Abstract
Outlier detection and clustering are important to analyze trajectory. While many algorithms have been developed to tackle these issues, they lack the combination with visualization to enable the involvement of human intelligence during the analyzing process. We propose a visual framework called M3, which combines data mining algorithms with visualization technique through three coordinated views: Map, MST, and FSDMatrix. Map view displays the spatial information of trajectories. MST is a minimum spanning tree, which presents the relationships between trajectories. In MST, each node represents a trajectory; edges between nodes denote the Fréchet distance between trajectories. FSDMatrix shows a matrix of pairwise Free Space Diagram to assist in detecting outliers and clustering trajectories. The three views are interacted with each other. Through case studies, we discuss the applicability of our framework and demonstrate the convenience brought by it.
Graphical abstract
Similar content being viewed by others
References
Aghaeepour N, Finak G, Hoos H et al (2013) Critical assessment of automated flow cytometry data analysis techniques. Nat Methods 10(3):228–38
Alt H, Godau M (1995) Computing the Fréchet distance between two polygonal curves. Int J Comput Geom Appl 5:75–91
Alt H, Behrends B, Blömer J (1995) Approximate matching of polygonal shapes (extended abstract). Ann Math Artif Intell 13(3):251–265
Andrienko G, Andrienko N, Fuchs G (2016) Understanding movement data quality. J Locat Based Serv 10(1):31–46
Andrienko N, Andrienko G (2011) Spatial generalization and aggregation of massive movement data. IEEE Trans Vis Comput Graph 17(2):205–19
Andrienko N, Andrienko G, Barrett L, Dostie M, Henzi P (2013) Space transformation for understanding group movement. IEEE Trans Vis Comput Graph 19(12):2169–2178. https://doi.org/10.1109/TVCG.2013.193
Ankerst M, Breunig MM, Kriegel HP, Sander J (1999) Optics: ordering points to identify the clustering structure. In: ACM SIGMOD international conference on management of data. pp 49–60
Buchin M (2010) Constrained Free Space Diagrams: a tool for trajectory analysis. Int J Geogr Inf Sci 24(7):1101–1125
Chang YJ, Hung PY, Newman M (2012) Traceviz: “brushing” for location based services. In: International conference on human–computer interaction with mobile devices and services ACM. pp 345–348
Eiter T, Mannila H (1994) Computing discrete Fréchet distance. Tech. Rep. CD-TR94/64, Information Systems Department, Technical University of Vienna
Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Conf on knowledge discovery and data mining. pp 226–231
Fruchterman TMJ, Reingold EM (1991) Graph drawing by force-directed placement. Softw Pract Exp 21(11):1129–1164
Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–6
Guo H, Wang Z, Yu B et al (2011) Tripvista: triple perspective visual trajectory analytics and its application on microscopic traffic data at a road intersection. IEEE Pac Vis Symp PACIFICVIS 2011:163–170
Hurter C, Tissoires B, Conversy S (2008) Fromdady: spreading aircraft trajectories across views to support iterative queries. IEEE Trans Vis Comput Graph 15(6):1017–1024
Knorr EM, Ng RT, Tucakov V (2000) Distance-based outliers: algorithms and applications. VLDB J 8(3):237–253
Kraak MJ (2003) The space-time cube revisited from a geovisualization perspective. In: Proceedings of the 21st international cartographic conference
Krüger R, Thom D, Wörner M, Bosch H, Ertl T (2013) Trajectorylenses—a set-based filtering and exploration technique for long-term trajectory data. In: Proceedings of the 15th Eurographics conference on visualization, The Eurographs Association & Wiley, Chichester, UK, EuroVis ’13. pp 451–460
Lee JG, Han J, Whang KY (2007) Trajectory clustering: a partition-and-group framework. In: ACM SIGMOD international conference on management of data. pp 593–604
Lee JG, Han J, Li X (2008) Trajectory outlier detection: a partition-and-detect framework. In: Data engineering, 2008. ICDE 2008. IEEE 24th international conference on, IEEE. pp 140–149
Li X, Han J, Kim S, Gonzalez H (2007) Roam: rule and motif-based anomaly detection in massive moving object data sets. In: 7th SIAM int’l conf on data mining
Lloyd S (1982) Least squares quantization in pcm. IEEE Trans Inf Theory 28(2):129–137
Pettie S, Ramachandran V (2000) An optimal minimum spanning tree algorithm. J ACM 49(1):16–34. https://doi.org/10.1145/505241.505243
Poiker T, Douglas DH (1973) Reflection essay: algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartogr Int J Geogr Inf Geovis 10(2):112–122
Prim RC (1957) Shortest connection networks and some generalizations. Bell Labs Tech J 36(6):1389–1401
Qiu P, Simonds EF, Bendall SC et al (2011) Extracting a cellular hierarchy from high-dimensional cytometry data with spade. Nat Biotechnol 29(10):886–91
Scheepens R, Hurter C, Van De WH (2016) Visualization, selection, and analysis of traffic flows. Vis Comput Graph IEEE Trans 22(1):379–388
Senechal M (1993) Spatial tessellations: concepts and applications of voronoi diagrams. Science 260(5111):1170–1173
Van Gassen S, Callebaut B, Van Helden MJ et al (2015) Flowsom: using self-organizing maps for visualization and interpretation of cytometry data. Cytom Part A 87(7):636–645
Wang W, Yang J, Muntz RR (1997) Sting: a statistical information grid approach to spatial data mining. In: 23rd int’l conf on very large data bases, Athens, Greece. pp 186–195
Wang Z, Ye T, Lu M, Yuan X, Qu H, Yuan J, Wu Q (2014) Visual exploration of sparse traffic trajectory data. IEEE Trans Vis Comput Graph 20(12):1813–1822. https://doi.org/10.1109/TVCG.2014.2346746
Wu W, Xu J, Zeng H, Zheng Y, Qu H, Ni B, Yuan M, Ni LM (2016) Telcovis: visual exploration of co-occurrence in urban human mobility based on telco data. IEEE Trans Vis Comput Graph 22(1):935–944. https://doi.org/10.1109/TVCG.2015.2467194
Zhang D, Li N, Zhou ZH, et al (2011) ibat: detecting anomalous taxi trajectories from gps traces. In: UBICOMP 2011: ubiquitous computing, international conference. pp 99–108
Zhang T, Ramakrishnan R, Livny M (1996) Birch: an efficient data clustering method for very large databases. In: ACM SIGMOD int’l conf on management of data. pp 103–114
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, H., Jia, S., Wang, J. et al. M3: visual exploration of spatial relationships between flight trajectories. J Vis 21, 457–470 (2018). https://doi.org/10.1007/s12650-017-0471-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-017-0471-1