A global optimization algorithm for sparse mixed membership matrix factorization
This work provides a global optimization solution for a specific data analysis problem, but it appears incremental as it builds on existing mixed membership factorization methods.
The authors tackled the problem of achieving global optimality in sparse mixed membership matrix factorization, which previously only guaranteed local optima, and demonstrated that their algorithm consistently bounds the global optimum across random initializations and explores multiple modes efficiently.
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.