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 $ε$-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.

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