Title: Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations,
Abstract: Non-negative matrix factorization is a basic tool for decomposing data into
the feature and weight matrices under non-negativity constraints, and in
practice is often solved in the alternating minimization framework. However, it
is unclear whether such algorithms can recover the ground-truth feature matrix
when the weights for different features are highly correlated, which is common
in applications. This paper proposes a simple and natural alternating gradient
descent based algorithm, and shows that with a mild initialization it provably
recovers the ground-truth in the presence of strong correlations. In most
interesting cases, the correlation can be in the same order as the highest
possible. Our analysis also reveals its several favorable features including
robustness to noise. We complement our theoretical results with empirical
studies on semi-synthetic datasets, demonstrating its advantage over several
popular methods in recovering the ground-truth.