GeoInformatica

, Volume 12, Issue 4, pp 497–528 | Cite as

Reporting Leaders and Followers among Trajectories of Moving Point Objects

  • Mattias Andersson
  • Joachim Gudmundsson
  • Patrick Laube
  • Thomas Wolle
Article

Abstract

Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects, opening new options for a better understanding of the processes involved. In this paper we investigate spatio-temporal movement patterns in large tracking data sets. We present a natural definition of the pattern ‘one object is leading others’, which is based on behavioural patterns discussed in the behavioural ecology literature. Such leadership patterns can be characterised by a minimum time length for which they have to exist and by a minimum number of entities involved in the pattern. Furthermore, we distinguish two models (discrete and continuous) of the time axis for which patterns can start and end. For all variants of these leadership patterns, we describe algorithms for their detection, given the trajectories of a group of moving entities. A theoretical analysis as well as experiments show that these algorithms efficiently report leadership patterns.

Keywords

moving point objects trajectories movement patterns leadership spatio-temporal data structures computational geometry 

Notes

Acknowledgements

Patrick Laube was partially supported by ARC Discovery grant DPDP0662906. National ICT Australia is funded through the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council. The authors wish to thank Karin Schütz, AgResearch Ruakura, Hamilton, New Zealand for valuable comments on animal movement patterns, Bojan Djordjevic for implementing the algorithms and the anonymous reviewers of this and earlier versions of this article.

