Data Mining and Knowledge Discovery

, Volume 31, Issue 5, pp 1294–1330 | Cite as

On temporal-constrained sub-trajectory cluster analysis

  • Nikos Pelekis
  • Panagiotis Tampakis
  • Marios Vodas
  • Christos Doulkeridis
  • Yannis Theodoridis
Part of the following topical collections:
  1. Journal Track of ECML PKDD 2017


Cluster analysis over Moving Object Databases (MODs) is a challenging research topic that has attracted the attention of the mobility data mining community. In this paper, we study the temporal-constrained sub-trajectory cluster analysis problem, where the aim is to discover clusters of sub-trajectories given an ad-hoc, user-specified temporal constraint within the dataset’s lifetime. The problem is challenging because: (a) the time window is not known in advance, instead it is specified at query time, and (b) the MOD is continuously updated with new trajectories. Existing solutions first filter the trajectory database according to the temporal constraint, and then apply a clustering algorithm from scratch on the filtered data. However, this approach is extremely inefficient, when considering explorative data analysis where multiple clustering tasks need to be performed over different temporal subsets of the database, while the database is updated with new trajectories. To address this problem, we propose an incremental and scalable solution to the problem, which is built upon a novel indexing structure, called Representative Trajectory Tree (ReTraTree). ReTraTree acts as an effective spatio-temporal partitioning technique; partitions in ReTraTree correspond to groupings of sub-trajectories, which are incrementally maintained and assigned to representative (sub-)trajectories. Due to the proposed organization of sub-trajectories, the problem under study can be efficiently solved as simply as executing a query operator on ReTraTree, while insertion of new trajectories is supported. Our extensive experimental study performed on real and synthetic datasets shows that our approach outperforms a state-of-the-art in-DBMS solution supported by PostgreSQL by orders of magnitude.


Cluster analysis Temporal-constrained (sub-)trajectory clustering Moving objects Indexing 



This work was partially supported by project datACRON, which has received funding from the European Union’s Horizon 2020 research and innovation Programme under Grant Agreement No 687591. The work of P. Tampakis and C. Doulkeridis has been co-financed by ESF and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Aristeia II, Project: ROADRUNNER.


