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 algorithm that provides a guaranteed 𝜖-global optimum for a sparse mixed membership matrix factorization problem. We test the algorithm on simulated data and a small real gene expression dataset and find the algorithm always bounds the global optimum across random initializations and explores multiple modes efficiently.

• Zhang, F., Wang, C., Trapp, A., and Flaherty, P. A Global Optimization Algorithm for Sparse Mixed Membership Matrix Factorization. In Contemporary Biostatistics with Biopharmaceutical Applications (pp. 129-156), ICSA Book Series in Statistics. Springer, Cham, 2019
• Zhang, F., Wang, C., Trapp, A., and Flaherty, P. A Global Optimization Algorithm for Sparse Mixed Membership Matrix Factorization. arXiv:1610.06145, 2016