Discovering the Graph Structure in Clustering Results

  • Evgeny Bauman
  • Konstantin Bauman
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 886)


In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them it is important to know if they are connected or well separated from each other. The main focus of this paper is discovering the relations between the resulting clusters. We propose a new method which is based on pairwise overlapping k-means clustering, that in addition to means of clusters provides the graph structure of their relations. The proposed method has a set of parameters that can be tuned in order to control the sensitivity of the model and the desired relative size of the pairwise overlapping interval between means of two adjacent clusters, i.e., level of overlapping. We present the exact formula for calculating that parameter. The empirical study presented in the paper demonstrates that our approach works well not only on toy data but also compliments standard clustering results with a reasonable graph structure on a real datasets, such as financial indices and restaurants.


Unsupervised learning Clustering k-means Overlapping clustering 


  1. 1.
    Jardine, N., Sisbon, R.: Mathematical Taxonomy. John Wiley, London (1971)zbMATHGoogle Scholar
  2. 2.
    Andersen, R., Gleich, D.F., Mirrokni, V.: Overlapping clusters for distributed computation. In: WSDM 2012. ACM, New York (2012)Google Scholar
  3. 3.
    Khandekar, R., Kortsarz, G., Mirrokni, V.: Advantage of overlapping clusters for minimizing conductance. In: Proceedings of the 10th Latin American International Conference on Theoretical Informatics, LATIN 2012, pp. 494–505. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Szalay-Bekő, M., Palotai, R., Szappanos, B., Kovács, I.A., Papp, B., Csermely, P.: Moduland plug-in for cytoscape. Bioinformatics 28(16), 2202–2204 (2012)CrossRefGoogle Scholar
  5. 5.
    Gregory, S.: A fast algorithm to find overlapping communities in networks. In Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I, ECML PKDD 2008, pp. 408–423. Springer, Heidelberg (2008)Google Scholar
  6. 6.
    Obadi, G., Drazdilova, P., Hlavacek, L., Martinovic, J., Snasel, V.: A tolerance rough set based overlapping clustering for the DBLP data. In: IEEE/WIC/ACM, WI-IAT 2010, pp. 57–60. IEEE Computer Society (2010).
  7. 7.
    Meilă, M., Heckerman, D.: An experimental comparison of model-based clustering methods. Mach. Learn. 42(1–2), 9–29 (2001). Scholar
  8. 8.
    Battle, A., Segal, E., Koller, D.: Probabilistic discovery of overlapping cellular processes and their regulation. In: RECOMB 2004. ACM, New York (2004).
  9. 9.
    Banerjee, A., Krumpelman, C., Ghosh, J., Basu, S., Mooney, R.J.: Model-based overlapping clustering. In: KDD 2005. ACM, New York (2005).
  10. 10.
    Fu, Q., Banerjee, A.: Bayesian overlapping subspace clustering. In: ICDM 2009, pp. 776–781. IEEE Computer Society, Washington (2009).
  11. 11.
    Shafiei, M.M., Milios, E.E.: Latent dirichlet co-clustering. In: ICDM 2006. IEEE Computer Society, Washington (2006).
  12. 12.
    Cleuziou, G.: A generalization of k-means for overlapping clustering. In: Research Report NRR-2007-15, LIFO - University of Orleans (2007)Google Scholar
  13. 13.
    Cleuziou, G.: Osom: a method for building overlapping topological maps. Pattern Recogn. Lett. 34(3), 239–246 (2013). Scholar
  14. 14.
    Whang, J., Dhillon, I.S., Gleich, D.: Non-exhaustive, overlapping k-means. In: SIAM International Conference on Data Mining (SDM), May 2015CrossRefGoogle Scholar
  15. 15.
    Bauman, E., Muchnik, I.: Restructuring algorithm in the graph approximation problem. Autom. Remote Control 37(6), 920–926 (1976)MathSciNetGoogle Scholar
  16. 16.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell (1981)CrossRefGoogle Scholar
  17. 17.
    Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022 (2003).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Markov Processes Inc.SummitUSA
  2. 2.Temple UniversityPhiladelphiaUSA

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