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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…
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…
On a minimum enclosing ball of a collection of linear subspaces
Timothy Marrinan, P. -A. Absil, Nicolas Gillis
This paper concerns the minimax center of a collection of linear subspaces. When the subspaces are -dimensional subspaces of , this can be cast as finding the cent…
A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization
Anthony Degleris, Nicolas Gillis
In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonn…
Generalized Separable Nonnegative Matrix Factorization
Junjun Pan, Nicolas Gillis
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and…
Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization
Nicolas Gillis, Le Thi Khanh Hien, Valentin Leplat +1
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function th…