54 citations · 128 across the 18 of their papers we have counts for
9 papers · 1 filter
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…