Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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)
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)
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)
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)
Buchin, K., Buchin, M., Gudmundsson, J., Horton, M., Sijben, S.: Compact flow diagrams for state sequences. CoRR, abs/1602.05622 (2016)
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)
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)
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)
Buchin, M., Kruckenberg, H., Kölzsch, A.: Segmenting trajectories based on movement states. In: Proceedings of 15th SDH, pp. 15–25. Springer (2012)
Cao, H., Wolfson, O., Trajcevski, G.: Spatio-temporal data reduction with deterministic error bounds. VLDB J. 15(3), 211–228 (2006)
Gudmundsson, J., Wolle, T.: Football analysis using spatio-temporal tools. Comput. Environ. Urban Syst. 47, 16–27 (2014)
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)
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)
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 2013
Prozone Sports Ltd: Prozone Sports - Our technology (2015). http://prozonesports.stats.com/about/technology/
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
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 2015
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 2013
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Buchin, K., Buchin, M., Gudmundsson, J., Horton, M., Sijben, S. (2016). Compact Flow Diagrams for State Sequences. In: Goldberg, A., Kulikov, A. (eds) Experimental Algorithms. SEA 2016. Lecture Notes in Computer Science(), vol 9685. Springer, Cham. https://doi.org/10.1007/978-3-319-38851-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-38851-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-38850-2
Online ISBN: 978-3-319-38851-9
eBook Packages: Computer ScienceComputer Science (R0)