Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization

Abstract

The $Q$-weighted nonnegative matrix tri-factorisation problem arising in clustering analysis is considered and a necessary condition for its optimal solution is obtained. The problem is solved by the proximal alternating nonnegative least squares method supplemented by an acceleration scheme. The convergence of the methods is studied. Numerical examples show the feasibility and efficiency of the methods proposed.