Rank-two residue iteration method for nonnegative matrix factorization

Rank-one residue iteration (RRI) is a recently developed block coordinate method for nonnegative matrix factorization (NMF). Numerical results show that the decomposed matrices generated by RRI method may have several columns, which are zero vectors. In this paper, by studying two special kinds of quadratic programming, we develop two block coordinate methods for NMF, rank-two residue iteration (RTRI) method and rank-two modified residue iteration (RTMRI) method. In the two algorithms, the exact solution of the subproblem can be obtained directly. We also provide that the consequence generated by our proposed algorithms can converge to a stationary point. Numerical results show that the RTRI method and the RTMRI method can yield better solutions, especially RTMRI method can remedy the limitation of the RRI method.