UNILATERAL ORTHOGONAL NONNEGATIVE MATRIX FACTORIZATION

A type of matrix decomposition called unilateral orthogonal nonnegative matrix factorization is proposed for decomposing real-valued matrices. The associated optimization problem is nonconvex and nonlinear. We design an iterative algorithm based on alternating minimization, where a data compensation mechanism is used to avoid ill-conditioned problems. We also show that there is an interesting connection between the iterative algorithm and switched nonlinear systems. By analyzing the switched systems, we prove that each iteration of the algorithm is rank-preserving and thus avoids ill-conditioned problems. The solution to the optimization problem is also strictly feasible without any approximations. The optimization variables are proved to be convergent, and the limit satisfies the Karush-Kuhn-Tucker conditions. Furthermore, it is proved that the limit is almost surely a local minimizer rather than a saddle point. For the equivalent switched systems, the states of all subsystems are convergent.