6 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…
bAdag: an adaptive block coordinate gradient method for smooth nonconvex functions
Giovanni Seraghiti
A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (O…
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…
An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU function
Nicolas Gillis, Margherita Porcelli, Giovanni Seraghiti
ReLU matrix decomposition (RMD) is the following problem: given a sparse, nonnegative matrix and a factorization rank , identify a rank- matrix such that $X\approx \m…
prunAdag: an adaptive pruning-aware gradient method
Margherita Porcelli, Giovanni Seraghiti, Philippe L. Toint
A pruning-aware adaptive gradient method is proposed which classifies the variables in two sets before updating them using different strategies. This technique extends the ``releva…
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…