References

  1. 1.
    P.K. Agarwal, L. Arge, and J. Erickson. “Indexing moving points,” Journal of Computer and System Sciences, Vol. 66(1):207–243, 2003.CrossRefGoogle Scholar
  2. 2.
    G. Al-Naymat, S. Chawla, and J. Gudmundsson. “Dimensionality reduction for long duration and complex spatio-temporal queries,” in Proc. of the 22nd ACM Symposium on Applied Computing, pp. 393–397, ACM, 2007.Google Scholar
  3. 3.
    M. Andersson, J. Gudmundsson, P. Laube, and T. Wolle. Reporting leaders and followers among trajectories of moving point objects. Technical Report PA006075, National ICT Australia, 2006. http://www.nicta.com.au, Extended abstract in Proceedings of the 22nd ACM Symposium on Applied Computing, pp. 3–7, ACM, 2007.
  4. 4.
    M.A. Bender and M. Farach-Colton. “The LCA problem revisited,” in LATIN ’00: Proc. of the 4th Latin American Symposium on Theoretical Informatics, volume 1776 of Lecture Notes in Computer Science, London, UK, pp. 88–94, Springer-Verlag, 2000.Google Scholar
  5. 5.
    M. Benkert, J. Gudmundsson, F. Hübner, and T. Wolle. “Reporting flock patterns,” in Proc. of the 14th European Symposium on Algorithms (ESA 2006), volume 4168 of Lecture Notes in Computer Science, pp. 660–671, Springer, 2006.Google Scholar
  6. 6.
    H. Cao, O. Wolfson, and G. Trajcevski. “Spatio-temporal data reduction with deterministic error bounds,” The VLDB Journal, Vol. 15(3):211–228, 2006.CrossRefGoogle Scholar
  7. 7.
    S.M.C. Cavalcanti and F.F. Knowlton. “Evaluation of physical and behavioral traits of llamas associated with aggressiveness toward sheep-threatening canids,” Applied Animal Behaviour Science, Vol. 61(2):143–158, 1998.CrossRefGoogle Scholar
  8. 8.
    N.R. Chrisman. “Beyond the snapshot: Changing the approach to change, error, and process,” in M.J. Egenhofer and R.G. Golledge (Eds.), Spatial and Temporal Reasoning in Geographic Information Systems, 85–93, Oxford University Press: Oxford, UK, 1998.Google Scholar
  9. 9.
    L. Conradt and T.J. Roper. “Group decision-making in animals,” Nature, Vol. 421(6919):155–158, 2003.CrossRefGoogle Scholar
  10. 10.
    M. D’Auria, M. Nanni, and D. Pedreschi. “Time-focused density-based clustering of trajectories of moving objects,” in Proc. of the Workshop on Mining Spatio-temporal Data (MSTD-2005), Porto, 2005.Google Scholar
  11. 11.
    C. Du Mouza and P. Rigaux. “Mobility patterns,” Geoinformatica, Vol. 9(4):297–319, 2005.CrossRefGoogle Scholar
  12. 12.
    B. Dumont, A. Boissy, C. Achard, A.M. Sibbald, and H.W. Erhard. “Consistency of animal order in spontaneous group movements allows the measurement of leadership in a group of grazing heifers,” Applied Animal Behaviour Science, Vol. 95(1–2):55–66, 2005.CrossRefGoogle Scholar
  13. 13.
    J.A. Dykes and D.M. Mountain. “Seeking structure in records of spatio-temporal behaviour: Visualization issues, efforts and application,” Computational Statistics and Data Analysis, Vol. 43(4):581–603, 2003.CrossRefGoogle Scholar
  14. 14.
    N. Eagle and A. Pentland. “Reality mining: Sensing complex social systems,” Personal and Ubiquitous Computing, Vol. 10(4):255–268, 2006.CrossRefGoogle Scholar
  15. 15.
    J. Erickson and R. Seidel. “Better lower bounds on detecting affine and spherical degeneracies,” Discrete & Computational Geometry, Vol. 13:41–57, 1995.CrossRefGoogle Scholar
  16. 16.
    M. Erwig and R.H. Güting. “Spatio-temporal data types: An approach to modeling and querying moving objects in databases,” Geoinformatica, Vol. 3(3):269–296, 1999.CrossRefGoogle Scholar
  17. 17.
    A.U. Frank. “Socio-economic units: Their life and motion,” in A.U. Frank, J. Raper, and J.P. Cheylan (Eds.), Life and Motion of Socio-economic Units, volume 8 of GISDATA, pp. 21–34, Taylor & Francis: London, 2001.Google Scholar
  18. 18.
