An Approximate Augmented Lagrangian Method for Nonnegative Low-Rank Matrix Approximation

Nonnegative low-rank (NLR) matrix approximation, which is different from the classical nonnegative matrix factorization, has been recently proposed for several data analysis applications. The approximation is computed by alternately projecting onto the fixed-rank matrix manifold and the nonnegative matrix manifold. To ensure the convergence of the alternating projection method, the given nonnegative matrix must be close to a non-tangential point in the intersection of the nonegative and the low-rank manifolds. The main aim of this paper is to develop an approximate augmented Lagrangian method for solving nonnegative low-rank matrix approximation. We show that the sequence generated by the approximate augmented Lagrangian method converges to a critical point of the NLR matrix approximation problem. Numerical results to demonstrate the performance of the approximate augmented Lagrangian method on approximation accuracy, convergence speed, and computational time are reported.