A global optimization algorithm for sparse mixed membership matrix factorization

TL;DR

This paper introduces a global optimization algorithm for sparse mixed membership matrix factorization, ensuring solutions are close to the true global optimum, unlike previous local methods.

Contribution

The paper presents a novel GOP algorithm that guarantees an epsilon-global optimum for sparse mixed membership matrix factorization, improving solution reliability.

Findings

Algorithm consistently bounds the global optimum

Efficiently explores multiple modes

Performs well on simulated data

Abstract

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.