    A. Gajentaan and M.H. Overmars. n 2-Hard Problems in Computational Geometry. Technical Report 1993-15, Department of Coumputer Science, Utrecht University, The Netherlands, 1993.Google Scholar
  19. 19.
    J. Gudmundsson, J. Katajainen, D. Merrick, C. Ong, and T. Wolle. “Compressing spatiotemporal trajectories,” in Proc. of the 18th International Symposium on Algorithms and Computation, 2007.Google Scholar
  20. 20.
    J. Gudmundsson and M. van Kreveld. “Computing longest duration flocks in trajectory data,” in Proc. of the 14th ACM Symposium on Advances in GIS, pp. 35–42, 2006.Google Scholar
  21. 21.
    J. Gudmundsson, M. van Kreveld, and B. Speckmann. “Efficient detection of motion patterns in spatio-temporal sets,” Geoinformatica, Vol. 11(2):195–215, 2007.CrossRefGoogle Scholar
  22. 22.
    S. Gueron and S.A. Levin. “Self-organization of front patterns in large wildebeest herds,” Journal of Theoretical Biology, Vol. 165(4):541–552, 1993.CrossRefGoogle Scholar
  23. 23.
    R. Güting, M.H. Boehlen, M. Erwig, C.S. Jensen, N. Lorentzos, E. Nardelli, M. Schneider, and M. Vazirgiannis. “A foundation for representing and querying moving objects,” ACM Transactions on Database Systems (TODS), Vol. 2520(1):1–42, 2000.CrossRefGoogle Scholar
  24. 24.
    R. Güting, M.H. Boehlen, M. Erwig, C.S. Jensen, N. Lorentzos, E. Nardelli, M. Schneider, and J.R.R. Viqueira. “Spatio-temporal models and languages: An approach based on data types,” in M. Koubarakis, T. Sellis, A.U. Frank, S. Grumbach, R.H. Güting, C.S. Jensen, N. Lorentzos, Y. Manolopoulos, E. Nardelli, B. Pernici, H.J. Schek, M. Scholl, B. Theodoulidis, and N. Tryfona (Eds.), Spatio-Temporal Databases: The CHOROCHRONOS Approach, volume 2520 of Lecture Notes in Computer Science, 117–176, Springer: Berlin, 2003.Google Scholar
  25. 25.
    R.H. Güting and M. Schneider. Moving Objects Databases. Morgan Kaufmann Publishers, 2005.Google Scholar
  26. 26.
    I.A.R. Hulbert. “GPS and its use in animal telemetry: The next five years,” in A.M. Sibbald and I.J. Gordon (Eds.), Proc. of the Conference on Tracking Animals with GPS, pp. 51–60, Macaulay Insitute: Aberdeen, UK, 2001.Google Scholar
  27. 27.
    Y. Inada and K. Kawachi. “Order and flexibility in the motion of fish schools,” Journal of Theoretical Biology, Vol. 214(3):371–387, 2002.CrossRefGoogle Scholar
  28. 28.
    Y. Ishikawa, Y. Tsukamoto, and H. Kitagawa. “Extracting mobility statistics from indexed spatiotemporal datasets,” in Proc. of the 2nd Workshop on Spatio-Temporal Database Management (STDBM), pp. 9–16, 2004.Google Scholar
  29. 29.
    A. Jadbabaie, J. Lin, and A.S. Morse. “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, Vol. 48(6):988–1001, 2003.CrossRefGoogle Scholar
  30. 30.
    T. Kapler, R. Harper, and W. Wright. “Correlating events with tracked movement in time and space: A geotime case study,” Presented at the 2005 Intelligence Analysis Conference, Washington, DC, 2005.Google Scholar
  31. 31.
    G. Kollios, S. Sclaroff, and M. Betke. “Motion mining: Discovering spatio-temporal patterns in databases of human motion,” in Proc. of the ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, 2001.Google Scholar
  32. 32.
    M. Koubarakis, Y. Theodoridis, and T. Sellis. “Spatio-temporal databases in the years ahead,” in M. Koubarakis, T. Sellis, A.U. Frank, S. Grumbach, R.H. Güting, C.S. Jensen, N. Lorentzos, Y. Manolopoulos, E. Nardelli, B. Pernici, H.J. Schek, M. Scholl, B. Theodoulidis, and N. Tryfona (Eds.), Spatio-Temporal Databases: The CHOROCHRONOS Approach, volume 2520 of Lecture Notes in Computer Science, pp. 345–347. Springer: Berlin, 2003.Google Scholar
  33. 33.
    J. Krause and G.D. Ruxton. Living in Groups. Oxford Series in Ecology and Evolution. Oxford University Press: New York, NY, 2002.Google Scholar
  34. 34.
