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A group-based signal filtering approach for trajectory abstraction and restoration

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Abstract

Trajectory abstraction is used to summarize the large amount of information delivered by the trajectory data, and trajectory restoration is used to reconstruct lost parts of trajectories. To cope with complex trajectory data, in this paper, we propose a new strategy for abstracting and restoring trajectories from the perspective of signal processing. That is, trajectories are treated as signals that bear copious information that varies with time and space, and information filtering is exploited to concisely communicate the trajectory data. As for trajectory abstraction, the resampling of trajectory data is first introduced based on achieving the minimum Jensen–Shannon divergence of the trajectories before and after being resampled. Then, a non-local filtering approach is developed to perform wavelet transformations of similarity groups of these resampled trajectories to produce the trajectory summaries. Trajectory abstraction can not only offer multi-granularity summaries of trajectory data, but also identify outliers by utilizing a probabilistic definition of a group of trajectories and the Shannon entropy. Furthermore, to handle incomplete trajectory data for which some sample points are lost, the proposed non-local filtering idea is exploited to restore the incomplete data. Extensive experimental studies have shown that the proposed trajectory abstraction and restoration can obtain very encouraging results, in terms of both objective evaluation metrics and subjective visual effects. To the best of our knowledge, this is the first attempt to deploy the group-based signal filtering technique in the context of dealing with trajectory data. In addition, as a preprocessing step, the proposed trajectory abstraction can be employed to improve the performance of trajectory clustering.

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References

  1. Aggarwal CC (2017) Outlier analysis. Springer, Berlin. doi:10.1007/978-3-319-47578-3

    Book  MATH  Google Scholar 

  2. Aggarwal CC, Reddy CK (2013) Data clustering: algorithms and applications. Chapman and Hall/CRC, London

    MATH  Google Scholar 

  3. Aircraft dataset. https://c3.nasa.gov/dashlink/resources/132/. Accessed 22 June 2017

  4. Allasia G, Besenghi R, Cavoretto R, Rossi AD (2011) Scattered and track data interpolation using an efficient strip searching procedure. Appl Math Comput 217(12):5949–5966. doi:10.1016/j.amc.2010.12.110

    MathSciNet  MATH  Google Scholar 

  5. Alt H (2009) The computational geometry of comparing shapes. In: Albers S, Alt H, Näher S (eds) Efficient algorithms: essays dedicated to Kurt Mehlhorn on the occasion of his 60th birthday. Springer, Berlin, pp 235–248. doi:10.1007/978-3-642-03456-5_16

    Chapter  Google Scholar 

  6. Anjum N, Cavallaro A (2008) Multifeature object trajectory clustering for video analysis. IEEE Trans Circuits Syst Video Technol 18(11):1555–1564. doi:10.1109/TCSVT.2008.2005603

    Article  Google Scholar 

  7. Ankerst M, Breunig MM, Kriegel HP, Sander J (1999) Optics: ordering points to identify the clustering structure. In: Proceedings of the 1999 ACM SIGMOD international conference on management of data, SIGMOD ’99, pp 49–60. ACM, New York. DOI:10.1145/304181.304187

  8. Best track dataset. http://weather.unisys.com/hurricane/atlantic/. Accessed 22 June 2017

  9. Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In: IEEE computer society conference on computer vision and pattern recognition, CVPR ’05, vol 2, pp 60–65. IEEE Computer Society, Washington, DC, USA. DOI:10.1109/CVPR.2005.38

  10. Calderara S, Prati A, Cucchiara R (2011) Mixtures of von mises distributions for people trajectory shape analysis. IEEE Trans Circuits Syst Video Technol 21(4):457–471. doi:10.1109/TCSVT.2011.2125550

    Article  Google Scholar 

  11. Chandola V, Banerjee A, Kumar V (2009) Anomaly detection: a survey. ACM Comput Surv 41(3):15:1–15:58. doi:10.1145/1541880.1541882

    Article  Google Scholar 

  12. Chen C, Zhang D, Castro PS, Li N, Sun L, Li S (2012) Real-time detection of anomalous taxi trajectories from GPS traces. In: Puiatti A, Gu I (eds) Mobile and ubiquitous systems: computing, networking, and services. MobiQuitous 2011, vol 104. Lecture notes of the institute for computer sciences, social informatics and telecommunications engineering. Springer, Berlin, pp 63–74. doi:10.1007/978-3-642-30973-1_6

    Chapter  Google Scholar 

  13. Chen W, Chang SF (2000) Motion trajectory matching of video objects. In: Storage and retrieval for media databases, vol 3972, pp 544–553. The International Society for Optical Engineering. DOI:10.1117/12.373587

