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Impact of Network Topology on Efficiency of Proximity Measures for Community Detection

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Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

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Abstract

Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or random graphs. However, graphs representing real systems can be completely different in topology: the difference can be in the size of the network, the structure of clusters, the distribution of degrees, the density of edges, and so on. Therefore, it is necessary to explicitly check whether the advantage of one measure over another is preserved for different network topologies. In this paper, we consider the efficiency of several proximity measures for clustering networks with different structures. The results show that the efficiency of measures really depends on the network topology in some cases. However, it is possible to find measures that behave well for most topologies.

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References

  1. Avrachenkov, K., Chebotarev, P., Rubanov, D.: Kernels on graphs as proximity measures. In: International Workshop on Algorithms and Models for the Web-Graph. LNCS, vol. 10519, pp. 27–41. Springer (2017)

    Google Scholar 

  2. Aynulin, R.: Efficiency of transformations of proximity measures for graph clustering. In: International Workshop on Algorithms and Models for the Web-Graph. LNCS, vol. 11631, pp. 16–29. Springer (2019)

    Google Scholar 

  3. Chebotarev, P.Y., Shamis, E.: On the proximity measure for graph vertices provided by the inverse Laplacian characteristic matrix. In: 5th Conference of the International Linear Algebra Society, Georgia State University, Atlanta, pp. 30–31 (1995)

    Google Scholar 

  4. Chebotarev, P.: The walk distances in graphs. Discrete Appl. Math. 160(10–11), 1484–1500 (2012)

    Article  MathSciNet  Google Scholar 

  5. Costa, L.d.F., Oliveira Jr., O.N., Travieso, G., Rodrigues, F.A., Villas Boas, P.R., Antiqueira, L., Viana, M.P., Correa Rocha, L.E.: Analyzing and modeling real-world phenomena with complex networks: a survey of applications. Adv. Phys. 60(3), 329–412 (2011)

    Article  Google Scholar 

  6. Deza, M.M., Deza, E.: Encyclopedia of Distances. Springer, Berlin (2016)

    Book  Google Scholar 

  7. Emmons, S., Kobourov, S., Gallant, M., Börner, K.: Analysis of network clustering algorithms and cluster quality metrics at scale. PLoS One 11(7), e0159161 (2016)

    Article  Google Scholar 

  8. Estrada, E.: The communicability distance in graphs. Linear Algebra Appl. 436(11), 4317–4328 (2012)

    Article  MathSciNet  Google Scholar 

  9. Fouss, F., Yen, L., Pirotte, A., Saerens, M.: An experimental investigation of graph kernels on a collaborative recommendation task. In: Sixth International Conference on Data Mining (ICDM 2006), pp. 863–868. IEEE (2006)

    Google Scholar 

  10. Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)

    Article  Google Scholar 

  11. Ivashkin, V., Chebotarev, P.: Do logarithmic proximity measures outperform plain ones in graph clustering? In: International Conference on Network Analysis. PROMS, vol. 197, pp. 87–105. Springer (2016)

    Google Scholar 

  12. Jeub, L.G., Balachandran, P., Porter, M.A., Mucha, P.J., Mahoney, M.W.: Think locally, act locally: detection of small, medium-sized, and large communities in large networks. Phys. Rev. E 91(1), 012821 (2015)

    Article  Google Scholar 

  13. Katz, L.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)

    Article  Google Scholar 

  14. Kondor, R., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: International Conference on Machine Learning, pp. 315–322 (2002)

    Google Scholar 

  15. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

    Article  Google Scholar 

  16. Milligan, G.W., Cooper, M.C.: A study of the comparability of external criteria for hierarchical cluster analysis. Multivar. Behav. Res. 21(4), 441–458 (1986)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: bringing order to the web. Technical report, Stanford InfoLab (1999)

    Google Scholar 

  19. Pasta, M.Q., Zaidi, F.: Topology of complex networks and performance limitations of community detection algorithms. IEEE Access 5, 10901–10914 (2017)

    Article  Google Scholar 

  20. Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336), 846–850 (1971)

    Article  Google Scholar 

  21. Schenker, A., Last, M., Bunke, H., Kandel, A.: Comparison of distance measures for graph-based clustering of documents. In: International Workshop on Graph-Based Representations in Pattern Recognition. LNCS, vol. 2726, pp. 202–213. Springer (2003)

    Google Scholar 

  22. Sommer, F., Fouss, F., Saerens, M.: Comparison of graph node distances on clustering tasks. In: International Conference on Artificial Neural Networks. LNCS, vol. 9886, pp. 192–201. Springer (2016)

    Google Scholar 

  23. Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  24. Ward Jr., J.H.: Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc. 58(301), 236–244 (1963)

    Article  MathSciNet  Google Scholar 

  25. Yen, L., Vanvyve, D., Wouters, F., Fouss, F., Verleysen, M., Saerens, M.: Clustering using a random walk based distance measure. In: ESANN, pp. 317–324 (2005)

    Google Scholar 

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Correspondence to Rinat Aynulin .

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Aynulin, R. (2020). Impact of Network Topology on Efficiency of Proximity Measures for Community Detection. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_16

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