Classifying Large Graphs with Differential Privacy

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9321)


We consider classification of graphs using graph kernels under differential privacy. We develop differentially private mechanisms for two well-known graph kernels, the random walk kernel and the graphlet kernel. We use the Laplace mechanism with restricted sensitivity to release private versions of the feature vector representations of these kernels. Further, we develop a new sampling algorithm for approximate computation of the graphlet kernel on large graphs with guarantees on sample complexity, and show that the method improves both privacy and computation speed. We also observe that the number of samples needed to obtain good accuracy in practice is much lower than the bound. Finally, we perform an extensive empirical evaluation examining the trade-off between privacy and accuracy and show that our private method is able to retain good accuracy in several classification tasks.


  1. 1.
    Blocki, J., Blum, A., Datta, A., Sheffet, O.: The johnson-lindenstrauss transform itself preserves differential privacy. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 410–419 (2012)Google Scholar
  2. 2.
    Blocki, J., Blum, A., Datta, A., Sheffet, O.: Differentially private data analysis of social networks via restricted sensitivity. In: ITCS, pp. 87–96 (2013)Google Scholar
  3. 3.
    Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Proceedings of ICDM, pp. 74–81 (2005)Google Scholar
  4. 4.
    Dobson, P.D., Doig, A.J.: Distinguishing enzyme structures from non-enzymes without alignments. J. Mol. Biol. 330(4), 771–783 (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  6. 6.
    Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Theoret. Comput. Sci. 9(3–4), 211–407 (2013)MathSciNetGoogle Scholar
  7. 7.
    Gärtner, T., Flach, P.A., Wrobel, S.: On graph kernels: hardness results and efficient alternatives. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 129–143. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  8. 8.
    Hermansson, L., Kerola, T., Johansson, F., Jethava, V., Dubhashi, D.: Entity disambiguation in anonymized graphs using graph kernels. In: CIKM 2013, pp. 1037–1046. ACM (2013)Google Scholar
  9. 9.
    Hubler, C., Kriegel, H.-P., Borgwardt, K., Ghahramani, Z.: Metropolis algorithms for representative subgraph sampling. In: Eighth IEEE International Conference on Data Mining, ICDM 2008, pp. 283–292. IEEE (2008)Google Scholar
  10. 10.
    Jain, P., Thakurta, A.: Differentially private learning with kernels. In: JMLR Proceedings of ICML 2013, vol. 28, pp. 118–126 (2013).
  11. 11.
    Jernigan, C., Mistree, B.F.: Gaydar: facebook friendships expose sexual orientation. First Monday 14(10) (2009)Google Scholar
  12. 12.
    Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of the 20th International Conference on Machine Learning (2003)Google Scholar
  13. 13.
    Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? In: CoRR (2008)Google Scholar
  14. 14.
    Kasiviswanathan, S.P., Nissim, K., Raskhodnikova, S., Smith, A.: Analyzing graphs with node differential privacy. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 457–476. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  15. 15.
    Kriege, N., Mutzel, P.: Subgraph matching kernels for attributed graphs. In: ICML. / Omnipress (2012)Google Scholar
  16. 16.
    Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6(1), 29–123 (2009)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Li, N., Qardaji, W., Su, D.: On sampling, anonymization, and differential privacy or, k-anonymization meets differential privacy. In: ASIACCS 2012, pp. 32–33. ACM, New York (2012)Google Scholar
  18. 18.
    McSherry, F., Mironov, I.: Differentially private recommender systems: building privacy into the net. In: IV Elder, J.F., Fogelman-Souli, F., Flach, P.A., Zaki, M. (eds.) KDD, pp. 627–636. ACM (2009)Google Scholar
  19. 19.
    Narayanan, A., Shmatikov, V.: Robust de-anonymization of large sparse datasets. In: 2013 IEEE Symposium on Security and Privacy, pp. 111–125 (2008)Google Scholar
  20. 20.
    Nissim, K., Raskhodnikova, S., Smith, A.: Smooth sensitivity and sampling in private data analysis. In: STOC 2007, pp. 75–84. ACM (2007)Google Scholar
  21. 21.
    Rahman, M., Bhuiyan, M., Hasan, M.A.: Graft: an approximate graphlet counting algorithm for large graph analysis. In: CIKM 2012, pp. 1467–1471. ACM (2012)Google Scholar
  22. 22.
    Schölkopf, B., Smola, A.J.: Learning With Kernels: Support Vector Machines, Regularization, Optimization, And Beyond. MIT Press, Cambridge (2001) Google Scholar
  23. 23.
    Shervashidze, N.: Scalable graph kernels. Ph.D. thesis, Eberhard Karls Universitt Tbingen (2012)Google Scholar
  24. 24.
    Shervashidze, N., Schweitzer, P., van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-lehman graph kernels. J. Mach. Learn. Res. 12, 2539–2561 (2011)MathSciNetGoogle Scholar
  25. 25.
    Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: Proceedings of AISTATS (2009)Google Scholar
  26. 26.
    Swarup, S., Eubank, S.G., Marathe, M.V.: Computational epidemiology as a challenge domain for multiagent systems. In: AAMAS 2014, pp. 1173–1176, Richland, SC (2014)Google Scholar
  27. 27.
    Vishwanathan, S., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. J. Mach. Learn. Res. 11, 1201–1242 (2010)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Vishwanathan, S.V.N., Borgwardt, K.M., Schraudolph, N.N.: Fast computation of graph kernels. In: Schkopf, B., Platt, J., Hoffman, T. (eds.) NIPS, pp. 1449–1456. MIT Press (2006)Google Scholar
  29. 29.
    Woznica, A., Kalousis, A., Hilario, M.: Matching based kernels for labeled graphs. In: ECML/PKDD Workshop on Mining and Learning with Graphs (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Chalmers University of TechnologyGöteborgSweden

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