Non-negative matrix factorization using stable alternating direction method of multipliers for source separation

Nonnegative matrix factorization (NMF) is a popular method for source separation. In this paper, an alternating direction method of multipliers (ADMM) for NMF is studied, which deals with the NMF problem using the cost function of beta-divergence. Our study shows that this algorithm outperforms state-of-the-art algorithms on synthetic data sets, but it presents unstable behavior and low accuracy on real data sets. Therefore, we propose two different stable ADMM algorithms for NMF to solve this problem. They differ slightly in the multiplicative factor utilized in the update rules. One algorithm is to adapt the step size to guarantee the convergence while the other minimizes the beta-divergence with a pivot element weighting iterative method (PEWI). Experimental results demonstrate that the proposed algorithms are more stable and accurate. Particularly, PEWI based ADMM shows superior performance in the source separation task.