A Note on the Effectiveness of the Least Squares Consensus Clustering

  • Boris MirkinEmail author
  • Andrey Shestakov
Part of the Springer Optimization and Its Applications book series (SOIA, volume 92)


We develop a consensus clustering framework proposed three decades ago in Russia and experimentally demonstrate that our least squares consensus clustering algorithm consistently outperforms several recent consensus clustering methods.


Consensus clustering Ensemble clustering Least squares 



This work was supported by the research grant “Methods for the analysis and visualization of texts” No. 13-05-0047 under The National Research University Higher School of Economics Academic Fund Program in 2013.


  1. 1.
    Ayad, H., Kamel, M.: On voting-based consensus of cluster ensembles. Pattern Recognit. 43(5), 1943–1953 (2010)CrossRefzbMATHGoogle Scholar
  2. 2.
    Cherny, L.B.: The method of the partition space in the analysis of categorical features. A Ph.D. thesis, Institute of Control Problems, Moscow (1973) (in Russian)Google Scholar
  3. 3.
    Cherny, L.B.: Relationship between the method of the partition space and other methods of data analysis. In: Mirkin, B. (ed.) Issues in Analysis of Complex Systems, pp. 84–89. Nauka, Novosibirsk (1974) (in Russian)Google Scholar
  4. 4.
    Dimitriadou, E., Weingessel, A., Hornik, K.: A combination scheme for fuzzy clustering. J. Pattern Recognit. Artif. Intell. 16(7), 901–912 (2002)CrossRefGoogle Scholar
  5. 5.
    Ghosh, J., Acharya, A.: Cluster ensembles. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 1, 1–12 (2011)CrossRefGoogle Scholar
  6. 6.
    Guenoche, A.: Consensus of partitions: a constructive approach. Adv. Data Anal. Classif. 5, 215–229 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Meila, M.: Comparing clusterings - an information based distance. J. Multivar. Anal. 98(5), 873–881 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Mirkin, B.G.: A new approach to the analysis of sociology data. In: Voronov, Y. (ed.) Measurement and Modeling in Sociology, pp. 51–61. Nauka, Novosibirsk (1969) (in Russian)Google Scholar
  9. 9.
    Mirkin, B.G.: Analysis of Categorical Features, 166 pp. Statistika, Moscow (1976) (in Russian)Google Scholar
  10. 10.
    Mirkin, B.: Core Concepts in Data Analysis: Summarization, Correlation, Visualization. Springer, Berlin (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Mirkin, B.: Clustering: A Data Recovery Approach. Chapman and Hall, London (2012)CrossRefGoogle Scholar
  12. 12.
    Mirkin, B., Muchnik, I.: Geometrical interpretation of clustering scoring functions. In: Mirkin, B. (ed.) Methods for the Analysis of Multivariate Data in Economics, pp. 3–11. Nauka, Novosibirsk (1981) (in Russian)Google Scholar
  13. 13.
    Netlab Neural Network software. Accessed 1 Dec (2013)
  14. 14.
    Sevillano, X., Socoro, J.C., Alias, F.: Fuzzy clusterers combination by positional voting for robust document clustering. Procesamiento del lenguaje Nat. 43, 245–253 (2009)Google Scholar
  15. 15.
    Strehl, A., Ghosh, J.: Cluster ensembles - a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3, 583–617 (2002)MathSciNetGoogle Scholar
  16. 16.
    Topchy, A., Jain, A.K., Punch, W.: A mixture model for clustering ensembles. In Proceedings SIAM International Conference on Data Mining (2004)Google Scholar
  17. 17.
    Wang, H., Shan, H., Banerjee, A.: Bayesian cluster ensembles. In: Proceedings of the Ninth SIAM International Conference on Data Mining, pp. 211–222 (2009)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Data Analysis and Machine IntelligenceNational Research University Higher School of EconomicsMoscowRussian Federation

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