An Alternating Direction Algorithm for Nonnegative Matrix Factorization

We extend the classic alternating direction method for convex optimization to solving the non-convex, nonnegative matrix factorization problem and conduct several carefully designed numerical experiments to compare the proposed algorithms with the most widely used two algorithms for solving this problem. In addition, the proposed algorithm is also briefly compared with two other more recent algorithms. Numerical evidence shows that the alternating direction algorithm tends to deliver higher-quality solutions with faster computing times on the tested problems. A convergence result is given showing that the algorithm converges to a Karush-KuhnTucker point whenever it converges.