Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Blocki, J., Blum, A., Datta, A., Sheffet, O.: Differentially private data analysis of social networks via restricted sensitivity. In: ITCS, pp. 87–96 (2013)
Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Proceedings of ICDM, pp. 74–81 (2005)
Dobson, P.D., Doig, A.J.: Distinguishing enzyme structures from non-enzymes without alignments. J. Mol. Biol. 330(4), 771–783 (2003)
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)
Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Theoret. Comput. Sci. 9(3–4), 211–407 (2013)
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)
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)
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)
Jain, P., Thakurta, A.: Differentially private learning with kernels. In: JMLR Proceedings of ICML 2013, vol. 28, pp. 118–126 (2013). JMLR.org
Jernigan, C., Mistree, B.F.: Gaydar: facebook friendships expose sexual orientation. First Monday 14(10) (2009)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of the 20th International Conference on Machine Learning (2003)
Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? In: CoRR (2008)
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)
Kriege, N., Mutzel, P.: Subgraph matching kernels for attributed graphs. In: ICML. icml.cc / Omnipress (2012)
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)
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)
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)
Narayanan, A., Shmatikov, V.: Robust de-anonymization of large sparse datasets. In: 2013 IEEE Symposium on Security and Privacy, pp. 111–125 (2008)
Nissim, K., Raskhodnikova, S., Smith, A.: Smooth sensitivity and sampling in private data analysis. In: STOC 2007, pp. 75–84. ACM (2007)
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)
Schölkopf, B., Smola, A.J.: Learning With Kernels: Support Vector Machines, Regularization, Optimization, And Beyond. MIT Press, Cambridge (2001)
Shervashidze, N.: Scalable graph kernels. Ph.D. thesis, Eberhard Karls Universitt Tbingen (2012)
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)
Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: Proceedings of AISTATS (2009)
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)
Vishwanathan, S., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. J. Mach. Learn. Res. 11, 1201–1242 (2010)
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)
Woznica, A., Kalousis, A., Hilario, M.: Matching based kernels for labeled graphs. In: ECML/PKDD Workshop on Mining and Learning with Graphs (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Johansson, F.D., Frost, O., Retzner, C., Dubhashi, D. (2015). Classifying Large Graphs with Differential Privacy. In: Torra, V., Narukawa, T. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2015. Lecture Notes in Computer Science(), vol 9321. Springer, Cham. https://doi.org/10.1007/978-3-319-23240-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-23240-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23239-3
Online ISBN: 978-3-319-23240-9
eBook Packages: Computer ScienceComputer Science (R0)