  14. Clifton DA, Clifton L, Hugueny S, Wong D, Tarassenko L (2013) An extreme function theory for novelty detection. IEEE J Select Top Signal Process 7(1):28–37. doi:10.1109/JSTSP.2012.2234081

    Article  Google Scholar 

  15. Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095. doi:10.1109/TIP.2007.901238

    Article  MathSciNet  Google Scholar 

  16. Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. Proce VLDB Endow 1(2):1542–1552. doi:10.14778/1454159.1454226

    Article  Google Scholar 

  17. Edinburgh dataset. http://homepages.inf.ed.ac.uk/rbf/FORUMTRACKING/. Accessed 22 June 2017

  18. Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the second international conference on knowledge discovery and data mining, KDD’96, pp 226–231. AAAI Press

  19. Faloutsos C, Ranganathan M, Manolopoulos Y (1994) Fast subsequence matching in time-series databases. SIGMOD Rec 23(2):419–429. doi:10.1145/191843.191925

    Article  Google Scholar 

  20. Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24(6):381–395. doi:10.1145/358669.358692

    Article  MathSciNet  Google Scholar 

  21. Gariel M, Srivastava AN, Feron E (2011) Trajectory clustering and an application to airspace monitoring. IEEE Trans Intell Transp Syst 12(4):1511–1524. doi:10.1109/TITS.2011.2160628

    Article  Google Scholar 

  22. Guo Y, Xu Q, Liang S, Fan Y, Sbert M (2015) Xaibo: an extension of AIB for trajectory clustering with outlier. In: Arik S, Huang T, Lai WK, Liu Q (eds) Neural information processing, vol 9490. Lecture notes in computer science. Springer, Berlin, pp 423–431. doi:10.1007/978-3-319-26535-3_48

    Chapter  Google Scholar 

  23. Guo Y, Xu Q, Yang Y, Liang S, Liu Y, Sbert M (2014) Anomaly detection based on trajectory analysis using kernel density estimation and information bottleneck techniques. Technical report 108, University of Girona. http://gilab.udg.edu/wp-content/uploads/publications/IIiA-15-01-RR.pdf

  24. Hazan A, Lacaille J, Madani K (2012) Extreme value statistics for vibration spectra outlier detection. In: International conference on condition monitoring and machinery failure prevention technologies, p 1. Londres, UK

  25. Johnstone IM, Silverman BW (1997) Wavelet threshold estimators for data with correlated noise. J R Stat Soc Ser B (Methodol) 59(2):319–351. doi:10.1111/1467-9868.00071

    Article  MathSciNet  MATH  Google Scholar 

  26. Jr, R.A., Forster CHQ (2012) Analysis of aircraft trajectories using fourier descriptors and kernel density estimation. In: 15th international IEEE conference on intelligent transportation systems, pp 1441–1446. IEEE, Anchorage, Alsaka, USA. DOI:10.1109/ITSC.2012.6338863

  27. Kragten J (1990) Least-squares polynomial curve-fitting for calibration purposes (statcal-calibra). Anal Chim Acta 241(1):1–13. doi:10.1016/S0003-2670(00)83259-6

    Article  Google Scholar 

  28. Laxhammar R, Falkman G (2014) Online learning and sequential anomaly detection in trajectories. IEEE Trans Pattern Anal Mach Intell 36(6):1158–1173. doi:10.1109/TPAMI.2013.172

    Article  MATH  Google Scholar 

  29. Lin J (1991) Divergence measures based on the Shannon entropy. IEEE Trans Inf Theory 37(1):145–151. doi:10.1109/18.61115

    Article  MathSciNet  MATH  Google Scholar 

  30. Lloyd S (1982) Least squares quantization in PCM. IEEE Trans Inf Theory 28(2):129–137. doi:10.1109/TIT.1982.1056489

    Article  MathSciNet  MATH  Google Scholar 

  31. Luo X, Xu Q, Guo Y, Wei H, Lv Y (2015) Trajectory abstracting with group-based signal denoising. In: Arik S, Huang T, Lai WK, Liu Q (eds) Neural information processing, vol 9491. Lecture notes in computer science. Springer, Berlin, pp 452–461. doi:10.1007/978-3-319-26555-1_51

    Chapter  Google Scholar 

  32. May R, Hanrahan P, Keim DA, Shneiderman B, Card S (2010) The state of visual analytics: views on what visual analytics is and where it is going. In: IEEE symposium on visual analytics science and technology, pp 257–259. IEEE. DOI:10.1109/VAST.2010.5649078

