# An effective and versatile distance measure for spatiotemporal trajectories

- 6 Downloads

## Abstract

The analysis of large-scale trajectory data has tremendous benefits for applications ranging from transportation planning to traffic management. A fundamental building block for the analysis of such data is the computation of similarity between trajectories. Existing work for similarity computation focuses mainly on the spatial aspects of trajectories, but more rarely takes into account time in conjunction with space. A key challenge when considering time is how to handle trajectories that are sampled asynchronously or at variable rates, which can lead to uncertainty. To tackle this problem, we quantify trajectory similarity as an interval, rather than a single value, to capture the uncertainty that can result from different sampling rates and asynchronous sampling. Based on this perspective, we develop a new trajectory similarity measure, Trajectory Interval Distance Estimation, which models similarity computation as a convex optimisation problem. Using two real datasets, we demonstrate that our proposed measure is extremely effective for assessing similarity in comparison to existing state of the art measures.

## Keywords

Spatiotemporal trajectory Similarity Distance Measure Uncertainty## Notes

## References

- Agrawal R, Faloutsos C, Swami A (1993) Efficient similarity search in sequence databases. International conference on foundations of data organization and algorithms. Springer, Heidelberg, pp 69–84CrossRefGoogle Scholar
- Alt H, Godau M (1995) Computing the Fréchet distance between two polygonal curves. Int J Comput Geom Appl 5(01n02):75–91Google Scholar
- Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. KDD Workshop 10(16):359–370Google Scholar
- Biagioni J, Eriksson J (2012) Map inference in the face of noise and disparity. In: Proceedings of the 20th international conference on advances in geographic information systems. ACM, pp 79–88Google Scholar
- Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
- Chen L, Ng R (2004) On the marriage of lp-norms and edit distance. In: Proceedings of the 30th international conference on very large data bases, vol 30. VLDB Endowment, pp 792–803Google Scholar
- Chen L, Ozsu MT, Oria V (2005) Robust and fast similarity search for moving object trajectories. In: Proceedings of the 2005 ACM international conference on management of data (ACM SIGMOD). ACM, pp 491–502Google Scholar
- Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. In: Proceedings of the 30th international conference on very large data, vol 1, no 2. VLDB Endowment, pp 1542–1552Google Scholar
- Eiter T, Mannila H (1994) Computing discrete Fréchet distance. In: Tech. report CD-TR 94/64, Information Systems Department, Technical University of ViennaGoogle Scholar
- Esling P, Agon C (2012) Time-series data mining. ACM Comput Surv (CSUR) 45(1):12Google Scholar
- Faloutsos C, Ranganathan M, Manolopoulos Y (1994) Fast subsequence matching in time-series databases. ACM 23(2):419–429Google Scholar
- Frentzos E, Gratsias K, Theodoridis Y (2007) Index-based most similar trajectory search. In: Proceedings of the 23rd international conference on data engineering (ICDE). IEEE, pp 816–825Google Scholar
- Järvelin K, Kekäläinen J (2002) Cumulated gain-based evaluation of IR techniques. ACM T Infor Syst 20(4):422–446CrossRefGoogle Scholar
- Keogh EJ, Pazzani MJ (1998) An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback. Kdd 98(1):239–243Google Scholar
- Keogh E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7(3):358–86CrossRefGoogle Scholar
- Kuijpers B, Moelans B, Othman W, Vaisman A (2009) Analyzing trajectories using uncertainty and background information. International symposium on spatial and temporal databases. Springer, Heidelberg, pp 135–152CrossRefGoogle Scholar
- Laube P, Imfeld S (2002) Analyzing relative motion within groups of trackable moving point objects. International conference on geographic information science. Springer, Heidelberg, pp 132–144CrossRefGoogle Scholar
- Lee JG, Han J, Whang KY (2007) Trajectory clustering: a partition-and-group framework. In: Proceedings of the international conference on management of data (ACM SIGMOD). ACM, pp 593–604Google Scholar
- Lin B, Su J (2005) Shapes based trajectory queries for moving objects. In: Proceedings of the 13th annual ACM international workshop on geographic information systems. ACM, pp 21–30Google Scholar
- Mamoulis N, Cao H, Kollios G, Hadjieleftheriou M, Tao Y, Cheung DW (2004) Mining, indexing, and querying historical spatiotemporal data. In: Proceedings of the 10th international conference on knowledge discovery and data mining (ACM SIGKDD). ACM, pp 236–245Google Scholar
- Paparrizos J, Gravano L (2015) k-shape: Efficient and accurate clustering of time series. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data. ACM, pp 1855–1870Google Scholar
- Pelekis N, Kopanakis I, Marketos G, Ntoutsi I, Andrienko G, Theodoridis Y (2007) Similarity search in trajectory databases. In: 14th international symposium on temporal representation and reasoning. IEEE, pp 129–140Google Scholar
- Piorkowski M, Sarafijanovic-Djukic N, Grossglauser M (2009) A parsimonious model of mobile partitioned networks with clustering. In: First international communication systems and networks and workshops. IEEE, pp 1–10Google Scholar
- Ranu S, Deepak P, Telang AD, Deshpande P, Raghavan S (2015) Indexing and matching trajectories under inconsistent sampling rates. In: Proceeding of IEEE 31st international conference on data engineering (ICDE). IEEE, pp 999–1010Google Scholar
- Su H, Zheng K, Wang H, Huang J, Zhou X (2013) Calibrating trajectory data for similarity-based analysis. In: Proceedings of the ACM international conference on management of data (ACM SIGMOD). ACM, pp 833–844Google Scholar
- Tang B, Yiu ML, Mouratidis K, Wang K (2017) Efficient motif discovery in spatial trajectories using discrete fréchet distance. In: International conference on extending database technology (EDBT)Google Scholar
- Trajcevski G, Ding H, Scheuermann P, Tamassia R, Vaccaro D (2007) Dynamics-aware similarity of moving objects trajectories. In: Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems. ACM, p 11Google Scholar
- Vlachos M, Hadjieleftheriou M, Gunopulos D, Keogh E (2003) Indexing multi-dimensional time-series with support for multiple distance measures. In: Proceedings of the 9th ACM international conference on knowledge discovery and data mining (ACM SIGKDD). ACM, pp 216–225Google Scholar
- Vlachos M, Kollios G, Gunopulos D (2002) Discovering similar multidimensional trajectories. In: Proceedings of the 18th international conference on data engineering (ICDE). IEEE, pp 673–684Google Scholar
- Yuan J, Zheng Y, Zhang C, Xie W, Xie X, Sun G, Huang Y (2010) T-drive: driving directions based on taxi trajectories. In: Proceedings of 18th international conference on advances in geographic information systems. ACM, pp 99–108Google Scholar
- Zheng K, Trajcevski G, Zhou X, Scheuermann P (2011) Probabilistic range queries for uncertain trajectories on road networks. In: Proceedings of the 14th international conference on extending database technology. ACM, pp 283–294Google Scholar
- Zheng K, Zheng Y, Xie X, Zhou X (2012) Reducing uncertainty of low-sampling-rate trajectories. In: IEEE 28th international conference on data engineering (ICDE). IEEE, pp 1144–1155Google Scholar