title: Theorems on positive data: on the uniqueness of NMF.
abstract: We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
authors.affiliation: Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark. Laurberg, hla@es.aau.dk
authors.forename: Hans
authors.initials: H
authors.lastname: Laurberg
authors.forename: Mads Graesbøll
authors.initials: MG
authors.lastname: Christensen
authors.forename: Mark D
authors.initials: MD
authors.lastname: Plumbley
authors.forename: Lars Kai
authors.initials: LK
authors.lastname: Hansen
authors.forename: Søren Holdt
authors.initials: SH
authors.lastname: Jensen