Abstract
Moving point object data can be analyzed through the discovery of patterns in trajectories. We consider the computational efficiency of detecting four such spatio-temporal patterns, namely flock, leadership, convergence, and encounter, as defined by Laube et al., Finding REMO—detecting relative motion patterns in geospatial lifelines, 201–214, (2004). These patterns are large enough subgroups of the moving point objects that exhibit similar movement in the sense of direction, heading for the same location, and/or proximity. By the use of techniques from computational geometry, including approximation algorithms, we improve the running time bounds of existing algorithms to detect these patterns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Aronov and S. Har-Peled. “On approximating the depth and related problems,” in Proc. of 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 886–894, 2005.
S. Arya, D.M. Mount, N.S. Netanyahu, R. Silverman, and A.Y. Wu. “An optimal algorithm for approximate nearest neighbor searching fixed dimensions,” Journal of the ACM, Vol. 45(6):891–923, 1998.
J.L. Bentley. “Decomposable searching problems,” Information Processing Letters, Vol. 8:244–251, 1979.
T.M. Chan. “Approximate nearest neighbor queries revisited,” Discrete and Computational Geometry, Vol. 20(3):359–373, 1998.
B. Chazelle. “Cutting hyperplanes for divide-and-conquer,” Discrete and Computational Geometry, Vol. 9(2):145–158, 1993.
T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein. Introduction to Algorithms. 2nd edition, MIT: Cambridge, MA, 2001.
J. Erickson. “New lower bounds for convex hull problems in odd dimensions,” SIAM Journal of Computing, Vol. 28(4):1198–1214, 1999.
A.U. Frank, J.F. Raper, and J.-P. Cheylan (Ed.). Life and Motion of Spatial Socio-economic Units, 353–373, Taylor & Francis: New York, 2001.
L.J. Guibas, M.H. Overmars, and J.-M. Robert. “The exact fitting problem for points,” Computational Geometry—Theory and Applications, Vol. 6:215–230, 1996.
D. Halperin. “Arrangements,” in J.E. Goodman and J. O’Rourke (Eds.), Handbook of Discrete and Computational Geometry, Chapter 24, 529–562, Chapman & Hall: London/CRC: Boca Raton, FL, 2004.
J. Han and M. Kamber. Data Mining: Concepts and Techniques. Morgan Kaufmann, 2001.
S. Iwase and H. Saito. “Tracking soccer player using multiple views,” in Proc. of the IAPR Workshop on Machine Vision Applications (MVA02), Nara, Japan, pp. 102–105, 2002.
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, Santa Barbara, CA, pp. 25–32, 2001.
P. Laube and S. Imfeld. “Analyzing relative motion within groups of trackable moving point objects,” in GIScience 2002, no. 2478, Lecture Notes in Computer Science, pp. 132–144. Springer, Berlin Heidelberg New York, 2002.
P. Laube, M. van Kreveld, and S. Imfeld. “Finding REMO—Detecting relative motion patterns in geospatial lifelines,” in Developments in Spatial Data Handling: Proc. of the 11th International Symposium on Spatial Data Handling, Leicester, London, pp. 201–214, Springer, Berlin Heildelberg New York, 2004.
H.J. Miller and J. Han (Eds.). Geographic Data Mining and Knowledge Discovery, 372, Taylor & Francis:London, 2001.
K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, 1994.
S. Openshaw, M. Charlton, C. Wymer, and A. Craft. “Developing a mark 1 geographical analysis machine for the automated analysis of point data sets,” International Journal of Geographical Information Systems, Vol. 1:335–358, 1987.
D. O’Sullivan and D.J. Unwin. Geographic Information Analysis. Wiley, 2003.
T. Ott and F. Swiaczny. Time-integrative Geographic Information Systems. Springer, 2001.
M.H. Overmars. “The design of dynamic data structures,” in Lecture Notes Computer Science, Vol. 156, Springer, Berlin Heidelberg New York, 1983.
Porcupine caribou herd satellite collar project. http://www.taiga.net/satellite/.
J. Roddick, K. Hornsby, and M. Spiliopoulou. “An updated bibliography of temporal, spatial, and spatio-temporal data mining research,” in TSDM 2000, no. 2007, Lecture Notes in Artificial Intelligence, pp. 147–163. Springer, Berlin Heidelberg New York, 2001.
H. Samet. The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
C.-B. Shim and J.-W.Chang. “A new similar trajectory retrieval scheme using k-warping distance algorithm for moving objects,” in Proc. of the 4th International Conference on Advances in Web-age Information Management, (WAIM 2003), no. 2762, Lecture Notes in Computer Science, pp. 433–444, Springer, Berlin Heidelberg New York, 2003.
A. Silberschatz and A. Tuzhilin. “What makes patterns interesting in knowledge discovery systems,” IEEE Transactions on Knowledge and Data Engineering, Vol. 8:970–974, 1996.
G. Sinha and D.M. Mark. “Measuring similarity between geospatial lifelines in studies of environmental health,” Journal of Geographical Systems, Vol. 7:115–136, 2005.
N. Sumpter and A.J. Bulpitt. “Learning spatio-temporal patterns for predicting object behaviour,” Image Vision and Computing, Vol. 18(9):697–704, 2000.
G. Fejes Tóth. “Packing and covering,” in J.E. Goodman and J. O’Rourke, (Eds.), Handbook of Discrete and Computational Geometry, Chapter 2, 2nd edition, 25–52, Chapman & Hall: London/CRC: Boca Raton, 2004.
M. Vlachos, G. Kollios, and D. Gunopulos. “Discovering similar multidimensional trajectories,” in Proc. of the 18th International Conference on Data Engineering (ICDE’02), San Jose, CA, pp. 673–684, 2002.
Author information
Authors and Affiliations
Corresponding author
Additional information
An extended abstract of the work presented in this paper appeared in Proc. 12th International Symposium on Advances in Geographic Information Systems (ACM GIS), 2004.
J. Gudmundsson’s research was partially supported by the Netherlands Organisation for Scientific Research (NWO). National ICT Australia Ltd is funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council.
M. van Kreveld’s research has been partially funded by the Netherlands Organisation for Scientific Research (NWO) under FOCUS/BRICKS grant number 642.065.503.
Rights and permissions
About this article
Cite this article
Gudmundsson, J., van Kreveld, M. & Speckmann, B. Efficient Detection of Patterns in 2D Trajectories of Moving Points. Geoinformatica 11, 195–215 (2007). https://doi.org/10.1007/s10707-006-0002-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10707-006-0002-z