A global optimization algorithm for sparse mixed membership matrix   factorization
  Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algorithm that provides a guaranteed $\epsilon$-global optimum for a sparse mixed membership matrix factorization problem. We test the algorithm on simulated data and find the algorithm always bounds the global optimum across random initializations and explores multiple modes efficiently. 
Fan Zhang, Chuangqi Wang, Andrew Trapp, Patrick Flaherty
stat.ME math.OC stat.ML