4 papers
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…
The uniqueness of Lyapunov rank among symmetric cones
Michael Orlitzky, Giovanni Barbarino
The Lyapunov rank of a cone is the dimension of the Lie algebra of its automorphism group. It is invariant under linear isomorphism and in general not unique - two or more non-isom…
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…