  We consider an adversarially-trained version of the nonnegative matrix
factorization, a popular latent dimensionality reduction technique. In our
formulation, an attacker adds an arbitrary matrix of bounded norm to the given
data matrix. We design efficient algorithms inspired by adversarial training to
optimize for dictionary and coefficient matrices with enhanced generalization
abilities. Extensive simulations on synthetic and benchmark datasets
demonstrate the superior predictive performance on matrix completion tasks of
our proposed method compared to state-of-the-art competitors, including other
variants of adversarial nonnegative matrix factorization.
