Revising algorithm for nonnegative matrix factorization based on minimizing quasi-L1 norm

Previously, we developed a nonnegative matrix factorization (NMF) algorithm named QL1-NMF that is based on minimizing the quasi-L1 norm of an error matrix. When the data includes many outliers, the QL1-NMF algorithm returns better results than ISRA, which is one of the basic NMF algorithms. However, the update functions in the QL1-NMF algorithm are based on a differential function with distortion. Moreover, the solutions it provides sometimes diverge to infinity. The method therefore required improvement to enable it to produce more accurate analysis. In the work described in this paper, we replaced its update functions with others that were based on a simple differential function without distortion. We also contrived ways to implement adjustment factors into the update functions. Computer simulation results confirm the revised algorithm works better than the previous one.