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A Global Optimization Algorithm for Sparse Mixed Membership Matrix Factorization

  • Fan Zhang
  • Chuangqi Wang
  • Andrew C. Trapp
  • Patrick FlahertyEmail author
Chapter
Part of the ICSA Book Series in Statistics book series (ICSABSS)

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 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.

Notes

Acknowledgements

We acknowledge Hachem Saddiki for valuable discussions and comments on the manuscript.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fan Zhang
    • 1
    • 2
    • 3
  • Chuangqi Wang
    • 4
  • Andrew C. Trapp
    • 5
  • Patrick Flaherty
    • 6
    Email author
  1. 1.Center for Data Sciences at Brigham and Women’s HospitalBostonUSA
  2. 2.Broad Institute of Massachusetts Institute of Technology and Harvard UniversityBostonUSA
  3. 3.Department of Biomedical InformaticsHarvard Medical SchoolBostonUSA
  4. 4.Department of Biomedical EngineeringWorcester Polytechnic InstituteWorcesterUSA
  5. 5.Robert A. Foisie Business School, Worcester Polytechnic InstituteWorcesterUSA
  6. 6.Department of Mathematics & StatisticsUniversity of Massachusetts AmherstAmherstUSA

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