  1. Ankerst M, Breunig MM, Kriegel H-P, Sander J (1999) OPTICS: ordering points to identify the clustering structure. In: Proceedings of ACM SIGMOD international conference on management of data, pp 49–60Google Scholar
  2. Benkert M, Gudmundsson J, Hubner F, Wolle T (2006) Reporting flock patterns. In: Proceedings of 14th annual european symposium (ESA), pp 660–671Google Scholar
  3. Buchin M, Driemel A, van Kreveld M, Sacristán V (2010) An algorithmic framework for segmenting trajectories based on spatio-temporal criteria. In: Proceedings of of the 18th SIGSPATIAL international conference on advances in geographic information systems, pp 202–211Google Scholar
  4. Cudre-Mauroux P, Wu E, Madden S (2010) Trajstore: an adaptive storage system for very large trajectory data sets. In: Proceedings of IEEE 26th international conference on data engineering (ICDE)Google Scholar
  5. Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the 2nd international conference on knowledge discovery and data mining (KDD), pp 226–231Google Scholar
  6. Ferreira N, Klosowski JT, Scheidegger CE, Silva CT (2013) Vector field k-means: clustering trajectories by fitting multiple vector fields. In: Proceedings of EuroVis, pp 201–210Google Scholar
  7. Frentzos E, Gratsias K, Theodoridis Y (2007) Index-based most similar trajectory search. In: Proceedings of IEEE 23rd international conference on data engineering (ICDE)Google Scholar
  8. Gaffney S, Smyth P (1999) Trajectory clustering with mixtures of regression models. In: Proceedings of the 5th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 63–72Google Scholar
  9. Giannotti F, Nanni M, Pedreschi D, Pinelli F, Renso C, Rinzivillo S, Trasarti R (2011) Unveiling the complexity of human mobility by querying and mining massive trajectory data. VLDB J Int J Very Large Data Bases 20(5):695–719CrossRefGoogle Scholar
  10. Guha S, Rastigi R, Shim K (1998) CURE: an efficient clustering algorithm for large databases. In: Proceedings of ACM SIGMOD international conference on management of data, pp 73–84Google Scholar
  11. Hadjieleftheriou M, Kollios G, Gunopulos D, Tsotras VJ (2006) Indexing spatio-temporal archives. VLDB J Int J Very Large Data Bases 15(2):143–164CrossRefzbMATHGoogle Scholar
  12. Hung CC, Peng WC, Lee WC (2015) Clustering and aggregating clues of trajectories for mining trajectory patterns and routes. VLDB J Int J Very Large Data Bases 24(2):169–192CrossRefGoogle Scholar
  13. Jeung H, Yiu ML, Zhou X, Jensen CS, Shen HT (2008) Discovery of convoys in trajectory databases. In: Proceedings of the VLDB endowment, pp 1068–1080Google Scholar
  14. Kalnis P, Mamoulis N, Bakiras S (2005) On discovering moving clusters in spatio-temporal data. In: Proceedings of the 9th international conference on advances in spatial and temporal databases (SSTD), pp 364–381Google Scholar
  15. Laube P, Imfeld S, Weibel R (2005) Discovering relative motion patterns in groups of moving point objects. Int J Geogr Inf Sci 19(6):639–668CrossRefGoogle Scholar
  16. Lee JG, Han J, Whang KY (2007) Trajectory clustering: a partition-and-group framework. In: Proceedings of ACM SIGMOD international conference on management of data, pp 593–604Google Scholar
  17. Li Z, Ding B, Han J, Kays R (2010) Swarm: mining relaxed temporal moving object clusters. Proc VLDB Endow 3(1–2):723–734CrossRefGoogle Scholar
  18. Li Z, Lee JG, Li X, Han J (2010b) Incremental clustering for trajectories. In: Proceedings of the 15th international conference on database systems for advanced applications (DASFAA), pp 32–46Google Scholar
  19. Li Y, Bailey J, Kulik L (2015) Efficient mining of platoon patterns in trajectory databases. Data Knowl Eng 100(PA):167–187CrossRefGoogle Scholar
  20. MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the \(5{{th}}\) Berkeley symposium on mathematical statistics and probability, pp 281–297Google Scholar
  21. Nanni M, Pedreschi D (2006) Time-focused clustering of trajectories of moving objects. J Intell Inf Syst 27(3):267–289CrossRefGoogle Scholar
  22. Ni J, Ravishankar CV (2007) Indexing spatio-temporal trajectories with efficient polynomial approximations. IEEE Trans Knowl Data Eng 19(5):663–678CrossRefGoogle Scholar
  23. Panagiotakis C, Pelekis N, Kopanakis I, Ramasso E, Theodoridis Y (2012) Segmentation and sampling of moving object trajectories based on representativeness. IEEE Trans Knowl Data Eng 24(7):1328–1343CrossRefGoogle Scholar
  24. Pelekis N, Theodoridis Y (2014) Mobility data management and exploration. Springer, BerlinCrossRefGoogle Scholar
  25. Pelekis N, Kopanakis I, Kotsifakos E, Frentzos E, Theodoridis Y (2011) Clustering uncertain trajectories. Knowl Inf Syst 28(1):117–147CrossRefGoogle Scholar
  26. Pfoser D, Jensen CS, Theodoridis Y (2000) Novel approaches to the indexing of moving object trajectories. In: Proceedings of the VLDB endowment, pp 395–406Google Scholar
  27. Tang LA, Zheng Y, Yuan J, Han J, Leung A, Peng W, Porta TL (2013) A framework of traveling companion discovery on trajectory data streams. ACM Trans Intell Syst Technol 5(1):3CrossRefGoogle Scholar
  28. Tao Y, Papadias D (2001) MV3R-tree: a spatio-temporal access method for timestamp and interval queries. In: Proceedings of the VLDB endowment, pp 431–440Google Scholar
  29. Theodoridis Y, Vazirgiannis M, Sellis T (1996) Spatio-temporal indexing for large multimedia applications. In: Proceedings of the 3rd IEEE international conference on multimedia computing and systems (ICMCS)Google Scholar
  30. Wang S, Wu L, Zhou F, Zheng C, Wang H (2015) Group pattern mining algorithm of moving objects’ uncertain trajectories. Int J Comput Commun Control 10(3):428–440CrossRefGoogle Scholar
  31. Xu H, Zhou Y, Lin W, Zha H (2015) Unsupervised trajectory clustering via adaptive multi-kernel-based shrinkage. In: Proceedings of IEEE international conference on computer vision (ICCV)Google Scholar
  32. Yuan G, Sun P, Zhao J, Li D, Wang C (2017) A review of moving object trajectory clustering algorithms. Artif Intell Rev 47(1):123–144CrossRefGoogle Scholar
  33. Zhang T, Ramakrishnan R, Livny M (1996) BIRCH: an efficient data clustering method for very large databases. In: Proceedings of ACM SIGMOD international conference on management of data, pp 103–114Google Scholar
  34. Zheng Y (2015) Trajectory data mining: an overview. ACM Trans Intell Syst Technol 6(3):29CrossRefGoogle Scholar
  35. Zheng Y, Xie X, Ma WY (2010) GeoLife: a collaborative social networking service among user, location and trajectory. IEEE Data Eng Bull 33(2):32–40Google Scholar
  36. Zheng K, Zheng Y, Yuan NJ, Shang S (2013) On discovery of gathering patterns from trajectories. In: Proceedings of IEEE 23rd international conference on data engineering (ICDE)Google Scholar
  37. Zheng K, Zheng Y, Yuan NJ, Shang S, Zhou X (2014) Online discovery of gathering patterns over trajectories. IEEE Trans Knowl Data Eng 26(8):1974–1988CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of Statistics and Insurance ScienceUniversity of PiraeusPiraeusGreece
  2. 2.Department of InformaticsUniversity of PiraeusPiraeusGreece
  3. 3.Department of Digital SystemsUniversity of PiraeusPiraeusGreece

Personalised recommendations