Publishing Trajectory with Differential Privacy: A Priori vs. A Posteriori Sampling Mechanisms

  • Dongxu Shao
  • Kaifeng Jiang
  • Thomas Kister
  • Stéphane Bressan
  • Kian-Lee Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8055)


It is now possible to collect and share trajectory data for any ship in the world by various means such as satellite and VHF systems. However, the publication of such data also creates new risks for privacy breach with consequences on the security and liability of the stakeholders. Thus, there is an urgent need to develop methods for preserving the privacy of published trajectory data. In this paper, we propose and comparatively investigate two mechanisms for the publication of the trajectory of individual ships under differential privacy guarantees. Traditionally, privacy and differential privacy is achieved by perturbation of the result or the data according to the sensitivity of the query. Our approach, instead, combines sampling and interpolation. We present and compare two techniques in which we sample and interpolate (a priori) and interpolate and sample (a posteriori), respectively. We show that both techniques achieve a (0, δ) form of differential privacy. We analytically and empirically, with real ship trajectories, study the privacy guarantee and utility of the methods.


Dynamic Time Warping Trajectory Data Differential Privacy Privacy Breach Original Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agard, B., Morency, C., Trépanier, M.: Mining public transport user behaviour from smart card data. In: The 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM (2006)Google Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007, pp. 94–103. IEEE (2007)Google Scholar
  5. 5.
    Dwork, C., Kenthapadi, K., McSherry, F., Mironov, I., Naor, M.: Our data, ourselves: Privacy via distributed noise generation. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 486–503. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Abul, O., Bonchi, F., Nanni, M.: Never walk alone: Uncertainty for anonymity in moving objects databases. In: Proceedings of the 2008 IEEE 24th International Conference on Data Engineering, ICDE 2008, pp. 376–385. IEEE Computer Society, Washington, DC (2008)CrossRefGoogle Scholar
  7. 7.
    Chen, R., Fung, B.C.M., Desai, B.C.: Differentially private trajectory data publication. CoRR abs/1112.2020 (2011)Google Scholar
  8. 8.
    Mandel, C., Frese, U.: Comparison of wheelchair user interfaces for the paralysed: Head-joystick vs. verbal path selection from an offered route-set. In: Proceedings of the 3rd European Conference on Mobile Robots, ECMR 2007 (2007)Google Scholar
  9. 9.
    Chaudhuri, K., Mishra, N.: When random sampling preserves privacy. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 198–213. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Gehrke, J., Hay, M., Lui, E., Pass, R.: Crowd-blending privacy. Cryptology ePrint Archive, Report 2012/456 (2012),
  11. 11.
    Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech and Signal Processing 26(1), 43–49 (1978)zbMATHCrossRefGoogle Scholar
  12. 12.
    Dwork, C., Rothblum, G., Vadhan, S.: Boosting and differential privacy. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 51–60. IEEE (2010)Google Scholar
  13. 13.
    Shao, D., Jiang, K., Kister, T., Bressan, S., TAN, K.L.: Publishing trajectory with differential privacy: A priori vs a posteriori sampling mechanisms. Technical Report: TRA4/13 (2013),

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dongxu Shao
    • 1
  • Kaifeng Jiang
    • 2
  • Thomas Kister
    • 1
  • Stéphane Bressan
    • 2
  • Kian-Lee Tan
    • 1
  1. 1.School of ComputingNational University of SingaporeSingapore
  2. 2.Center for Maritime StudiesNational University of SingaporeSingapore

Personalised recommendations