On Identifiability of Nonnegative Matrix Factorization
This work addresses a foundational issue in machine learning for researchers and practitioners using NMF, offering incremental improvements in theoretical guarantees.
The paper tackles the problem of identifiability in nonnegative matrix factorization by proposing a new criterion that guarantees recovery of latent factors under mild conditions, specifically requiring one factor's rows to be sufficiently scattered while the other is full-rank, which is the mildest condition proven to date.
In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are \emph{sufficiently scattered} over the nonnegative orthant, while no structural assumption is imposed on the other factor except being full-rank. This is by far the mildest condition under which the latent factors are provably identifiable from the NMF model.