Joachim Gudmundsson
ABSTRACT
We study one of the basic tasks in moving object analysis, namely the location of hotspots. A hotspot is a (small) region in which an entity spends a significant amount of time. Finding such regions is useful in many applications, for example in segmentation, clustering, and locating popular places. We may be interested in locating a minimum size hotspot in which the entity spends a fixed amount of time, or locating a fixed size hotspot maximizing the time that the entity spends inside it. Furthermore, we can consider the total time, or the longest contiguous time the entity spends in the hotspot. We solve all four versions of the problem. For a square hotspot, we can solve the contiguous-time versions in O(nlogn) time, where n is the number of trajectory vertices. The algorithms for the total-time versions are roughly quadratic. Finding a hotspot containing relatively the most time, compared to its size, takes O(n3) time. Even though we focus on a single moving entity, our algorithms immediately extend to multiple entities. Finally, we consider hotspots of different shape.
- P. Agarwal, M. Sharir, and S. Toledo. Applications of parametric searching in geometric optimization. J. of Algorithms, 17(3):292--318, 1994. Google Scholar
Digital Library
- H. Alt, B. Behrends, and J. Blömer. Approximate matching of polygonal shapes. Ann. Math. Artif. Intell., 13(3-4):251--265, 1995.Google ScholarCross Ref
- H. Alt and M. Godau. Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl., 5:75--91, 1995.Google ScholarCross Ref
- L. O. Alvares, V. Bogorny, B. Kuijpers, J. de Macêdo, B. Moelans, and A. Vaisman. A model for enriching trajectories with semantic geographical information. In Proc. 15th ACM Int. Sympos. on Geographic Information Systems, page 22. ACM, 2007. Google ScholarDigital Library
- R. Anderson, P. Beanie, and E. Brisson. Parallel algorithms for arrangements. Algorithmica, 15(2):104--125, 1996.Google ScholarDigital Library
- B. Aronov, A. Driemel, M. van Kreveld, M. Löffler, and F. Staals. Segmentation of trajectories for non-monotone criteria. In Proc. 24th Annual ACM-SIAM Sympos. on Discrete Algorithms, pages 1897--1911, 2013.Google ScholarCross Ref
- M. Benkert, B. Djordjevic, J. Gudmundsson, and T. Wolle. Finding popular places. Int. J. Comput. Geometry Appl., 20(1):19--42, 2010.Google ScholarCross Ref
- M. Benkert, J. Gudmundsson, F. Hübner, and T. Wolle. Reporting flock patterns. Comput. Geom., 41:111--125, 2008. Google ScholarDigital Library
- K. Buchin, M. Buchin, and J. Gudmundsson. Detecting single file movement. In Proc. 16th ACM Int. Conf. on Advances in Geographic Information Systems, pages 288--297, 2008. Google ScholarDigital Library
- K. Buchin, M. Buchin, J. Gudmundsson, M. Löffler, and J. Luo. Detecting commuting patterns by clustering subtrajectories. Int. J. Comput. Geom. Appl., 21(3):253--282, 2011.Google ScholarCross Ref
- K. Buchin, M. Buchin, M. van Kreveld, and J. Luo. Finding long and similar parts of trajectories. Comput. Geom., 44(9):465--476, 2011. Google ScholarDigital Library
- M. Buchin, A. Driemel, M. van Kreveld, and V. Sacristan. An algorithmic framework for segmenting trajectories based on spatio-temporal criteria. In Proc. 18th ACM Int. Sympos. on Advances in Geographic Information Systems, pages 202--211, 2010. Google ScholarDigital Library
- T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. MIT Press, 2001. Google ScholarDigital Library
- S. Dodge, R. Weibel, and A.-K. Lautenschütz. Towards a taxonomy of movement patterns. Information Visualization, 7(3-4):240--252, 2008. Google ScholarDigital Library
- P. Fauchald and T. Tveraa. Using first-passage time in the analysis of area-restricted search and habitat selection. Ecology, 84(2):282--288, 2003.Google ScholarCross Ref
