GAMer: a synthesis of subspace clustering and dense subgraph mining


In this work, we propose a new method to find homogeneous object groups in a single vertex-labeled graph. The basic premise is that many prevalent datasets consist of multiple types of information: graph data to represent the relations between objects and attribute data to characterize the single objects. Analyzing both information types simultaneously can increase the expressiveness of the resulting patterns. Our patterns of interest are sets of objects that are densely connected within the associated graph and as well show high similarity regarding their attributes. As for attribute data it is known that full-space clustering often is futile, we have to analyze the similarity of objects regarding subsets of their attributes. In order to take full advantage of all present information, we combine the paradigms of dense subgraph mining and subspace clustering. For our approach, we face several challenges to achieve a sound combination of the two paradigms. We maximize our twofold clusters according to their density, size, and number of relevant dimensions. The optimization of these three objectives usually is conflicting; thus, we realize a trade-off between these characteristics to obtain meaningful patterns. We develop a redundancy model to confine the clustering to a manageable size by selecting only the most interesting clusters for the result set. We prove the complexity of our clustering model and we particularly focus on the exploration of various pruning strategies to design the efficient algorithm GAMer (Graph & Attribute Miner). In thorough experiments on synthetic and real world data we show that GAMer achieves low runtimes and high clustering qualities. We provide all datasets, measures, executables, and parameter settings on our website

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19


  1. 1.

  2. 2.

  3. 3.


  1. 1.

    Abello J, Resende M, Sudarsky S et al. (2002) Massive quasi-clique detection. Lecture Notes in Computer Science pp. 598–612

  2. 2.

    Aggarwal C, Wang H (2010) Managing and mining graph data. Springer, New York

    Google Scholar 

  3. 3.

    Aggarwal C, Wolf J, Yu P, Procopiuc C, Park J (1999) Fast algorithms for projected clustering. In: SIGMOD, pp 61–72

  4. 4.

    Al Hasan M, Chaoji V, Salem S, Besson J, Zaki M (2007) Origami: mining representative orthogonal graph patterns. In: ICDM, pp 153–162

  5. 5.

    Beyer KS, Goldstein J, Ramakrishnan R, Shaft U (1999) When is ”nearest neighbor” meaningful?. In: ICDT, pp 217–235

  6. 6.

    Condon A, Karp RM (2001) Algorithms for graph partitioning on the planted partition model. Random Struct Algorithms 18(2):116–140

    Article  MATH  MathSciNet  Google Scholar 

  7. 7.

    Ding CHQ, He X, Zha H, Gu M, Simon HD (2001) A min-max cut algorithm for graph partitioning and data clustering. In: ICDM, pp 107–114

  8. 8.

    Du N, Wu B, Pei X, Wang B, Xu L (2007) Community detection in large-scale social networks. In: WebKDD/SNA-KDD, pp 16–25

  9. 9.

    Ester M, Ge R, Gao BJ, Hu Z, Ben-Moshe B (2006) Joint cluster analysis of attribute data and relationship data: the connected k-center problem. In: SDM

  10. 10.

    Garey M, Johnson D (1979) Computers and intractability: a guide to NP-completeness. W.H Freeman and Company, San Francisco

    Google Scholar 

  11. 11.

    Günnemann S, Färber I, Boden B, Seidl T (2010) Subspace clustering meets dense subgraph mining: a synthesis of two paradigms. In: ICDM, pp 845–850

  12. 12.

    Günnemann S, Färber I, Müller E, Assent I, Seidl T (2011) External evaluation measures for subspace clustering. In: CIKM, pp 1363–1372

  13. 13.

    Günnemann S, Kremer H, Seidl T (2010) Subspace clustering for uncertain data. In: SDM, pp 385–396

  14. 14.

    Günnemann S, Müller E, Färber I, Seidl T (2009) Detection of orthogonal concepts in subspaces of high dimensional data. In: CIKM, pp 1317–1326

  15. 15.

    Han J, Kamber M (2006) Data mining: concepts and techniques. Morgan Kaufmann, San Francisco

    Google Scholar 

  16. 16.

    Hanisch D, Zien A, Zimmer R, Lengauer T (2002) Co-clustering of biological networks and gene expression data. Bioinformatics 18:145–154

    Article  Google Scholar 

  17. 17.

    Jolliffe I (2002) Principal component analysis, 2nd edn. Springer, New York

    Google Scholar 

  18. 18.

    Kailing K, Kriegel HP, Kroeger P (2004) Density-connected subspace clustering for high-dimensional data. In: SDM, pp 246–257

  19. 19.

    Kriegel HP, Kröger P, Zimek A (2009) Clustering high-dimensional data: a survey on subspace clustering, pattern-based clustering, and correlation clustering. TKDD 3(1):1–58

    Article  Google Scholar 

  20. 20.

    Kubica J, Moore AW, Schneider JG (2003) Tractable group detection on large link data sets. In: ICDM, pp 573–576

  21. 21.

    Liu G, Wong L (2008) Effective pruning techniques for mining quasi-cliques. In: ECML/PKDD (2). pp 33–49

  22. 22.

