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A More Secure Spatial Decompositions Algorithm via Indefeasible Laplace Noise in Differential Privacy

  • Xiaocui Li
  • Yangtao Wang
  • Xinyu Zhang
  • Ke ZhouEmail author
  • Chunhua Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11323)

Abstract

Spatial decompositions are often used in the statistics of location information. For security, current works split the whole domain into sub-domains recursively to generate a hierarchical private tree and add Laplace noise to each node’s points count, as called differentially private spatial decompositions. However Laplace distribution is symmetric about the origin, the mean of a large number of queries may cancel the Laplace noise. In private tree, the point count of intermediate nodes may be real since the summation of all its descendants may cancel the Laplace noise and reveal privacy. Moreover, existing algorithms add noises to all nodes of the private tree which leads to higher noise cost, and the maximum depth h of the tree is not intuitive for users. To address these problems, we propose a more secure algorithm which avoids canceling Laplace noise. That splits the domains depending on its real point count, and only adds indefeasible Laplace noise to leaves. The ith randomly selected leaf of one intermediate node is added noise by \(\frac{\left( \beta -i+1 \right) +1+\beta }{(\beta -i+1)+\beta }Lap(\lambda )\). We also replace h with a more intuitive split unit u. The experiment results show that our algorithm performs better both on synthetic and real datasets with higher security and data utility, and the noise cost is highly decreased.

Keywords

Indefeasible Laplace noise Low noise cost Differential privacy Spatial decompositions 

References

  1. 1.
    Yin, H., Chen, H., Sun, X., et al.: SPTF: a scalable probabilistic tensor factorization model for semantic-aware behavior prediction. In: IEEE International Conference on Data Mining, pp. 585–594. IEEE Press, New Orleans (2017)Google Scholar
  2. 2.
    Chen, H., Yin, H., Wang, W., et al.: PME: projected metric embedding on heterogeneous networks for link prediction. In: 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1177–1186. ACM Press, London (2018)Google Scholar
  3. 3.
    Chen, T., Yin, H., Chen, H., et al.: TADA: trend alignment with dual-attention multi-task recurrent neural networks for sales prediction. In: IEEE International Conference on Data Mining. IEEE Press, Singapore (2018)Google Scholar
  4. 4.
    Yin, H., Wang, W., Wang, H., et al.: Spatial-aware hierarchical collaborative deep learning for POI recommendation. IEEE Trans. Knowl. Data Eng. 29(11), 2537–2551 (2017)CrossRefGoogle Scholar
  5. 5.
    Yin, H., Sun, Y., Cui, B., et al.: LCARS: a location-content-aware recommender system. In: 19th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 221–229. IEEE Press, Chicago (2013)Google Scholar
  6. 6.
    Friedman, A., Schuster, A.: Data mining with differential privacy. In: 16th International Conference on Knowledge Discovery and Data Mining, pp. 493–502. ACM Press, Washington (2010)Google Scholar
  7. 7.
    Fung, B.C.M.: Privacy-preserving data publishing. ACM Comput. Surv. 42(4), 1–53 (2010)CrossRefGoogle Scholar
  8. 8.
    Hardt, M., Ligett, K., Mcsherry, F.: A simple and practical algorithm for differentially private data release. In: Advances in Neural Information Processing Systems, pp. 2339–2347 (2010)Google Scholar
  9. 9.
    Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006).  https://doi.org/10.1007/11787006_1CrossRefGoogle Scholar
  10. 10.
    Dwork, C.: Differential privacy: a survey of results. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-79228-4_1CrossRefzbMATHGoogle Scholar
  11. 11.
    Dwork, C.: A firm foundation for private data analysis. Commun. ACM 54(1), 86–95 (2011)CrossRefGoogle Scholar
  12. 12.
    Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Found. Trends Theor. Comput. Sci. 9(3–4), 211–407 (2014)MathSciNetzbMATHGoogle Scholar
  13. 13.
    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).  https://doi.org/10.1007/11681878_14CrossRefGoogle Scholar
  14. 14.
    Xu, J., Zhang, Z., Xiao, X., et al.: Differentially private histogram publication. In: 29th IEEE International Conference on Data Engineering, pp. 32–43. IEEE Press, Brisbane (2013)Google Scholar
  15. 15.
    Xiao, X., Wang, G., Gehrke, J.: Differential privacy via wavelet transforms. In: 26th IEEE International Conference on Data Engineering, pp. 225–236. IEEE Press (2010)Google Scholar
  16. 16.
    Mohammed, N., Chen, R., Fung, B.C.M., et al.: Differentially private data release for data mining. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 493–501. ACM press (2011)Google Scholar
  17. 17.
    Cormode, G., Procopiuc, C., Srivastava, D., et al.: Differentially private spatial decompositions. In: 28th IEEE International Conference on Data Engineering, pp. 20–31. IEEE Press, Washington (2012)Google Scholar
  18. 18.
    Li, N., Yang, W., Qardaji, W.: Differentially private grids for geospatial data. In: 28th IEEE International Conference on Data Engineering, pp. 757–768. IEEE Press, Washington (2012)Google Scholar
  19. 19.
    Zhang, J., Xiao, X., Xie, X.: PrivTree: a differentially private algorithm for hierarchical decompositions. In: 35th ACM Conference on Management of Data, pp. 155–170. ACM Press, San Franciso (2016)Google Scholar
  20. 20.
    Zhang, J., Cormode, G., et al.: PrivBayes: private data release via Bayesian networks. In: 33th ACM Conference on Management of Data, pp. 1423–1434. ACM Press, Utah (2014)Google Scholar
  21. 21.
    Zhang, J., Cormode, G., et al.: Private release of graph statistics using ladder functions. In: 34th ACM Conference on Management of Data, pp. 731–745. ACM Press, Melbourne (2015)Google Scholar
  22. 22.
    Miller, F.P., Vandome, A.F., Mcbrewster, J.: KD-tree (2009)Google Scholar
  23. 23.
    Guttman, A.: R-trees: a dynamic index structure for spatial searching. In: International Conference on Management of Data 1984, pp. 47–57. ACM Press, Massachusetts (1984)Google Scholar
  24. 24.
    Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. In: The 25th ACM Symposium on Theory of Computing, pp. 226–234 (1993)Google Scholar
  25. 25.
    Demaine, E.D., Mozes, S., Rossman, B., et al.: An optimal decomposition algorithm for tree edit distance. ACM Trans. Algorithms 6(1), 1–19 (2007)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Li, B., et al.: Dynamic reverse furthest neighbor querying algorithm of moving objects. In: Li, J., Li, X., Wang, S., Li, J., Sheng, Q.Z. (eds.) ADMA 2016. LNCS (LNAI), vol. 10086, pp. 266–279. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-49586-6_18CrossRefGoogle Scholar
  27. 27.
    Xiao, X., Wang, G., Gehrke, J.: Differential privacy via wavelet transforms. IEEE Trans. Knowl. Data Eng. 23(8), 1200–1214 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Xiaocui Li
    • 1
  • Yangtao Wang
    • 1
  • Xinyu Zhang
    • 2
  • Ke Zhou
    • 1
    Email author
  • Chunhua Li
    • 1
  1. 1.Wuhan National Laboratory for OptoelectronicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of ComputerWuhan UniversityWuhanChina

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