6 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 =…
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 cone-constrained singular values of matrices
Giovanni Barbarino, Nicolas Gillis, David Sossa
This paper deals with the numerical computation of the least singular value of a rectangular matrix relative to a pair of closed convex cones , which is defined as the o…
Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition
Giovanni Barbarino, Nicolas Gillis, Subhayan Saha
Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic…
Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory
Subhayan Saha, Giovanni Barbarino, Nicolas Gillis
Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many…
On the Robustness of the Successive Projection Algorithm
Giovanni Barbarino, Nicolas Gillis
The successive projection algorithm (SPA) is a workhorse algorithm to learn the vertices of the convex hull of a set of -dimensional data points, a.k.a. a latent simplex…