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Weighted clustering of attributed multi-graphs

Abstract

An information network modeled as an attributed multi-graph contains objects described by heterogeneous attributes and connected by multiple types of edges. In this paper we study the problem of identifying groups of related objects, namely clusters, in an attributed multi-graph. It is a challenging task since a good balance between the structural and attribute properties of the objects must be achieved, while each edge-type and each attribute contains different information and is of different importance to the clustering task. We propose a unified distance measure for attributed multi-graphs which is the first to consider simultaneously the individual importance of each object property, i.e. attribute and edge-type, as well as the balance between the sets of attributes and edges. Based on this, we design an iterative parallelizable algorithm for CLustering Attributed Multi-graPhs called CLAMP, which automatically balances the structural and attribute properties of the vertices, and clusters the network such that objects in the same cluster are characterized by similar attributes and connections. Extensive experimentation on synthetic and real-world datasets demonstrates the superiority of the proposed approach over several state-of-the-art clustering methods.

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Notes

  1. 1.

    Similarly, overlapping clustering assigns an object to multiple clusters with binary memberships [32]. Though, membership probabilities provide more information, i.e. importance of an object in a cluster [14].

  2. 2.

    This dataset is available online at EU Open Data Portal—http://open-data.europa.eu.

  3. 3.

    Edge weights have been scaled to [0, 1].

  4. 4.

    Type-similar Connectivity can be calculated on directed graphs as well.

  5. 5.

    Other distance functions such as Minkowski or Semantic could be adopted as well.

  6. 6.

    Hence, \(\mathscr {C}_k\) is a valid parameter to Eqs. (1)–(6).

  7. 7.

    Also, it is suitable for our problem since Eq. (8) is differentiable. Alternatively, optimization techniques such as simulated annealing and Newton’s optimization method could be adopted. However, these techniques may impose new parameters to the model, i.e. temperature parameter, or require expensive computations at each iteration, i.e. second order derivatives, while they do not guarantee better results.

  8. 8.

    Alternatively, several centroid initialization methods could be extended and used in the proposed approach, such as the works of Bahmani et al. [3] and Shen and Meng [23], to preprocess the network aiming to reduce the number of iterations and/or improve clustering accuracy.

  9. 9.

    The full DBLP dataset is available at http://kdl.cs.umass.edu/data/dblp/dblp-info.html.

References

  1. 1.

    Akoglu L, Tong H, Meeder B, Faloutsos C (2012) PICS: parameter-free identification of cohesive subgroups in large attributed graphs. In: Proceedings of the 12th SIAM international conference on data mining, SDM 2012

  2. 2.

    Akoglu L, Tong H, Koutra D (2015) Graph based anomaly detection and description: a survey. Data Min Knowl Discov 29(3):626–688

    MathSciNet  Article  Google Scholar 

  3. 3.

    Bahmani B, Moseley B, Vattani A, Kumar R, Vassilvitskii S (2012) Scalable k-means++. Proc VLDB Endow 5(7):622–633

    Article  Google Scholar 

  4. 4.

    Barbieri N, Bonchi F, Galimberti E, Gullo F (2015) Efficient and effective community search. Data Min Knowl Discov 29(5):1406–1433

    MathSciNet  Article  Google Scholar 

  5. 5.

    Bezdek JC, Ehrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203

    Article  Google Scholar 

  6. 6.

    Bothorel C, Cruz JD, Magnani M, Micenkova B (2015) Clustering attributed graphs: models, measures and methods. Netw Sci 3:408–444

    Article  Google Scholar 

  7. 7.

    Cheng H, Zhou Y, Huang X, Yu J (2012) Clustering large attributed information networks: an efficient incremental computing approach. Data Min Knowl Discov 25(3):450–477

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Galbrun E, Gionis A, Tatti N (2014) Overlapping community detection in labeled graphs. Data Min Knowl Discov 28(5–6):1586–1610

    MathSciNet  Article  Google Scholar 

  9. 9.

    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman & Co., New York

    MATH  Google Scholar 

  10. 10.

    Gunnemann S, Farber I, Raubach S, Seidl T (2013) Spectral subspace clustering for graphs with feature vectors. In: 2013 IEEE 13th international conference on data mining (ICDM), pp 231–240. doi:10.1109/ICDM.2013.110

  11. 11.

    Hu X, Xu L (2004) Investigation on several model selection criteria for determining the number of cluster. Neural Inf Process Lett Rev 4(1):1–10

    MathSciNet  Google Scholar 

  12. 12.

    Huang HC, Chuang YY, Chen CS (2012) Multiple kernel fuzzy clustering. IEEE Trans Fuzzy Syst 20(1):120–134

    Article  Google Scholar 

  13. 13.

    Huang Z (1998) Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Min Knowl Discov 2(3):283–304

    Article  Google Scholar 

  14. 14.

    Klawonn F, Höppner F, (2003) What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier. Advances in Intelligent Data Analysis V, vol 2810, Lecture Notes in Computer Science. Springer, Berlin, pp 254–264

  15. 15.

    Kumar A, Rai P, Daume H (2011) Co-regularized multi-view spectral clustering. In: Shawe-Taylor J, Zemel R, Bartlett P, Pereira F, Weinberger K (eds) Advances in neural information processing systems, vol 24. Curran Associates, Inc., pp 1413–1421

  16. 16.

