# Discovering recurring activity in temporal networks

**Part of the following topical collections:**

## Abstract

Recent advances in data-acquisition technologies have equipped team coaches and sports analysts with the capability of collecting and analyzing detailed data of team activity in the field. It is now possible to monitor a sports event and record information regarding the position of the players in the field, passing the ball, coordinated moves, and so on. In this paper we propose a new method to analyze such team activity data. Our goal is to segment the overall activity stream into a sequence of potentially recurrent modes, which reflect different strategies adopted by a team, and thus, help to analyze and understand team tactics. We model team activity data as a temporal network, that is, a sequence of time-stamped edges that capture interactions between players. We then formulate the problem of identifying a small number of team modes and segmenting the overall timespan so that each segment can be mapped to one of the team modes; hence the set of modes summarizes the overall team activity. We prove that the resulting optimization problem is \(\mathrm {NP}\)-hard, and we discuss its properties. We then present a number of different algorithms for solving the problem, including an approximation algorithm that is practical only for one mode, as well as heuristic methods based on iterative and greedy approaches. We benchmark the performance of our algorithms on real and synthetic datasets. Of all methods, the iterative algorithm provides the best combination of performance and running time. We demonstrate practical examples of the insights provided by our algorithms when mining real sports-activity data. In addition, we show the applicability of our algorithms on other types of data, such as social networks.

## Keywords

Temporal networks Dynamic graphs Summarising Segmentation Sports analytics Basketball Football Handball Social networks## References

