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Memberships Networks for High-Dimensional Fuzzy Clustering Visualization

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Part of the Communications in Computer and Information Science book series (CCIS,volume 1052)


Visualizing the cluster structure of high-dimensional data is a non-trivial task that must be able to deal with the large dimensionality of the input data. Unlike hard clustering structures, visualization of fuzzy clusterings is not as straightforward because soft clustering algorithms yield more complex clustering structures. Here is introduced the concept of membership networks, an undirected weighted network constructed based on the fuzzy partition matrix that represents a fuzzy clustering. This simple network-based method allows understanding visually how elements involved in this kind of complex data clustering structures interact with each other, without relying on a visualization of the input data themselves. Experiment results demonstrated the usefulness of the proposed method for the exploration and analysis of clustering structures on the Iris flower data set and two large and unlabeled financial datasets, which describes the financial profile of customers of a local bank.


  • Fuzzy clustering
  • Clustering visualization
  • Membership network
  • High-dimensional data

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  • DOI: 10.1007/978-3-030-31019-6_23
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  1. Abonyi, J., Babuska, R.: FUZZSAM - visualization of fuzzy clustering results by modified Sammon mapping. In: IEEE International Conference on Fuzzy Systems, vol. 1, pp. 365–370 (2004).

  2. Bécavin, C., Benecke, A.: New dimensionality reduction methods for the representation of high dimensional ‘omics’ data. Expert Rev. Mol. Diagn. 11(1), 27–34 (2011).

    CrossRef  Google Scholar 

  3. Berthold, M.R., Wiswedel, B., Patterson, D.E.: Interactive exploration of fuzzy clusters using neighborgrams. Fuzzy Sets Syst. 149(1), 21–37 (2005).

    MathSciNet  CrossRef  MATH  Google Scholar 

  4. Everitt, B.S., Landau, S., Leese, M., Stahl, D.: Cluster Analysis. Wiley, Hoboken (2011)

    CrossRef  Google Scholar 

  5. Feil, B., Balasko, B., Abonyi, J.: Visualization of fuzzy clusters by fuzzy Sammon mapping projection: application to the analysis of phase space trajectories. Soft Comput. 11(5), 479–488 (2007).

    CrossRef  Google Scholar 

  6. Fortunato, S., Hric, D.: Community detection in networks: a user guide. Phys. Rep. 659, 1–44 (2016).

    MathSciNet  CrossRef  Google Scholar 

  7. Francalanci, C., Hussain, A.: Influence-based Twitter browsing with NavigTweet. Inf. Syst. 64, 119–131 (2017).

    CrossRef  Google Scholar 

  8. Fruchterman, T.M., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991).

    CrossRef  Google Scholar 

  9. Gajer, P., Goodrich, M.T., Kobourov, S.G.: A multi-dimensional approach to force-directed layouts of large graphs. Comput. Geom. 29(1), 3–18 (2004).

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. Gibson, H., Faith, J., Vickers, P.: A survey of two-dimensional graph layout techniques for information visualisation. Inf. Vis. 12(3–4), 324–357 (2013).

    CrossRef  Google Scholar 

  11. Heberle, H., Carazzolle, M.F., Telles, G.P., Meirelles, G.V., Minghim, R.: Cell NetVis: a web tool for visualization of biological networks using force-directed layout constrained by cellular components. BMC Bioinform. 18(S10), 395 (2017).

    CrossRef  Google Scholar 

  12. Höppner, F., Klawonn, F.: Visualising clusters in high-dimensional data sets by intersecting spheres. In: Proceedings of 2006 International Symposium on Evolving Fuzzy Systems, EFS 2006, vol. 2, no. 2, pp. 106–111 (2006).

  13. Hu, Y., Shi, L.: Visualizing large graphs. Wiley Interdiscip. Rev. Comput. Stat. 7(2), 115–136 (2015).

    MathSciNet  CrossRef  Google Scholar 

  14. Ishida, Y., Itoh, T.: A force-directed visualization of conversation logs. In: Proceedings of Computer Graphics International Conference - CGI 2017, pp. 1–5. ACM Press, New York (2017).