- S. Gaffney and P. Smyth. Trajectory clustering with mixtures of regression models. In Proc. 5th Int. Conf. on Data Discovery and Data Mining, pages 63--72, 1999. Google ScholarDigital Library
- J. Gudmundsson, P. Laube, and T. Wolle. Movement patterns in spatio-temporal data. In S. Shekhar and H. Xiong, editors, Encyclopedia of GIS, pages 726--732. Springer, 2008.Google ScholarCross Ref
- J. Gudmundsson, M. van Kreveld, and B. Speckmann. Efficient detection of patterns in 2D trajectories of moving points. GeoInformatica, 11:195--215, 2007. Google ScholarDigital Library
- A. Jain, M. N. Murty, and P. Flynn. Data clustering: A review. ACM Comput. Surv., 31(3):264--323, 1999. Google ScholarDigital Library
- H. Jeung, M. Yiu, and C. Jensen. Trajectory pattern mining. In Y. Zheng and X. Zhou, editors, Computing with Spatial Trajectories, pages 143--177. Springer, 2011.Google ScholarCross Ref
- A. Johnson, J. Wiens, B. Milne, and T. Crist. Animal movements and population dynamics in heterogeneous landscapes. Landscape Ecology, 7:63--75, 1992.Google ScholarCross Ref
- E. J. Keogh. Exact indexing of dynamic time warping. In Proc. 28th Int. Conf. on Very Large Data Bases, pages 406--417, 2002. Google ScholarDigital Library
- P. Laube, M. van Kreveld, and S. Imfeld. Finding REMO -- detecting relative motion patterns in geospatial lifelines. In P. Fisher, editor, Developments in Spatial Data Handling: 11th Int. Sympos. on Spatial Data Handling, pages 201--215, 2004.Google Scholar
- J. Lee, J. Han, and K.-Y. Whang. Trajectory clustering: a partition-and-group framework. In Proc. ACM Int. Conf. on Management of Data, pages 593--604, 2007. Google ScholarDigital Library
- N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852--865, 1983. Google ScholarDigital Library
- B. Moreno, V. Times, C. Renso, and V. Bogorny. Looking inside the stops of trajectories of moving objects. In Proc. XI Brazilian Sympos. on Geoinformatics, pages 9--20. MCT/INPE, 2010.Google Scholar
- D. Mount, R. Silverman, and A. Wu. On the area of overlap of translated polygons. Computer Vision and Image Understanding, 64(1):53--61, 1996. Google ScholarDigital Library
- M. Nanni and D. Pedreschi. Time-focused clustering of trajectories of moving objects. J. of Intelligent Information Systems, 27:285--289, 2006. Google ScholarDigital Library
- A. Palma, V. Bogorny, B. Kuijpers, and L. O. Alvares. A clustering-based approach for discovering interesting places in trajectories. In Proc. 2008 ACM Sympos. on Applied Computing, pages 863--868, 2008. Google ScholarDigital Library
- Y. Shiloach and U. Vishkin. An O(log n) parallel connectivity algorithm. J. of Algorithms, 3(1):57--67, 1982.Google ScholarCross Ref
- S. Spaccapietra, C. Parent, M. Damiani, J. de Macêdo, F. Porto, and C. Vangenot. A conceptual view on trajectories. Data Knowl. Eng., 65(1):126--146, 2008. Google ScholarDigital Library
- S. Tiwari and S. Kaushik. Mining popular places in a geo-spatial region based on GPS data using semantic information. In Proc. 8th Int. Workshop on Databases in Networked Information Systems, volume 7813 of LNCS, pages 262--276. Springer, 2013.Google ScholarCross Ref
- F. Verhein and S. Chawla. Mining spatio-temporal association rules, sources, sinks, stationary regions and thoroughfares in object mobility databases. In Proc. 11th Int. Conf. on Database Systems for Advanced Applications, volume 3882 of LNCS, pages 187--201. Springer, 2006. Google ScholarDigital Library
- M. Vlachos, D. Gunopulos, and G. Kollios. Discovering similar multidimensional trajectories. In Proc. 18th Int. Conf. on Data Engineering, pages 673--684, 2002. Google ScholarDigital Library
- H. Yoon and C. Shahabi. Robust time-referenced segmentation of moving object trajectories. In Proc. 8th IEEE Int. Conf. on Data Mining, pages 1121--1126, 2008. Google ScholarDigital Library
Index Terms
- Algorithms for hotspot computation on trajectory data
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