    Long B, Wu X, Zhang ZM, Yu PS (2006) Unsupervised learning on k-partite graphs. In: KDD, pp 317–326

  23. 23.

    Long B, Zhang ZM, Yu PS (2007) A probabilistic framework for relational clustering. In: KDD, pp 470–479

  24. 24.

    Moise G, Sander J (2008) Finding non-redundant, statistically significant regions in high dimensional data: a novel approach to projected and subspace clustering. In: KDD, pp 533–541

  25. 25.

    Moise G, Sander J, Ester M (2006) P3C: a robust projected clustering algorithm. In: ICDM, pp 414–425

  26. 26.

    Moser F, Colak R, Rafiey A, Ester M (2009) Mining cohesive patterns from graphs with feature vectors. In: SDM, pp 593–604

  27. 27.

    Müller E, Assent I, Günnemann S, Krieger R, Seidl T (2009) Relevant subspace clustering: Mining the most interesting non-redundant concepts in high dimensional data. In: ICDM, pp 377–386

  28. 28.

    Müller E, Günnemann S, Assent I, Seidl T (2009) Evaluating clustering in subspace projections of high dimensional data. In: VLDB, pp 1270–1281

  29. 29.

    Neville J, Adler M, Jensen D (2004) Spectral clustering with links and attributes. Dept of Computer Science, University of Massachusetts Amherst, Tech. rep

  30. 30.

    Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. SIGKDD Explor 6(1):90–105

    Article  Google Scholar 

  31. 31.

    Pei J, Jiang D, Zhang A (2005) On mining cross-graph quasi-cliques. In: KDD, pp 228–238

  32. 32.

    Procopiuc CM, Jones M, Agarwal PK, Murali TM (2002) A monte carlo algorithm for fast projective clustering. In: SIGMOD, pp 418–427

  33. 33.

    Ruan J, Zhang W (2007) An efficient spectral algorithm for network community discovery and its applications to biological and social networks. In: ICDM, pp 643–648

  34. 34.

    Rymon R (1992) Search through systematic set enumeration. In: K.R., pp 539–550

  35. 35.

    Sequeira K, Zaki MJ (2004) Schism: a new approach for interesting subspace mining. In: ICDM, pp 186–193

  36. 36.

    Shiga M, Takigawa I, Mamitsuka H (2007) A spectral clustering approach to optimally combining numerical vectors with a modular network. In: SIGKDD, pp 647–656

  37. 37.

    Shyamsundar R, et al. (2005) A DNA microarray survey of gene expression in normal human tissues. Genome Biol 6(3):R22

    Google Scholar 

  38. 38.

    Silva A, Meira W Jr, Zaki M (2010) Structural correlation pattern mining for large graphs. In: Workshop on mining and learning with graphs, pp 119–126

  39. 39.

    Stark C, et al. (2006) BioGRID: a general repository for interaction datasets. Nucleic Acids Res 34(suppl 1):D535–D539

    Google Scholar 

  40. 40.

    Ulitsky I, Shamir R (2007) Identification of functional modules using network topology and high-throughput data. BMC Syst Biol 1(1):8

    Google Scholar 

  41. 41.

    Wang J, Zeng Z, Zhou L (2006) Clan: an algorithm for mining closed cliques from large dense graph databases. In: ICDE, p 73

  42. 42.

    Yiu ML, Mamoulis N (2003) Frequent-pattern based iterative projected clustering. In: ICDM, pp 689–692

  43. 43.

    Yiu ML, Mamoulis N (2005) Iterative projected clustering by subspace mining. IEEE Trans Knowl Data Eng (TKDE) 17(2):176–189

    Article  Google Scholar 

  44. 44.

    Zeeberg B, et al (2003) GoMiner: a resource for biological interpretation of genomic and proteomic data. Genome Biol 4(4):R28

    Google Scholar 

  45. 45.

    Zeng Z, Wang J, Zhou L, Karypis G (2006) Coherent closed quasi-clique discovery from large dense graph databases. In: KDD, pp 797–802

  46. 46.

    Zeng Z, Wang J, Zhou L, Karypis G (2007) Out-of-core coherent closed quasi-clique mining from large dense graph databases. TODS 32(2):13

    Google Scholar 

  47. 47.

    Zhang S, Yang J, Li S (2009) RING: an integrated method for frequent representative subgraph mining. In: ICDM, pp 1082–1087

  48. 48.

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

  49. 49.

    Zhou Y, Cheng H, Yu JX (2010) Clustering large attributed graphs: an efficient incremental approach. In: ICDM, pp 689–698

Download references

Author information



Corresponding author

Correspondence to Stephan Günnemann.

Additional information

Stephan Günnemann is supported by a fellowship within the postdoc-program of the German Academic Exchange Service (DAAD).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Günnemann, S., Färber, I., Boden, B. et al. GAMer: a synthesis of subspace clustering and dense subgraph mining. Knowl Inf Syst 40, 243–278 (2014).

Download citation


  • Subspace clustering
  • Dense subgraph mining
  • Pruning techniques