Abstract
The visualization of spatial data is becoming increasingly important in science, business and many other areas. There are two main reasons for this: First, the amount of spatial data is growing continuously, making it impossible for people to manually process the data in raw form. Secondly, users have very high demands on the interactive processing of big spatial data in visual form. For instance in geography, data often corresponds to a large number of point observations that should be displayed on a constrained screen with limited resolution. This causes two crucial problems: drawing a lot of points is expensive at runtime and leads to a loss of information due to an overloaded and occluded visualization. In this paper we present a new efficient visualization algorithm that avoids these problems by aggregating point data into a set of non-overlapping circles with the following properties: (i) they follow the distribution of the data, (ii) they represent the cardinality of the underlying point subset by the circle area, (iii) they reveal hot spots while simultaneously keeping outliers, and (iv) the number of circles is typically much smaller than the number of points. Based on a quadtree, our algorithm computes the circles in linear time with respect to the number of points. Experimental results confirm its excellent runtime and quality in comparison to competitors.
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https://www.w3.org/TR/css-values-4/, visited December 2, 2018
Global Biodiversity Information Facility, https://www.gbif.org
References
Madhavan J, Balakrishnan S, Brisbin K, Gonzalez H, Gupta N, Halevy AY, Jacqmin-Adams K, Lam H, Langen A, Lee H (2012) Big data storytelling through interactive maps. IEEE Data Eng Bull 35(2):46
Zhang L, Stoffel A, Behrisch M, Mittelstadt S, Schreck T, Pompl R, Weber S, Last H, Keim D (2012) Visual analytics for the big data era - a comparative review of state-of-the-art commercial systems. In: VAST’12: Proceedings of the 2012 IEEE conference on visual analytics science and technology. IEEE Computer Society, Washington, pp 173–182
Keim D, Andrienko G, Fekete JD, Görg C, Kohlhammer J, Melançon G (2008). In: Kerren A, Stasko JT, Fekete JD, North C (eds) Information visualization. Springer, Berlin, pp 154–175
Diepenbroek M, Glöckner F, Grobe P et al (2014) Towards an integrated biodiversity and ecological research data management and archiving platform: the German federation for the curation of biological data (GFBio). In: GI-Jahrestagung, pp 1711–1721
Authmann C, Beilschmidt C, Drönner J, Mattig M, Seeger B (2015) Rethinking spatial processing in data-intensive science. In: BTW 2015: Datenbanksysteme für business, Technologie und Web - Workshopband, vol P242. Gesellschaft für Informatik e.V., Bonn, pp 161–170
Beilschmidt C, Drönner J, Mattig M, Schmidt M, Authmann C, Niamir A, Hickler T, Seeger B (2017) Interactive data exploration for geoscience. In: BTW 2017: Datenbanksysteme für Business, Technologie und Web - Workshopband, vol P-266. Gesell-schaft für Informatik e.V., Bonn, pp 117–126
Beilschmidt C, Drȯnner J., Mattig M, Seeger B (2017) VAT: a system for data-driven biodiversity research. In: EDBT 2017: Proceedings of the 20th international conference on extending database technology. OpenProceedings.org, Konstanz, pp 546–549
Beilschmidt C, Fober T, Mattig M, Seeger B (2017) A linear-time algorithm for the aggregation and visualization of big spatial point data. In: SIGSPATIAL ’17: proceedings of the 25th ACM SIGSPATIAL international conference on advances in geographic information systems. ACM, New York, pp 73:1–73:4
Jänicke S, Heine C, Scheuermann G (2013) GeoTemCo: comparative visualization of geospatial-temporal data with clutter removal based on dynamic delaunay triangulations. In: VISIGRAPP 2012: proceedings of the 7th international joint conference on computer vision, imaging and computer graphics. Theory and application, vol 359. Springer, Berlin, pp 160–175
Beilschmidt C, Fober T, Mattig M, Seeger B (2017) Quality measures for visual point clustering in geospatial mapping. In: W2GIS 2017: proceedings of the 15th international symposium on web and wireless geographical information systems. Springer International Publishing, Cham, pp 153–168
