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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 763469, 8 pages
http://dx.doi.org/10.1155/2014/763469
Research Article

Robust Missing Traffic Flow Imputation Considering Nonnegativity and Road Capacity

1Department of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, China
2Department of Civil and Environmental Engineering, University of Wisconsin-Madison, Madison, WI, USA

Received 18 December 2013; Accepted 13 February 2014; Published 18 March 2014

Academic Editor: Huimin Niu

Copyright © 2014 Huachun Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Zhang, F.-Y. Wang, K. Wang, W.-H. Lin, X. Xu, and C. Chen, “Data-driven intelligent transportation systems: a survey,” IEEE Transactions on Intelligent Transportation Systems, vol. 12, no. 4, pp. 1624–1639, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. R. C. Jou and K. H. Chen, “A study of freeway drivers’demand for real-time traffic information along main freeways and alternative routes,” Transportation Research C, vol. 31, pp. 62–72, 2013. View at Google Scholar
  3. E. Azimirad, N. Pariz, and M. B. N. Sistani, “A novel fuzzy model and control of single intersection at urban traffic network,” IEEE Systems Journal, vol. 4, no. 1, pp. 107–111, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. C. P. I. J. van Hinsbergen, T. Schreiter, F. S. Zuurbier, J. W. C. van Lint, and H. J. van Zuylen, “Localized extended kalman filter for scalable real-time traffic state estimation,” IEEE Transactions on Intelligent Transportation Systems, vol. 13, no. 1, pp. 385–394, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Qiao, A. Haghani, and M. Hamedi, “A nonparametric model for short-term travel time prediction using bluetooth data,” Journal of Intelligent Transportation Systems, vol. 17, no. 2, pp. 165–175, 2013. View at Publisher · View at Google Scholar
  6. S. A. Zargari, S. Z. Siabil, A. H. Alavi, and A. H. Gandomi, “A computational intelligence-based approach for short-term traffic flow prediction,” Expert Systems, vol. 29, no. 2, pp. 124–142, 2012. View at Google Scholar
  7. L. Qu, L. Li, Y. Zhang, and J. Hu, “PPCA-based missing data imputation for traffic flow volume: a systematical approach,” IEEE Transactions on Intelligent Transportation Systems, vol. 10, no. 3, pp. 512–522, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Turner, L. Albert, B. Gajewski, and W. Eisele, “Archived intelligent transportation system data quality: preliminary analyses of San Antonio TransGuide data,” Transportation Research Record, vol. 1719, pp. 77–84, 2000. View at Google Scholar · View at Scopus
  9. PeMS, “California performance measurement system,” http://pems.dot.ca.gov/.
  10. R. C. Carlson, I. Papamichail, M. Papageorgiou, and A. Messmer, “Optimal mainstream traffic flow control of large-scale motorway networks,” Transportation Research C, vol. 18, no. 2, pp. 193–212, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. L. H. Nguyen and W. T. Scherer, “Imputation techniques to account for missing data in support of intelligent transportation systems applications,” Tech. Rep. UVACTS-13-0-78, University of Virginia, Center for Transportation Studies, 2003. View at Google Scholar
  12. J. R. Xu, X. Y. Li, and H. J. Shi, “Short-term traffic flow forecasting model under missing data,” Journal of Computer Applications, vol. 30, pp. 1117–1120, 2010. View at Google Scholar
  13. J. W. C. van Lint, S. P. Hoogendoorn, and H. J. van Zuylen, “Accurate freeway travel time prediction with state-space neural networks under missing data,” Transportation Research C, vol. 13, no. 5-6, pp. 347–369, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. W. Yin, P. Murray-Tuite, and H. Rakha, “Imputing erroneous data of single-station Loop detectors for nonincident conditions: comparison between temporal and spatial methods,” Journal of Intelligent Transportation Systems, vol. 16, no. 3, pp. 159–176, 2012. View at Google Scholar
  15. M. Zhong, P. Lingras, and S. Sharma, “Estimation of missing traffic counts using factor, genetic, neural, and regression techniques,” Transportation Research C, vol. 12, no. 2, pp. 139–166, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. L. Li, Y. Li, and Z. Li, “Efficient missing data imputing for traffic flow by considering temporal and spatial dependence,” Transportation Research C, vol. 34, pp. 108–120, 2013. View at Publisher · View at Google Scholar
  17. H. Tan, G. Feng, J. Feng, W. Wang, Y. J. Zhang, and F. Li, “A tensor-based method for missing traffic data completion,” Transportation Research C, vol. 28, pp. 15–27, 2013. View at Publisher · View at Google Scholar
  18. H. Tan, J. Feng, Z. Chen, F. Yang, and W. Wang, “Low multilinear rank approximation of tensors and application in missing traffic data,” Advances in Mechanical Engineering, vol. 2014, Article ID 157597, 12 pages, 2014. View at Publisher · View at Google Scholar
  19. H. Tan, B. Cheng, J. Feng, G. Feng, W. Wang, and Y. J. Zhang, “Low-n-rank tensor recovery based on multi-linear augmented Lagrange multiplier method,” Neurocomputing, vol. 119, pp. 144–152, 2013. View at Google Scholar
  20. H. Tan, C. Bin, W. Wuhong, Z. Yu-Jin, and R. Bin, “Tensor recovery via multi-linear augmented lagrange multiplier method,” in Proceedings of the 6th International Conference on Image and Graphics (ICIG '11), pp. 141–146, August 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. X. Yuan and Y. Junfeng, “Sparse and low-rank matrix decomposition via alternating direction methods,” preprint 2009.
  22. F. de la Torre and M. J. Black, “A framework for robust subspace learning,” International Journal of Computer Vision, vol. 54, no. 1–3, pp. 117–142, 2003. View at Google Scholar · View at Scopus
  23. E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Foundations of Computational Mathematics, vol. 9, no. 6, pp. 717–772, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM Journal on Optimization, vol. 20, no. 4, pp. 1956–1982, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. Z. Lin, M. Chen, and Y. Ma, “The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices,” 2010, http://arxiv.org/abs/1009.5055.
  26. E. J. Candes and Y. Plan, “Matrix completion with noise,” Proceedings of the IEEE, vol. 98, no. 6, pp. 925–936, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. E. J. Candès, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM, vol. 58, no. 3, article 11, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM Journal on Computing, vol. 24, no. 2, pp. 227–234, 1995. View at Google Scholar · View at Scopus
  29. P. Indyk and M. Ružić, “Near-optimal sparse recovery in the L1 norm,” in Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS '08), pp. 199–207, October 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. G. W. Stewart, “On the early history of the singular value decomposition,” SIAM Review, vol. 35, no. 4, pp. 551–566, 1993. View at Google Scholar · View at Scopus
  31. C. Chen, J. Kwon, J. Rice, A. Skabardonis, and P. Varaiya, “Detecting errors and imputing missing data for single-loop surveillance systems,” Transportation Research Record, no. 1855, pp. 160–167, 2003. View at Google Scholar · View at Scopus
  32. S. Chen, W. Wang, and H. van Zuylen, “A comparison of outlier detection algorithms for ITS data,” Expert Systems with Applications, vol. 37, no. 2, pp. 1169–1178, 2010. View at Publisher · View at Google Scholar · View at Scopus