Maxima Units Search (MUS) Algorithm: Methodology and Applications

  • Leonardo Egidi
  • Roberta Pappadà
  • Francesco Pauli
  • Nicola Torelli
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 227)


An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture models. Here we introduce it on its own and explore possible applications in different contexts.


Identity matrix Pivotal unit Label switching 


  1. 1.
    Ana, L.N.F., Jain, A.K.: Data clustering using evidence accumulation. In: 2002 Proceedings 16th International Conference on Pattern Recognition, vol. 4, pp. 276–280 (2002)Google Scholar
  2. 2.
    Egidi, L., Pappadà, R., Pauli, F., Torelli, N.: Relabelling in Bayesian mixture models by pivotal units. arXiv:1501.05478v2 (2015)
  3. 3.
    Jasra, A., Holmes, C.C., Stephens, D.A.: Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Stat. Sci. 50–67 (2005)Google Scholar
  4. 4.
    Kaiser, Henry F.: An index of factorial simplicity. Psychometrika 39(1), 31–36 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2(1–2), 83–97 (1955)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Puolamäki, K., Kaski, S.: Bayesian solutions to the label switching problem. In: Advances in Intelligent Data Analysis VIII, pp. 381–392. Springer (2009)Google Scholar
  8. 8.
    Stephens, M.: Dealing with label switching in mixture models. J. R. Stat. Soc. Ser. B (Stat. Methodo.) 62(4), 795–809 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Leonardo Egidi
    • 1
  • Roberta Pappadà
    • 2
  • Francesco Pauli
    • 2
  • Nicola Torelli
    • 2
  1. 1.Dipartimento di Scienze StatisticheUniversità degli Studi di PadovaPadovaItaly
  2. 2.Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche,‘Bruno de Finetti’Università degli Studi di TriesteTriesteItaly

Personalised recommendations