    M.P. Kwan. “Interactive geovisualization of activity-travel patterns using three dimensional geographical information systems: A methodological exploration with a large data set,” Transportation Research Part C, Vol. 8(1–6):185–203, 2000.CrossRefGoogle Scholar
  35. 35.
    R.F. Lachlan, L. Crooks, and K.N. Laland. “Who follows whom? Shoaling preferences and social learning of foraging information in guppies,” Animal Behaviour, Vol. 56(1):181–190, 1998.CrossRefGoogle Scholar
  36. 36.
    P. Laube and S. Imfeld. “Analyzing relative motion within groups of trackable moving point objects,” in M.J. Egenhofer and D.M. Mark (Eds.), Geographic Information Science 2002, volume 2478 of Lecture Notes in Computer Science, pp. 132–144, Springer: Berlin, 2002.CrossRefGoogle Scholar
  37. 37.
    P. Laube, S. Imfeld, and R. Weibel. “Discovering relative motion patterns in groups of moving point objects,” International Journal of Geographical Information Science, Vol. 19(6):639–668, 2005.CrossRefGoogle Scholar
  38. 38.
    P. Laube and R.S. Purves. “An approach to evaluating motion pattern detection techniques in spatiotemporal data,” Computers, Environment and Urban Systems, Vol. 30(3):347–374, 2006.CrossRefGoogle Scholar
  39. 39.
    P. Laube, M. van Kreveld, and S. Imfeld. “Finding REMO – detecting relative motion patterns in geospatial lifelines,” in P.F. Fisher (Ed.), Developments in Spatial Data Handling: Proc. of the 11th International Symposium on Spatial Data Handling, pp. 201–214, Springer: Berlin, 2004.Google Scholar
  40. 40.
    J.B. Leca, N. Gunst, B. Thierry, and O. Petit. “Distributed leadership in semifree-ranging white-faced capuchin monkeys,” Animal Behaviour, Vol. 66:1045–1052, 2003.CrossRefGoogle Scholar
  41. 41.
    Y. Li, J. Han, and J. Yang. “Clustering moving objects,” in Proc. of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM Press: Seattle, WA, 2004.Google Scholar
  42. 42.
    N. Mamoulis, H. Cao, G. Kollios, M. Hadjieleftheriou, Y. Tao, and D. Cheung. “Mining, indexing, and querying historical spatiotemporal data,” in Proc. of the 10th ACM SIGKDD International Conference On Knowledge Discovery and Data Mining, pp. 236–245, ACM, 2004.Google Scholar
  43. 43.
    D.M. Mark. “Geospatial lifelines,” in Integrating Spatial and Temporal Databases, volume 98471, Dagstuhl Seminars, 1998.Google Scholar
  44. 44.
    H.J. Miller and J. Han. “Geographic data mining and knowledge discovery: An overview,” in H.J. Miller and J. Han (Eds.), Geographic Data Mining and Knowledge Discovery, pp. 3–32. Taylor & Francis, London, 2001.Google Scholar
  45. 45.
    K. Mouratidis, D. Papadias, and M. Hadjieleftheriou. “Conceptual partitioning: An efficient method for continuous nearest neighbor monitoring,” in Proc. of the 2005 ACM SIGMOD Conference on Management of Data, pp. 634–645, 2005.Google Scholar
  46. 46.
    R.T. Ng. “Detecting outliers from large datasets,” in H.J. Miller and J. Han (Eds.), Geographic Data Mining and Knowledge Discovery, pp. 218–235, Taylor & Francis: London, 2001.Google Scholar
  47. 47.
    R.O. Peterson, A.K. Jacobs, T.D. Drummer, L.D. Mech, and D.W. Smith. “Leadership behavior in relation to dominande and reproductive status in gray wolves, canis lupus,” Canadian Journal of Zoology, Vol. 80(8):1405–1412, 2002.CrossRefGoogle Scholar
  48. 48.
    F. Porikli. “Trajectory distance metric using hidden Markov model based representation,” in Proceedings of the 6th IEEE European Conference on Computer Vision, Workshop on PETS, Prague, 2004.Google Scholar
  49. 49.
    Y. Qu, C. Wang, and X.S. Wang. “Supporting fast search in time series for movement patterns in multiple scales,” in Seventh International Conference on Information and Knowledge Management, pp. 251–258, ACM Press: Bethesda, MD, 1998.CrossRefGoogle Scholar
  50. 50.
