Compact Flow Diagrams for State Sequences

  • Kevin BuchinEmail author
  • Maike Buchin
  • Joachim Gudmundsson
  • Michael Horton
  • Stef Sijben
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9685)


We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified, our aim is to generate a small flow diagram that models the flow of states of all the state sequences given as input. For a small number of state sequences we present efficient algorithms to compute a minimal flow diagram. For a large number of state sequences we show that it is unlikely that efficient algorithms exist. More specifically, the problem is W[1]-hard if the number of state sequences is taken as a parameter. We thus introduce several heuristics for this problem. We argue about the usefulness of the flow diagram by applying the algorithms to two problems in sports analysis. We evaluate the performance of our algorithms on a football data set and generated data.


Heuristic Algorithm Flow Diagram State Sequence Exact Algorithm Compact Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Alewijnse, S.P.A., Buchin, K., Buchin, M., Kölzsch, A., Kruckenberg, H., Westenberg, M.: A framework for trajectory segmentation by stable criteria. In: Proceedings of 22nd ACM SIGSPATIAL/GIS, pp. 351–360. ACM (2014)Google Scholar
  2. 2.
    Aronov, B., Driemel, A., van Kreveld, M.J., Löffler, M., Staals, F.: Segmentation of trajectories for non-monotone criteria. In: Proceedings of 24th ACM-SIAM SODA, pp. 1897–1911 (2013)Google Scholar
  3. 3.
    Bialkowski, A., Lucey, P., Carr, G.P.K., Yue, Y., Sridharan, S., Matthews, I.: Identifying team style in soccer using formations learned from spatiotemporal tracking data. In: ICDM Workshops, pp. 9–14. IEEE (2014)Google Scholar
  4. 4.
    Bialkowski, A., Lucey, P., Carr, P., Yue, Y., Matthews, I.: Win at home and draw away: automatic formation analysis highlighting the differences in home and away team behaviors. In: Proceedings of 8th Annual MIT Sloan Sports Analytics Conference (2014)Google Scholar
  5. 5.
    Buchin, K., Buchin, M., Gudmundsson, J., Horton, M., Sijben, S.: Compact flow diagrams for state sequences. CoRR, abs/1602.05622 (2016)Google Scholar
  6. 6.
    Buchin, K., Buchin, M., Gudmundsson, J., Löffler, M., Luo, J.: Detecting commuting patterns by clustering subtrajectories. Int. J. Comput. Geom. Appl. 21(3), 253–282 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Buchin, K., Buchin, M., van Kreveld, M., Speckmann, B., Staals, F.: Trajectory grouping structure. In: Dehne, F., Solis-Oba, R., Sack, J.-R. (eds.) WADS 2013. LNCS, vol. 8037, pp. 219–230. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Buchin, M., Driemel, A., van Kreveld, M., Sacristan, V.: Segmenting trajectories: a framework and algorithms using spatiotemporal criteria. J. spat. inf. sci. 3, 33–63 (2011)Google Scholar
  9. 9.
    Buchin, M., Kruckenberg, H., Kölzsch, A.: Segmenting trajectories based on movement states. In: Proceedings of 15th SDH, pp. 15–25. Springer (2012)Google Scholar
  10. 10.
    Cao, H., Wolfson, O., Trajcevski, G.: Spatio-temporal data reduction with deterministic error bounds. VLDB J. 15(3), 211–228 (2006)CrossRefGoogle Scholar
  11. 11.
    Gudmundsson, J., Wolle, T.: Football analysis using spatio-temporal tools. Comput. Environ. Urban Syst. 47, 16–27 (2014)CrossRefGoogle Scholar
  12. 12.
    Han, C.-S., Jia, S.-X., Zhang, L., Shu, C.-C.: Sub-trajectory clustering algorithm based on speed restriction. Comput. Eng. 37(7), 219–221 (2011)Google Scholar
  13. 13.
    Kim, H.-C., Kwon, O., Li, K.-J.: Spatial and spatiotemporal analysis of soccer. In: Proceedings of 19th ACM SIGSPATIAL/GIS, pp. 385–388. ACM (2011)Google Scholar
  14. 14.
    Lucey, P., Bialkowski, A., Carr, G.P.K., Morgan, S., Matthews, I., Sheikh, Y.: Representing and discovering adversarial team behaviors using player roles. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2013), Portland, pp. 2706–2713. IEEE, June 2013Google Scholar
  15. 15.
    Prozone Sports Ltd: Prozone Sports - Our technology (2015).
  16. 16.
    Van Haaren, J., Dzyuba, V., Hannosset, S., Davis, J.: Automatically discovering offensive patterns in soccer match data. In: Fromont, E., De Bie, T., van Leeuwen, M. (eds.) IDA 2015. LNCS, vol. 9385, pp. 286–297. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24465-5_25 CrossRefGoogle Scholar
  17. 17.
    Wang, Q., Zhu, H., Hu, W., Shen, Z., Yao, Y.: Discerning tactical patterns for professional soccer teams. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD 2015, Sydney, pp. 2197–2206. ACM Press, August 2015Google Scholar
  18. 18.
    Wei, X., Sha, L., Lucey, P., Morgan, S., Sridharan, S.: Large-scale analysis of formations in soccer. In: 2013 International Conference on Digital Image Computing: Techniques and Applications (DICTA), Hobart, pp. 1–8. IEEE, November 2013Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Kevin Buchin
    • 1
    Email author
  • Maike Buchin
    • 2
  • Joachim Gudmundsson
    • 3
  • Michael Horton
    • 3
  • Stef Sijben
    • 2
  1. 1.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.Department of MathematicsRuhr-Universität BochumBochumGermany
  3. 3.School of Information TechnologiesThe University of SydneySydneyAustralia

Personalised recommendations