  15. Jacomy, M., Venturini, T., Heymann, S., Bastian, M.: ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the Gephi software. PLoS ONE 9(6), 1–12 (2014).

    CrossRef  Google Scholar 

  16. Leisch, F.: A toolbox for K-centroids cluster analysis. Comput. Stat. Data Anal. 51(2), 526–544 (2006).

    MathSciNet  CrossRef  MATH  Google Scholar 

  17. Leisch, F.: Neighborhood graphs, stripes and shadow plots for cluster visualization. Stat. Comput. 20(4), 457–469 (2010).

    MathSciNet  CrossRef  Google Scholar 

  18. van der Maaten, L.: Accelerating t-SNE using tree-based algorithms. J. Mach. Learn. Res. 15, 3221–3245 (2014).

  19. van der Maaten, L., Hinton, G.: Visualizing high-dimensional data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008).

  20. Martin, S., Brown, W.M., Klavans, R., Boyack, K.W.: OpenOrd: an open-source toolbox for large graph layout. In: Proceedings of SPIE, p. 7868, January 2011.

  21. Metsalu, T., Vilo, J.: ClustVis: a web tool for visualizing clustering of multivariate data using Principal Component Analysis and heatmap. Nucleic Acids Res. 43(W1), W566–W570 (2015).

    CrossRef  Google Scholar 

  22. Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003).

    MathSciNet  CrossRef  MATH  Google Scholar 

  23. Pison, G., Struyf, A., Rousseeuw, P.J.: Displaying a clustering with CLUSPLOT. Comput. Stat. Data Anal. 30(4), 381–392 (1999).

    CrossRef  MATH  Google Scholar 

  24. Sato-Ilic, M., Ilic, P.: Visualization of fuzzy clustering result in metric space. Proc. Comput. Sci. 96, 1666–1675 (2016).

    CrossRef  Google Scholar 

  25. Serra, A., Galdi, P., Tagliaferri, R.: Machine learning for bioinformatics and neuroimaging. Wiley Interdisc. Rev.: Data Min. Knowl. Discov. 8(5), 1–33 (2018).

    CrossRef  Google Scholar 

  26. Sharko, J., Grinstein, G.: Visualizing fuzzy clusters using RadViz. In: Proceedings of International Conference Information Visualisation, pp. 307–316 (2009).

  27. Wang, K.J., Yan, X.H., Chen, L.F.: Geometric double-entity model for recognizing far-near relations of clusters. Sci. China Inf. Sci. 54(10), 2040–2050 (2011).

    MathSciNet  CrossRef  Google Scholar 

  28. Wang, W., Zhang, Y.: On fuzzy cluster validity indices. Fuzzy Sets Syst. 158(19), 2095–2117 (2007).

    MathSciNet  CrossRef  MATH  Google Scholar 

  29. Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005).

    CrossRef  Google Scholar 

  30. Xu, R., Wunsch, D.C.: Clustering algorithms in biomedical research: a review. IEEE Rev. Biomed. Eng. 3, 120–54 (2010).

    CrossRef  Google Scholar 

  31. Zhou, F., et al.: A radviz-based visualization for understanding fuzzy clustering results. In: Proceedings of 10th International Symposium on Visual Information Communication and Interaction, pp. 9–15. ACM, New York (2017).

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This research work was supported by Centro de Excelencia y Apropiación en Big Data y Data Analytics -Alianza CAOBA- and Universidad EAFIT.

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Correspondence to Leandro Ariza-Jiménez .

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Ariza-Jiménez, L., Villa, L.F., Quintero, O.L. (2019). Memberships Networks for High-Dimensional Fuzzy Clustering Visualization. In: Figueroa-García, J., Duarte-González, M., Jaramillo-Isaza, S., Orjuela-Cañon, A., Díaz-Gutierrez, Y. (eds) Applied Computer Sciences in Engineering. WEA 2019. Communications in Computer and Information Science, vol 1052. Springer, Cham.

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