    Li N, Sun H, Chipman KC, George J, Yan X (2014) A probabilistic approach to uncovering attributed graph anomalies. In: Zaki MJ, Obradovic Z, Tan P, Banerjee A, Kamath C, Parthasarathy S (eds) Proceedings of the 2014 SIAM international conference on data mining, Philadelphia, SIAM, pp 82–90

  17. 17.

    Mann GS, McCallum A (2007) Efficient computation of entropy gradient for semi-supervised conditional random fields. Human Language Technologies 2007: The Conference of the North American Chapter of the Association for Computational Linguistics; Companion Volume. Short Papers, Association for Computational Linguistics, pp 109–112

  18. 18.

    Papadopoulos A, Pallis G, Dikaiakos MD (2013) Identifying clusters with attribute homogeneity and similar connectivity in information networks. IEEE/WIC/ACM international conference on web intelligence

  19. 19.

    Papadopoulos A, Rafailidis D, Pallis G, Dikaiakos M (2015) Clustering attributed multi-graphs with information ranking. In: database and expert systems applications, Lecture Notes in Computer Science. Springer International Publishing

  20. 20.

    Perozzi B, Akoglu L, Sánchez PI, Müller E (2014) Focused clustering and outlier detection in large attributed graphs. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, ACM, KDD ’14

  21. 21.

    Rissanen J (1978) Modeling by shortest data description. Automatica 14(5):465–471

    Article  MATH  Google Scholar 

  22. 22.

    Schaeffer SE (2007) Graph clustering. Comput Sci Rev 1(1):27–64

    Article  MATH  Google Scholar 

  23. 23.

    Shen S, Meng Z (2012) Optimization of initial centroids for k-means algorithm based on small world network. In: Shi Z, Leake D, Vadera S (eds) Intelligent information processing VI, IFIP Advances in Information and Communication Technology, vol 385. Springer, Berlin, pp 87–96

    Google Scholar 

  24. 24.

    Steinbach M, Kumar V (2005) Cluster analysis: basic concepts and algorithms. In: Introduction to data mining, 1st edn. Pearson Addison Wesley

  25. 25.

    Steinhaeuser K, Chawla N (2008) Community detection in a large real-world social network. In: Liu H, Salerno J, Young M (eds) Social computing, behavioral modeling, and prediction. Springer, USA, pp 168–175

    Chapter  Google Scholar 

  26. 26.

    Sun H, Huang J, Han J, Deng H, Zhao P, Feng B (2010) gSkeletonClu: density-based network clustering via structure-connected tree division or agglomeration. In: Proceedings of the 2010 IEEE international conference on data mining. IEEE Computer Society, Washington, DC, ICDM ’10, pp 481–490. doi:10.1109/ICDM.2010.69

  27. 27.

    Sun Y, Aggarwal CC, Han J (2012) Relation strength-aware clustering of heterogeneous information networks with incomplete attributes. Proc VLDB Endow 5

  28. 28.

    Vuokko N, Terzi E (2010) Reconstructing randomized social networks. In: Proceedings of the SIAM international conference on data mining, SDM 2010, April 29–May 1, 2010, Columbus, pp 49–59

  29. 29.

    Xu X, Yuruk N, Feng Z, Schweiger TAJ (2007) SCAN: a structural clustering algorithm for networks. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, New York, KDD ’07, pp 824–833. doi:10.1145/1281192.1281280

  30. 30.

    Xu Z, Ke Y, Wang Y, Cheng H, Cheng J (2012) A model-based approach to attributed graph clustering. In: Proceedings of the 2012 international conference on management of data. ACM, New York, SIGMOD ’12

  31. 31.

    Xu Z, Ke Y, Wang Y, Cheng H, Cheng J (2014) GBAGC: a general bayesian framework for attributed graph clustering. ACM Trans Knowl Discov Data 9(1):5:1–5:43

  32. 32.

    Yang J, McAuley J, Leskovec J (2013) Community detection in networks with node attributes. In: IEEE international conference on data mining, IEEE, pp 1151–1156. doi:10.1109/ICDM.2013.167

  33. 33.

    Zhong E, Fan W, Yang Q, Verscheure O, Ren J (2010) Cross validation framework to choose amongst models and datasets for transfer learning. In: Proceedings of the 2010 European conference on machine learning and knowledge discovery in databases: part III. Springer, Berlin, ECML PKDD’10, pp 547–562

  34. 34.

    Zhou Y, Cheng H, Yu JX (2009) Graph clustering based on structural/attribute similarities. Proc VLDB Endow 2(1):718–729

    Article  Google Scholar 

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Acknowledgements

This work was partially supported by the EU Commission in terms of the PaaSport 605193 FP7 Project (FP7-SME-2013).

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Correspondence to Andreas Papadopoulos.

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Papadopoulos, A., Pallis, G. & Dikaiakos, M.D. Weighted clustering of attributed multi-graphs. Computing 99, 813–840 (2017). https://doi.org/10.1007/s00607-016-0526-5

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Keywords

  • Clustering
  • Information networks
  • Attributed multi-graphs

Mathematics Subject Classification

  • 05C22
  • 05C40
  • 05C78
  • 68W10
  • 68W15
  • 62H30
  • 91C20