  33. Morris BT, Trivedi MM (2008) A survey of vision-based trajectory learning and analysis for surveillance. IEEE Trans Circuits Syst Video Technol 18(8):1114–1127. doi:10.1109/TCSVT.2008.927109

    Article  Google Scholar 

  34. Morris BT, Trivedi MM (2011) Trajectory learning for activity understanding: unsupervised, multilevel, and long-term adaptive approach. IEEE Trans Pattern Anal Mach Intell 33(11):2287–2301. doi:10.1109/TPAMI.2011.64

    Article  Google Scholar 

  35. Morris BT, Trivedi MM (2013) Understanding vehicular traffic behavior from video: a survey of unsupervised approaches. J Electron Imaging 22(4):041,113–041,113. doi:10.1117/1.JEI.22.4.041113

    Article  Google Scholar 

  36. Ntalampiras S, Potamitis I, Fakotakis N (2011) Probabilistic novelty detection for acoustic surveillance under real-world conditions. IEEE Trans Multimed 13(4):713–719. doi:10.1109/TMM.2011.2122247

    Article  Google Scholar 

  37. Omni dataset. http://cvrr.ucsd.edu/bmorris/datasets/dataset_trajectory_analysis.html. Accessed 22 June 2017

  38. Piciarelli C, Micheloni C, Foresti GL (2008) Trajectory-based anomalous event detection. IEEE Trans Circuits Syst Video Technol 18(11):1544–1554. doi:10.1109/TCSVT.2008.2005599

    Article  Google Scholar 

  39. Pimentel MA, Clifton DA, Clifton L, Tarassenko L (2014) A review of novelty detection. Signal Process 99:215–249. doi:10.1016/j.sigpro.2013.12.026

    Article  Google Scholar 

  40. Recorded video dataset. http://www-users.cs.umn.edu/~aleks/inclof/. Accessed 22 June 2017

  41. Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496. doi:10.1126/science.1242072

    Article  Google Scholar 

  42. Sahouria E, Zakhor A (1997) Motion indexing of video. In: International conference on image processing, vol 2, pp 526–529. IEEE, Santa Barbara, CA, USA. DOI:10.1109/ICIP.1997.638824

  43. Süli E, Mayers DF (2003) An introduction to numerical analysis. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  44. Synthetic dataset. http://avires.dimi.uniud.it/papers/trclust/. Accessed 22 June 2017

  45. Vlachos M, Lin J, Keogh E, Gunopulos D (2003) A wavelet-based anytime algorithm for k-means clustering of time series. In: Proceedings of workshop on clustering high dimensionality data and its applications, Citeseer, pp 23–30

  46. Wang W, Yang J, Muntz R (1997) Sting: A statistical information grid approach to spatial data mining. In: Proceedings of the 23rd international conference on very large data bases, VLDB ’97, vol 97. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, pp 186–195

  47. Zhang T, Ramakrishnan R, Livny M (1996) Birch: An efficient data clustering method for very large databases. In: ACM SIGMOD international conference on management of data, SIGMOD ’96, pp 103–114. ACM, New York, NY, USA. DOI:10.1145/235968.233324

  48. Zheng Y (2015) Trajectory data mining: an overview. ACM Trans Intell Syst Technol 6(3):29:1–29:41. doi:10.1145/2743025

    Article  Google Scholar 

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Acknowledgements

Yuejun Guo and Xiaoxiao Luo contributed equally to this work and share the first authorship.

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Authors and Affiliations

  1. School of Computer Science and Technology, Tianjin University, Tianjin, China

    Yuejun Guo, Qing Xu, Xiaoxiao Luo, Hao Wei, Hongjuan Bu & Mateu Sbert

  2. Graphics and Imaging Lab, University of Girona, Girona, Spain

    Yuejun Guo & Mateu Sbert

Authors
  1. Yuejun Guo
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  2. Qing Xu
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  3. Xiaoxiao Luo
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Corresponding authors

Correspondence to Qing Xu or Mateu Sbert.

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Additional information

This work has been funded by the Natural Science Foundation of China (61471261, 61179067, U1333110), and by the Grants TIN2013-47276-C6-1-R from the Spanish government and 2014-SGR-1232 from the Catalan government (Spain). The first author acknowledges the support from Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya and the European Social Fund.

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Guo, Y., Xu, Q., Luo, X. et al. A group-based signal filtering approach for trajectory abstraction and restoration. Neural Comput & Applic 29, 371–387 (2018). https://doi.org/10.1007/s00521-017-3148-8

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