    S.A. Rands, G. Cowlishaw, R.A. Pettifor, J.M. Rowcliffe, and R.A. Johnstone. “Spontaneous emergence of leaders and followers in foraging pairs,” Nature, Vol. 423(6938):432–434, 2003.CrossRefGoogle Scholar
  51. 51.
    J. Raper. The Dimensions of GIScience, 2002. Keynote speech of GIScience 2002.Google Scholar
  52. 52.
    C.W. Reynolds. “Flocks, herds and schools: A distributed behavioral model,” in Proc. of the 14th annual conference on Computer graphics and interactive techniques, volume 21, pp. 25–34, ACM Press, 1987.Google Scholar
  53. 53.
    J.F. Roddick, K. Hornsby, and M. Spiliopoulou. “An updated bibliography of temporal, spatial, and spatio-temporal data mining research,” in J.F. Roddick and K. Hornsby (Eds.), Temporal, spatial and spatio-temporal data mining, TSDM 2000, volume 2007 of Lecture Notes in Artificial Intelligence, pp. 147–163, Springer: Berlin, 2001.Google Scholar
  54. 54.
    T. Shirabe. “Correlation analysis of discrete motions,” in Proc. of the Fourth International Conference on Geographic Information Science, GIScience 2006, volume 4197 of Lecture Notes in Computer Science, pp. 370–382, Springer-Verlag, Berlin, 2006.Google Scholar
  55. 55.
    G. Sinha and D.M. Mark. “Measuring similarity between geospatial lifelines in studies of environmental health,” Journal of Geographical Systems, Vol. 7(1):115–136, 2005.CrossRefGoogle Scholar
  56. 56.
    A.P. Sistla, O. Wolfson, S. Chamberlain, and S. Dao. “Modeling and querying moving objects,” in 13th International Conference on Data Engineering (ICDE13), 1997.Google Scholar
  57. 57.
    C.S. Smyth. “Mining mobile trajectories,” in H.J. Miller and J. Han (Eds.), Geographic Data Mining and Knowledge Discovery, pp. 337–361. Taylor & Francis, London, 2001.Google Scholar
  58. 58.
    J.J. Thomas and K.A. Cook. “A visual analytics agenda,” IEEE Computer Graphics and Applications, Vol. 26(1):10–13, 2006.CrossRefGoogle Scholar
  59. 59.
    S. Tisue and U. Wilensky. “NetLogo: A simple environment for modeling complexity,” in International Conference on Complex Systems, Boston, 2004.Google Scholar
  60. 60.
    F. Verhein and S. Chawla. “Mining spatio-temporal association rules, sources, sinks, stationary regions and thoroughfares in object mobility databases,” in Proc. of the 11th International Conference on Database Systems for Advanced Applications (DASFAA), volume 3882 of Lecture Notes in Computer Science, pp. 187–201, Springer, 2006.Google Scholar
  61. 61.
    U. Wilensky. “NetLogo flocking model,” http://ccl.northwestern.edu/netlogo/models/Flocking, 1998.
  62. 62.
    U. Wilensky. “NetLogo (and NetLogo User Manual),” http://ccl.northwestern.edu/netlogo, 1999.
  63. 63.
    O. Wolfson and E. Mena. “Applications of moving objects databases,” in Y. Manolopoulos, A. Papadopoulos, and M. Vassilakopoulos (Eds.), Spatial Databases: Technologies, Techniques and Trends, Idea group Co., 2004.Google Scholar
  64. 64.
    O. Wolfson, B. Xu, S. Chamberlain, and L. Jiang. “Moving objects databases: Issues and solutions,” in M. Rafanelli and M. Jarke (Eds.), 10th International Conference on Scientific and Statistical Database Management, Proceedings, Capri, July 1–3, 1998, pp. 111–131, IEEE Computer Society, 1998.Google Scholar
  65. 65.
    X. Xiong, M.F. Mokbel, and W.G. Aref. “Sea-cnn: Scalable processing of continuous k-nearest neighbor queries in spatio-temporal databases,” in Proc. of the 21st International Conference on Data Engineering (ICDE 2005), pp. 643–654, 2005.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Mattias Andersson
    • 1
  • Joachim Gudmundsson
    • 2
  • Patrick Laube
    • 3
  • Thomas Wolle
    • 2
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.NICTA SydneyAlexandria NSWAustralia
  3. 3.Department of GeomaticsThe University of MelbourneVictoriaAustralia

Personalised recommendations