Jȧnicke S, Heine C, Stockmann R, Scheuermann G (2012) Comparative visualization of geospatial-temporal data. In: GRAPP & IVAPP 2012 proceedings of the international conference on computer graphics theory and applications and international conference on information visualization theory and application. SciTePress, Setu̇bal, pp 613–625
Slocum T, McMaster R, Kessler F, Howard H (2009) Thematic cartography and geovisualization. Prentice Hall, Upper Saddle River
Pickering S (2017) A new way to proxy levels of infrastructure development research and politics, 4(1)
Forrest D, Castner HW (1985) The design and perception of point symbols for tourist maps. Cartogr J 22(1):11
de Berg M, Cheong O, van Kreveld MJ, Overmars MH (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, Berlin
Bereuter P, Weibel R (2013) Real-time generalization of point data in mobile and web mapping using quadtrees. Cartogr Geogr Inf Sci 40(4):271
Samet H (2006) Foundations of multidimensional and metric data structures. Morgan Kaufmann, San Francisco
Aggarwal CC, Reddy CK (2014) Data clustering: algorithms and applications. CRC Press, Boca Raton
Park Y, Cafarella MJ, Mozafari B (2016) Visualization-aware sampling for very large databases. In: Proceedings of the IEEE 32nd international conference on data engineering (ICDE). IEEE Computer Society, Washington, pp 755–766
Wang L, Christensen R, Li F, Yi K (2015) Spatial Online Sampling and Aggregation. Proc VLDB Endow 9(3):84
Sarma AD, Lee H, Gonzalez H, Madhavan J, Halevy AY (2012) Efficient spatial sampling of large geographical tables. In: SIGMOD ’12: proceedings of the 2012 ACM SIGMOD international conference on management of data. ACM, New York, pp 193–204
Grȯbe M, Burghardt D (2017) Micro diagrams: a multi-scale approach for mapping large categorised point datasets. In: Proceedings of AGILE 2017: the 20th AGILE international conference on geographic information science
Liu Z, Jiang B, Heer J (2013) imMens: real-time visual querying of big data. Comput Graph Forum 32(3):421
Zhang L, Rooney C, Nachmanson L, Wong BLW, Kwon BC, Stoffel F, Hund M, Qazi N, Singh U, Keim DA (2016) Spherical similarity explorer for comparative case analysis. In: Proceedings of the IS&T international symposium on electronic imaging 2016 visualization and data analysis. Ingenta, Oxford, pp 1–10
Ghanem TM, Magdy A, Musleh M, Ghani S, Mokbel MF (2014) VisCAT: spatio-temporal visualization and aggregation of categorical attributes in twitter data. In: SIGSPATIAL ’14: proceedings of the 22th ACM SIGSPATIAL international conference on advances in geographic information systems. ACM, New York, pp 537–540
Ellis G, Dix A (2007) A taxonomy of clutter reduction for information visualisation. IEEE Trans Vis Comput Graph 13(6):1216
Samet H (1990) The design and analysis of spatial data structures. Addison-Wesley, Reading
Konheim AG (2010) Hashing in computer science: fifty years of slicing and dicing. Wiley, Hoboken
Bader M (2013) Space-filling curves - an introduction with applications in scientific computing. Springer, Berlin
Lipowski A, Lipowska D (2012) Roulette-wheel selection via stochastic acceptance. Physica A: Statist Mech Appl 391(6):2193
Liu Z, Heer J (2014) The effects of interactive latency on exploratory visual analysis. IEEE Trans Vis Comput Graph 20(12):2122
Corder GW, Foreman DI (2014) Nonparametric statistics: a step-by-step approach. Wiley, Hoboken
Grbiċ R, Grahovac D, Scitovski R (2016) A method for solving the multiple ellipses detection problem. Pattern Recogn 60:824
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This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) under grant no. SE 553/7-2.
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Beilschmidt, C., Mattig, M., Fober, T. et al. An efficient aggregation and overlap removal algorithm for circle maps. Geoinformatica 23, 473–498 (2019). https://doi.org/10.1007/s10707-019-00342-5
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DOI: https://doi.org/10.1007/s10707-019-00342-5