8 papers
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 =…
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…
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}^{…
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…
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…
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, , by the product of two nonnegative factors, , where has columns and has rows. In t…