Multi-graph Clustering Based on Interior-Node Topology with Applications to Brain Networks

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9851)


Learning from graph data has been attracting much attention recently due to its importance in many scientific applications, where objects are represented as graphs. In this paper, we study the problem of multi-graph clustering (i.e., clustering multiple graphs). We propose a multi-graph clustering approach (MGCT) based on the interior-node topology of graphs. Specifically, we extract the interior-node topological structure of each graph through a sparsity-inducing interior-node clustering. We merge the interior-node clustering stage and the multi-graph clustering stage into a unified iterative framework, where the multi-graph clustering will influence the interior-node clustering and the updated interior-node clustering results will be further exerted on multi-graph clustering. We apply MGCT on two real brain network data sets (i.e., ADHD and HIV). Experimental results demonstrate the superior performance of the proposed model on multi-graph clustering.


Multi-graph clustering Interior-node topology Brain network 



This work is supported in part by NSF through grants III-1526499, NSFC through grants 61503253 and 61472089, and NIH through grant \(R01-MH080636\).


  1. 1.
    Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009)zbMATHGoogle Scholar
  2. 2.
    Aggarwal, C.C., Ta, N., Wang, J., Feng, J., Zaki, M.: XProj: a framework for projected structural clustering of XML documents. In: KDD, pp. 46–55. ACM (2007)Google Scholar
  3. 3.
    Aggarwal, C.C., Wang, H.: A survey of clustering algorithms for graph data. In: Aggarwal, C.C., Wang, H. (eds.) Managing and Mining Graph Data, pp. 275–301. Springer, New York (2010)CrossRefGoogle Scholar
  4. 4.
    Berkhin, P.: A survey of clustering data mining techniques. In: Kogan, J., Nicholas, C., Teboulle, M. (eds.) Grouping Multidimensional Data, pp. 25–71. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Cai, D.: Litekmeans: the fastest matlab implementation of kmeans. Software (2011).
  6. 6.
    Cao, B., Kong, X., Zhang, J., Philip, S.Y., Ragin, A.B.: Mining brain networks using multiple side views for neurological disorder identification. In: ICDM, pp. 709–714. IEEE (2015)Google Scholar
  7. 7.
    Donath, W.E., Hoffman, A.J.: Lower bounds for the partitioning of graphs. IBM J. Res. Dev. 17(5), 420–425 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    He, L., Lu, C.T., Ma, J., Cao, J., Shen, L., Philip, S.Y.: Joint community and structural hole spanner detection via harmonic modularity. In: KDD. ACM (2016)Google Scholar
  9. 9.
    He, R., Tan, T., Wang, L., Zheng, W.S.: \(\ell _{2,1}\) regularized correntropy for robust feature selection. In: CVPR, pp. 2504–2511 (2012)Google Scholar
  10. 10.
    Jie, B., Zhang, D., Gao, W., Wang, Q., Wee, C., Shen, D.: Integration of network topological and connectivity properties for neuroimaging classification. Biomed. Eng. 61(2), 576 (2014)Google Scholar
  11. 11.
    Kong, X., Ragin, A.B., Wang, X., Yu, P.S.: Discriminative feature selection for uncertain graph classification. In: SDM, pp. 82–93. SIAM (2013)Google Scholar
  12. 12.
    Kong, X., Yu, P.S.: Brain network analysis: a data mining perspective. ACM SIGKDD Explor. Newsl. 15(2), 30–38 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kuhn, H.W.: The hungarian method for the assignment problem. Naval Res. Logistics Q. 2(1–2), 83–97 (1955)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kuo, C.T., Wang, X., Walker, P., Carmichael, O., Ye, J., Davidson, I.: Unified and contrasting cuts in multiple graphs: application to medical imaging segmentation. In: KDD, pp. 617–626. ACM (2015)Google Scholar
  15. 15.
    Lian, W., Mamoulis, N., Yiu, S.M., et al.: An efficient and scalable algorithm for clustering XML documents by structure. IEEE Trans. Knowl. Data Eng. 16(1), 82–96 (2004)CrossRefGoogle Scholar
  16. 16.
    Nikolova, M., Ng, M.K.: Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J. Sci. Comput. 27(3), 937–966 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Onnela, J.P., Saramäki, J., Kertész, J., Kaski, K.: Intensity and coherence of motifs in weighted complex networks. Phys. Rev. E 71(6), 065103 (2005)CrossRefGoogle Scholar
  18. 18.
    Ragin, A.B., Du, H., Ochs, R., Wu, Y., Sammet, C.L., Shoukry, A., Epstein, L.G.: Structural brain alterations can be detected early in HIV infection. Neurology 79(24), 2328–2334 (2012)CrossRefGoogle Scholar
  19. 19.
    Saul, L.K., Roweis, S.T.: An introduction to locally linear embedding (2000).
  20. 20.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  21. 21.
    Spielman, D.A.: Algorithms, graph theory, and linear equations in Laplacian matrices. In: ICM, vol. 4, pp. 2698–2722 (2010)Google Scholar
  22. 22.
    Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wee, C.Y., Yap, P.T., Zhang, D., Denny, K., Browndyke, J.N., Potter, G.G., Welsh-Bohmer, K.A., Wang, L., Shen, D.: Identification of MCI individuals using structural and functional connectivity networks. Neuroimage 59(3), 2045–2056 (2012)CrossRefGoogle Scholar
  24. 24.
    Wen, Z., Yin, W.: A feasible method for optimization with orthogonality constraints. Math. Program. 142(1–2), 397–434 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Zhang, J., Yu, P.S.: Community detection for emerging networks. In: SDM. SIAM (2015)Google Scholar
  26. 26.
    Zhang, J., Yu, P.S.: Mutual clustering across multiple heterogeneous networks. In: IEEE BigData Congress (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.School of Computer Science and Software EngineeringShenzhen UniversityShenzhenChina
  3. 3.Institute for Data ScienceTsinghua UniversityBeijingChina
  4. 4.Department of RadiologyNorthwestern UniversityChicagoUSA

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