- Aggarwal A, Klawe M, Moran S, Shor P, Wilber R (1987) Geometric applications of a matrix-searching algorithm. Algorithmica 2(1–4):195–208MathSciNetCrossRefMATHGoogle Scholar
- Alamar BC (2013) Sports analytics: a guide for coaches, managers, and other decision makers. Columbia University Press, New YorkCrossRefGoogle Scholar
- Appan P, Sundaram H, Tseng B (2006) Summarization and visualization of communication patterns in a large-scale social network. In: Pacific-Asia conference on knowledge discovery and data mining. Springer, pp 371–379Google Scholar
- Araujo M, Papadimitriou S, Günnemann S, Faloutsos C, Basu P, Swami A, Papalexakis EE, Koutra D (2014) Com2: fast automatic discovery of temporal (comet) communities. In: Pacific-Asia conference on knowledge discovery and data mining. Springer, pp 271–283Google Scholar
- Arthur D, Vassilvitskii S (2007) k-means++: the advantages of careful seeding. In: ACM-SIAM symposium on discrete algorithms, society for industrial and applied mathematics, pp 1027–1035Google Scholar
- Asur S, Parthasarathy S, Ucar D (2009) An event-based framework for characterizing the evolutionary behavior of interaction graphs. ACM Trans Knowl Discov Data 3(4):16:1–16:36Google Scholar
- Bellman R (1961) On the approximation of curves by line segments using dynamic programming. Commun ACM 4(6):284. doi: 10.1145/366573.366611
- Berlingerio M, Bonchi F, Bringmann B, Gionis A (2009) Mining graph evolution rules. In: European conference on machine learning and knowledge discovery in databases, pp 115–130Google Scholar
- Chen KT, Jiang JW, Huang P, Chu HH, Lei CL, Chen WC (2009) Identifying mmorpg bots: a traffic analysis approach. EURASIP J Adv Signal Process 2009:3Google Scholar
- Crowder M, Dixon M, Ledford A, Robinson M (2002) Dynamic modelling and prediction of english football league matches for betting. J R Stat Soc D 51(2):157–168MathSciNetCrossRefGoogle Scholar
- Denman H, Rea N, Kokaram A (2003) Content-based analysis for video from snooker broadcasts. Comput Vis Image Underst 92(23):176–195CrossRefMATHGoogle Scholar
- Eagle N, Pentland A (2006) Reality mining: sensing complex social systems. Pers Ubiquit Comput 10(4):255–268CrossRefGoogle Scholar
- Eppstein D, Galil Z, Italiano GF (1998) Dynamic graph algorithms. CRC Press, Boca RatonCrossRefMATHGoogle Scholar
- Gao X, Xiao B, Tao D, Li X (2010) A survey of graph edit distance. Pattern Anal Appl 13(1):113–129MathSciNetCrossRefGoogle Scholar
- Gift P, Rodenberg RM (2014) Napoleon complex: height bias among national basketball association referees. J Sports Econ 15(5):541–558CrossRefGoogle Scholar
- Gionis A, Mannila H (2003) Finding recurrent sources in sequences. In: International conference on research in computational molecular biology, RECOMB, pp 123–130Google Scholar
- Goldsberry K (2012) Courtvision: new visual and spatial analytics for the nba. In: MIT sloan sports analytics conferenceGoogle Scholar
- Greene D, Doyle D, Cunningham P (2010) Tracking the evolution of communities in dynamic social networks. In: IEEE of international conference on advances in social network analysis and mining, pp 176–183Google Scholar
- Gudmundsson J, Horton M (2016) Spatio-temporal analysis of team sports—a survey. arXiv preprint arXiv:1602.06994
- Guha S, Koudas N, Shim K (2006) Approximation and streaming algorithms for histogram construction problems. ACM Trans Database Syst 31(1):396–438CrossRefGoogle Scholar
- Halvorsen P, Sægrov S, Mortensen A, Kristensen DK, Eichhorn A, Stenhaug M, Dahl S, Stensland HK, Gaddam VR, Griwodz C, et al (2013) Bagadus: an integrated system for arena sports analytics: a soccer case study. In: Proceedings of the ACM multimedia systems conference. ACM, pp 48–59Google Scholar
- Harville D (1980) Predictions for national football league games via linear-model methodology. J Am Stat Assoc 75(371):516–524CrossRefGoogle Scholar
- Hayet JB, Mathes T, Czyz J, Piater J, Verly J, Macq B (2005) A modular multi-camera framework for team sports tracking. In: IEEE conference on advanced video and signal based surveillance, pp 493–498Google Scholar
- Heinen T (1996) Latent class and discrete latent trait models: similarities and differences. Sage Publications, Inc, Thousand OaksGoogle Scholar
- Henzinger M, King V (1999) Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J ACM 46(4):502–516MathSciNetCrossRefMATHGoogle Scholar
- Himberg J, Korpiaho K, Mannila H, Tikanmäki J, Toivonen H (2001) Time series segmentation for context recognition in mobile devices. In: IEEE international conference on data mining, pp 203–210Google Scholar
- Holm J, De Lichtenberg K, Thorup M (2001) Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J ACM 48(4):723–760MathSciNetCrossRefMATHGoogle Scholar
- Holme P, Saramäki J (2012) Temporal networks. Phys Rep 519(3):97–125CrossRefGoogle Scholar
- Hvattum LM, Arntzen H (2010) Using elo ratings for match result prediction in association football. Int J Forecast 26(3):460–470CrossRefGoogle Scholar
- Ide T, Kashima H (2004) Eigenspace-based anomaly detection in computer systems. In: ACM SIGKDD international conference on knowledge discovery and data miningGoogle Scholar
