Anomalous Traffic Pattern Detection in Large Urban Areas: Tensor-Based Approach with Continuum Modeling of Traffic Flow

  • Stanislav LykovEmail author
  • Yasuo Asakura


Analysis of traffic dynamics in large urban transportation networks is a complicated procedure, yet critical for many areas of transportation research and contemporary intelligent transportation systems. The degree of complexity is increasing, considering the existence of unexpected events such as natural or manmade disasters. The study addresses the needs of detection and description of abnormal traffic patterns formed due to the presence of aforementioned disruptions. In order to take into account complex spatiotemporal structure of traffic dynamics and preserve multi-mode correlations, tensor-based traffic data representation is put forward. Tensor robust principal component analysis is applied for the purpose of discovering distinctive normal and abnormal traffic patterns. For validation purposes, continuum modeling approach is employed to emulate traffic dynamics, with consideration of the effect of disruptions. The results suggested applicability of proposed approach in order to discover abnormal patterns in large urban networks.


Anomaly detection Tensor robust principal component analysis Continuum modeling approach 



  1. 1.
    Rempe, F., Huber, G., Bogenberger, K.: Spatio-temporal congestion patterns in urban traffic networks. Transportation Research Procedia. 15, 513–524 (2016)CrossRefGoogle Scholar
  2. 2.
    Li, L., Li, Y., Li, Z.: Efficient missing data imputing for traffic flow by considering temporal and spatial dependence. Transportation Research Part C: Emerging Technologies. 34, 108–120 (2013)CrossRefGoogle Scholar
  3. 3.
    Goulart, J.H.M., de Kibangou, A.Y., Favier, G.: Traffic data imputation via tensor completion based on soft thresholding of Tucker core. In: Transportation Research Part C: Emerging Technologies. 85, 348–362 (2017)CrossRefGoogle Scholar
  4. 4.
    Ran, B., Tan, H., Wu, Y., Jin, P.J.: Tensor based missing traffic data completion with spatial-temporal correlation. Physica A: Statistical Mechanics and its Applications. 446, 54–63 (2016)CrossRefGoogle Scholar
  5. 5.
    Chen, X., He, Z., Wang, J.: Spatial-temporal traffic speed patterns discovery and incomplete data recovery via SVD-combined tensor decomposition. Transportation Research Part C: Emerging Technologies. 86, 59–77 (2018)CrossRefGoogle Scholar
  6. 6.
    Han, Y., Moutarde, F.: Analysis of large-scale traffic dynamics in an urban transportation network using non-negative tensor factorization. Int. J. Intell. Transp. Syst. Res. 14(1), 36–49 (2016)Google Scholar
  7. 7.
    Chi, E.C., Kolda, T.G.: “Making tensor factorizations robust to non-Gaussian noise”. In: tech. Rep. No. SAND2011-1877. Sandia National Laboratories. (2011)Google Scholar
  8. 8.
    Du, J., Wong, S.C., Shu, C.W., Xiong, T., Zhang, M., Choi, K.: Revisiting Jiang’s dynamic continuum model for urban cities. Transp. Res. B Methodol. 56, 96–119 (2013)CrossRefGoogle Scholar
  9. 9.
    Jiang, Y., Xiong, T., Wong, S. C., Shu, C. W., Zhang, M., Zhang, P., Lam., W.H.K., "A reactive dynamic continuum user equilibrium model for bi-directional pedestrian flows". In: Acta Math. Sci., Vol. 29(6), pp. 1541–1555 (2009)Google Scholar
  10. 10.
    Long, J., Szeto, W.Y., Du, J., Wong, R.C.P.: A dynamic taxi traffic assignment model: a two-level continuum transportation system approach. In: Transportation Research Part B: Methodological. Vol. 100, 222–254 (2017)CrossRefGoogle Scholar
  11. 11.
    Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Edie L., “Discussion of traffic stream measurements and definitions”. In: Almond, J (Ed.), Proceedings of the 2nd International Symposium on the Theory of Traffic Flow, pp. 139–154Google Scholar
  13. 13.
    Xue, N., Papamakarios, G., Bahri, M., Panagakis, Y., Zafeiriou, S.: Robust low-rank tensor modelling using Tucker and CP decomposition. In: 25th European Signal Processing Conference (EUSIPCO). 1185–1189 (2017)Google Scholar
  14. 14.
    Goldfarb, D., Qin, Z.: Robust low-rank tensor recovery: models and algorithms. SIAM Journal on Matrix Analysis and Applications. 35(1), 225–253 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sossoe, K.S., Lebacque, J.P., Mokrani, A., Haj-Salem, H.: Traffic flow within a two-dimensional continuum anisotropic network. Transportation Research Procedia. 10, 217–225 (2015)CrossRefGoogle Scholar
  16. 16.
    Chopp, D.L.: Some improvements of the fast marching method. In: SIAM Journal on Scientific Computing, 23(1), pp. 230–244 (2002)Google Scholar
  17. 17.
    Signoretto, M., De Lathauwer, L., Suykens, J. A. K. “Nuclear Norms for Tensors and Their Use for Convex Multilinear Estimation”. Technical report, ESAT-SISTA, K. U. Leuven, Belgium. (2010)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan

Personalised recommendations