Nicolas Gillis
The nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank-one factors that sum to . Since computing the nonnegative rank is NP-hard, it is comm…
Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data
Giovanni Seraghiti, Kévin Dubrulle, Arnaud Vandaele +1
Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns and H has r rows. In this paper, w…
Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model
Alexandra Dache, Arnaud Vandaele, Nicolas Gillis
Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpre…
Algorithms for Boolean Matrix Factorization using Integer Programming and Heuristics
Christos Kolomvakis, Thomas Bobille, Arnaud Vandaele +1
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arith…
Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions
Atharva Awari, Nicolas Gillis, Arnaud Vandaele
We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{…
Efficient algorithms for the Hadamard decomposition
Samuel Wertz, Arnaud Vandaele, Nicolas Gillis
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank m…
Algorithms for Boolean Matrix Factorization using Integer Programming
Christos Kolomvakis, Arnaud Vandaele, Nicolas Gillis
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses stand…
Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function
Giovanni Seraghiti, Atharva Awari, Arnaud Vandaele +2
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix , find a low-rank matrix such that , wh…
Matrix-wise -constrained Sparse Nonnegative Least Squares
Nicolas Nadisic, Jeremy E Cohen, Arnaud Vandaele +1
Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most non…
Sparse Separable Nonnegative Matrix Factorization
Nicolas Nadisic, Arnaud Vandaele, Jeremy E. Cohen +1
We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor…
Off-diagonal Symmetric Nonnegative Matrix Factorization
François Moutier, Arnaud Vandaele, Nicolas Gillis
Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be p…
Near-Convex Archetypal Analysis
Pierre De Handschutter, Nicolas Gillis, Arnaud Vandaele +1
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a conve…
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…
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)…
Heuristics for Exact Nonnegative Matrix Factorization
Arnaud Vandaele, Nicolas Gillis, François Glineur +1
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an -by- nonnegative matrix and a factorization rank , find, if possible, an -…
Computing The Extension Complexities of All 4-Dimensional 0/1-Polytopes
Michael Oelze, Arnaud Vandaele, Stefan Weltge
We present slight refinements of known general lower and upper bounds on sizes of extended formulations for polytopes. With these observations we are able to compute the extension…