Attributed Graph Clustering with Unimodal Normalized Cut

  • Wei YeEmail author
  • Linfei Zhou
  • Xin Sun
  • Claudia Plant
  • Christian Böhm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10534)


Graph vertices are often associated with attributes. For example, in addition to their connection relations, people in friendship networks have personal attributes, such as interests, age, and residence. Such graphs (networks) are called attributed graphs. The detection of clusters in attributed graphs is of great practical relevance, e.g., targeting ads. Attributes and edges often provide complementary information. The effective use of both types of information promises meaningful results. In this work, we propose a method called UNCut (for Unimodal Normalized Cut) to detect cohesive clusters in attributed graphs. A cohesive cluster is a subgraph that has densely connected edges and has as many homogeneous (unimodal) attributes as possible. We adopt the normalized cut to assess the density of edges in a graph cluster. To evaluate the unimodality of attributes, we propose a measure called unimodality compactness which exploits Hartigans’ dip test. Our method UNCut integrates the normalized cut and unimodality compactness in one framework such that the detected clusters have low normalized cut and unimodality compactness values. Extensive experiments on various synthetic and real-world data verify the effectiveness and efficiency of our method UNCut compared with state-of-the-art approaches. Code and data related to this chapter are available at:


  1. 1.
    Akoglu, L., Tong, H., Meeder, B., Faloutsos, C.: PICS: parameter-free identification of cohesive subgroups in large attributed graphs. In: SDM, pp. 439–450. SIAM (2012)Google Scholar
  2. 2.
    Günnemann, S., Färber, I., Boden, B., Seidl, T.: Subspace clustering meets dense subgraph mining: a synthesis of two paradigms. In: ICDM, pp. 845–850 (2010)Google Scholar
  3. 3.
    Günnemann, S., Färber, I., Raubach, S., Seidl, T.: Spectral subspace clustering for graphs with feature vectors. In: ICDM, pp. 231–240 (2013)Google Scholar
  4. 4.
    Hartigan, J.A., Hartigan, P.: The dip test of unimodality. Ann. Stat. 13, 70–84 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)CrossRefzbMATHGoogle Scholar
  6. 6.
    Krause, A., Liebscher, V.: Multimodal projection pursuit using the dip statistic. Preprint-Reihe Mathematik, vol. 13 (2005)Google Scholar
  7. 7.
    Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)CrossRefGoogle Scholar
  8. 8.
    Lin, F., Cohen, W.W.: Power iteration clustering. In: ICML, pp. 655–662 (2010)Google Scholar
  9. 9.
    Lin, F., Cohen, W.W.: A very fast method for clustering big text datasets. In: ECAI, pp. 303–308 (2010)Google Scholar
  10. 10.
    Maurus, S., Plant, C.: Skinny-dip: clustering in a sea of noise. In: SIGKDD, pp. 1055–1064. ACM (2016)Google Scholar
  11. 11.
    Moser, F., Colak, R., Rafiey, A., Ester, M.: Mining cohesive patterns from graphs with feature vectors. In: SDM, pp. 593–604 (2009)Google Scholar
  12. 12.
    Müller, E., Sánchez, P.I., Mülle, Y., Böhm, K.: Ranking outlier nodes in subspaces of attributed graphs. In: ICDEW, pp. 216–222. IEEE (2013)Google Scholar
  13. 13.
    Perozzi, B., Akoglu, L., Sánchez, P.I., Müller, E.: Focused clustering and outlier detection in large attributed graphs. In: SIGKDD, pp. 1346–1355 (2014)Google Scholar
  14. 14.
    Sánchez, P.I., Müller, E., Böhm, K., Kappes, A., Hartmann, T., Wagner, D.: Efficient algorithms for a robust modularity-driven clustering of attributed graphs. In: SDM, vol. 15. SIAM (2015)Google Scholar
  15. 15.
    Sánchez, P.I., Müller, E., Laforet, F., Keller, F., Böhm, K.: Statistical selection of congruent subspaces for mining attributed graphs. In: ICDM, pp. 647–656 (2013)Google Scholar
  16. 16.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  17. 17.
    Shiga, M., Takigawa, I., Mamitsuka, H.: A spectral clustering approach to optimally combining numericalvectors with a modular network. In: SIGKDD, pp. 647–656. ACM (2007)Google Scholar
  18. 18.
    Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wagner, D., Wagner, F.: Between min cut and graph bisection. In: Borzyszkowski, A.M., Sokołowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 744–750. Springer, Heidelberg (1993). CrossRefGoogle Scholar
  20. 20.
    Xu, Z., Ke, Y., Wang, Y., Cheng, H., Cheng, J.: A model-based approach to attributed graph clustering. In: SIGMOD, pp. 505–516 (2012)Google Scholar
  21. 21.
    Zhou, Y., Cheng, H., Yu, J.X.: Graph clustering based on structural/attribute similarities. PVLDB 2(1), 718–729 (2009)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Wei Ye
    • 1
    Email author
  • Linfei Zhou
    • 1
  • Xin Sun
    • 1
    • 2
  • Claudia Plant
    • 3
  • Christian Böhm
    • 1
  1. 1.Ludwig-Maximilians-Universität MünchenMunichGermany
  2. 2.Ocean University of ChinaQingdaoChina
  3. 3.University of ViennaViennaAustria

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