- Kasiri-Bidhendi S, Fookes C, Morgan S, Martin DT, Sridharan S (2015) Combat sports analytics: boxing punch classification using overhead depthimagery. In: IEEE International Conference on image processing (ICIP), pp 4545–4549Google Scholar
- Kleinberg J, Papadimitriou C, Raghavan P (1998) Segmentation problems. In: ACM symposium on theory of computing, pp 473–482Google Scholar
- Klimt B, Yang Y (2004) The enron corpus: a new dataset for email classification research. In: Machine learning: ECML 2004. Springer, pp 217–226Google Scholar
- Kostakis O (2014) Classy: fast clustering streams of call-graphs. Data Min Knowl Disc 28(5–6):1554–1585MathSciNetCrossRefGoogle Scholar
- Kumar R, Calders T, Gionis A, Tatti N (2015) Maintaining sliding-window neighborhood profiles in interaction networks. In: European conference on machine learning and knowledge discovery in databases. Springer, pp 719–735Google Scholar
- Lucey P, Bialkowski A, Carr P, Morgan S, Matthews I, Sheikh Y (2013a) Representing and discovering adversarial team behaviors using player roles. In: IEEE conference on computer vision and pattern recognition, pp 2706–2713Google Scholar
- Lucey P, Oliver D, Carr P, Roth J, Matthews I (2013b) Assessing team strategy using spatiotemporal data. In: ACM SIGKDD international conference on knowledge discovery and data mining, pp 1366–1374Google Scholar
- Maheswaran R, Chang YH, Henehan A, Danesis S (2012) Deconstructing the rebound with optical tracking data. In: MIT sloan sports analytics conferenceGoogle Scholar
- Miller TW (2015) Sports analytics and data science: winning the game with methods and models. FT Press, Upper Saddle RiverGoogle Scholar
- Mongiovi M, Bogdanov P, Singh AK (2013) Mining evolving network processes. In: IEEE international conference on data mining, pp 537–546Google Scholar
- Obradovic Z (2007) Panathinaikos offense. Fiba Assist Mag 26:33–36Google Scholar
- Papadimitriou P, Dasdan A, Garcia-Molina H (2010) Web graph similarity for anomaly detection. J Internet Serv Appl 1(1):19–30CrossRefGoogle Scholar
- Pei SC, Chen F (2003) Semantic scenes detection and classification in sports videos. In: IPPR conference on computer vision, graphics and image processing (CVGIP), pp 210–217Google Scholar
- Pers J, Bon M, Vuckovic G (2006) Cvbase 06 datasetGoogle Scholar
- Perše M, Kristan M, Kovačič S, Vučkovič G, Perš J (2009) A trajectory-based analysis of coordinated team activity in a basketball game. Comput Vis Image Underst 113(5):612–621CrossRefGoogle Scholar
- Pingali GS, Jean Y, Carlbom I (1998) Real time tracking for enhanced tennis broadcasts. In: Proceedings IEEE computer society conference on computer vision and pattern recognition, pp 260–265Google Scholar
- Rayana S, Akoglu L (2016) Less is more: building selective anomaly ensembles. ACM Trans Knowl Discov Data 10(4):42CrossRefGoogle Scholar
- Rodenberg RM, Feustel ED (2014) Forensic sports analytics: detecting and predicting match-fixing in tennis. J Predict Mark 8(1):77–95Google Scholar
- Rozenshtein P, Tatti N, Gionis A (2014) Discovering dynamic communities in interaction networks. In: European conference on machine learning and knowledge discovery in databases, pp 678–693Google Scholar
- Sakoe H, Chiba S (1971) A dynamic programming approach to continuous speech recognition. Int Congr Acoust 3:65–69Google Scholar
- Shah N, Koutra D, Zou T, Gallagher B, Faloutsos C (2015) Timecrunch: Interpretable dynamic graph summarization. In: ACM SIGKDD international conference on knowledge discovery and data mining, ACM, pp 1055–1064Google Scholar
- Shatkay H, Zdonik SB (1996) Approximate queries and representations for large data sequences. In: IEEE international conference on data engineering, pp 536–545Google Scholar
- Sricharan K, Das K (2014) Localizing anomalous changes in time-evolving graphs. In: ACM SIGMOD international conference on management of data, pp 1347–1358Google Scholar
- Stensland HK, Gaddam VR, Tennøe M, Helgedagsrud E, Næss M, Alstad HK, Mortensen A, Langseth R, Ljødal S, Landsverk Ø et al (2014) Bagadus: An integrated real-time system for soccer analytics. ACM Trans Multimedia Comput Commun Appl 10(1s):14CrossRefGoogle Scholar
- Sun J, Faloutsos C, Papadimitriou S, Yu PS (2007) Graphscope: parameter-free mining of large time-evolving graphs. In: ACM SIGKDD international conference on knowledge discovery and data mining, pp 687–696Google Scholar
- Thorup M (2000) Near-optimal fully-dynamic graph connectivity. In: ACM symposium on theory of computing, pp 343–350Google Scholar
- Travassos B, Davids K, Araújo D, Esteves PT (2013) Performance analysis in team sports: advances from an ecological dynamics approach. Int J Perform Anal Sport 13(1):83–95Google Scholar
- Wei X, Sha L, Lucey P, Morgan S, Sridharan S (2013) Large-scale analysis of formations in soccer. In: International conference on digital image computing: techniques and applications, pp 1–8Google Scholar
- Zhong D, Chang SF (2001) Structure analysis of sports video using domain models. In: IEEE international conference on multimedia and expo, pp 713–716Google Scholar