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Generating Orthogonal Voronoi Treemap for Visualization of Hierarchical Data

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Advances in Computer Graphics (CGI 2020)

Abstract

A novel space partitioning strategy is presented for implicit hierarchy visualization. The proposed orthogonal Voronoi treemap (OVT) partitions an empty canvas into nested orthogonal rectangles, thus the generated layout is not only flexible to diversified data value, but also much tidier than the Voronoi treemap with nested polygons. To achieve this, we first introduce a new distance calculation strategy in order to generate axis-aligned segmentation among the sites. To cope with the new segmentation strategy, we then design a sweepline + skyline heuristic algorithm to partition the canvas to generate an orthogonal Voronoi treemap. Comparative analyses on the computational experiment results in terms of aspect ratio is discussed.

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Notes

  1. 1.

    https://d3js.org/.

  2. 2.

    https://github.com/Kcnarf/.

References

  1. Balzer, M., Deussen, O.: Voronoi treemaps. In: Proceedings of the INFOVIS, pp. 49–56. IEEE (2005)

    Google Scholar 

  2. Bederson, B.B., Shneiderman, B., Wattenberg, M.: Ordered and quantum treemaps: making effective use of 2D space to display hierarchies. ACM Trans. Graph. 21(4), 833–854 (2002)

    Article  Google Scholar 

  3. Bruls, M., Huizing, K., van Wijk, J.J.: Squarified treemaps. In: de Leeuw, W.C., van Liere, R. (eds.) Data Visualization 2000. EUROGRAPH, pp. 33–42. Springer, Vienna (2000). https://doi.org/10.1007/978-3-7091-6783-0_4

    Chapter  Google Scholar 

  4. Burke, E.K., Kendall, G., Whitwell, G.: A new placement heuristic for the orthogonal stock-cutting problem. Oper. Res. 52(4), 655–671 (2004)

    Article  Google Scholar 

  5. Duarte, F.S., Sikansi, F., Fatore, F.M., Fadel, S.G., Paulovich, F.V.: Nmap: a novel neighborhood preservation space-filling algorithm. IEEE Trans. Visual Comput. Graphics 20(12), 2063–2071 (2014)

    Article  Google Scholar 

  6. Fortune, S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2(1–4), 153 (1987). https://doi.org/10.1007/BF01840357

    Article  MathSciNet  MATH  Google Scholar 

  7. Görtler, J., Schulz, C., Weiskopf, D., Deussen, O.: Bubble treemaps for uncertainty visualization. IEEE Trans. Visual Comput. Graphics 24(1), 719–728 (2018)

    Article  Google Scholar 

  8. Gotz, D.: Dynamic Voronoi treemaps: a visualization technique for time-varying hierarchical data. Phys. Rev. A 30(2), 150–156 (2011)

    Google Scholar 

  9. Graham, M., Kennedy, J.: A survey of multiple tree visualisation. Inf. Vis. 9(4), 235–252 (2010)

    Article  Google Scholar 

  10. Hahn, S., Trümper, J., Moritz, D., Döllner, J.: Visualization of varying hierarchies by stable layout of Voronoi treemaps. In: Proceedings of the IVAPP, pp. 50–58. IEEE (2014)

    Google Scholar 

  11. Kieffer, S., Dwyer, T., Marriott, K., Wybrow, M.: Hola: human-like orthogonal network layout. IEEE Trans. Visual Comput. Graphics 22(1), 349–358 (2016)

    Article  Google Scholar 

  12. Leong, M.C., Prasad, D.K., Lee, Y.T., Lin, F.: Semi-CNN architecture for effective spatio-temporal learning in action recognition. Appl. Sci. 10(2), 557 (2020)

    Article  Google Scholar 

  13. Lin, F.: Subspace learning and Hopfield neural networks in biomedical classification. Basic Clin. Pharmacol. Toxicol. 125, 144–145 (2019)

    Google Scholar 

  14. Ma, J., Wang, A., Lin, F., Wesarg, S., Erdt, M.: A novel robust kernel principal component analysis for nonlinear statistical shape modeling from erroneous data. Comput. Med. Imaging Graph. 77, 101638 (2019)

    Article  Google Scholar 

  15. Nocaj, A., Brandes, U.: Computing Voronoi treemaps: faster, simpler, and resolution-independent. Comput. Graph. Forum 31, 855–864 (2012)

    Article  Google Scholar 

  16. Schulz, H.J.: Treevis.net: a tree visualization reference. IEEE Comput. Graphics Appl. 6, 11–15 (2011)

    Article  Google Scholar 

  17. Schulz, H.J., Hadlak, S., Schumann, H.: The design space of implicit hierarchy visualization: a survey. IEEE Trans. Visual Comput. Graphics 17(4), 393–411 (2011)

    Article  Google Scholar 

  18. Shneiderman, B.: Tree visualization with tree-maps: 2-D space-filling approach. ACM Trans. Graph. 11(1), 92–99 (1992)

    Article  Google Scholar 

  19. Shneiderman, B., Wattenberg, M.: Ordered treemap layouts. In: Proceedings of the INFOVIS, pp. 73–78. IEEE (2001)

    Google Scholar 

  20. Sud, A., Fisher, D., Lee, H.P.: Fast dynamic Voronoi treemaps. In: Proceedings of the ISVD, pp. 85–94. IEEE (2010)

    Google Scholar 

  21. Tennekes, M., de Jonge, E.: Tree colors: color schemes for tree-structured data. IEEE Trans. Visual Comput. Graphics 20(12), 2072–2081 (2014)

    Article  Google Scholar 

  22. Tu, Y., Shen, H.W.: Visualizing changes of hierarchical data using treemaps. IEEE Trans. Visual Comput. Graphics 13(6), 1286–1293 (2007)

    Article  Google Scholar 

  23. Wang, G., Nakanishi, T., Fukuda, A.: 2-D layout for tree visualization: a survey. In: Proceedings of the MATEC Web of Conferences, vol. 56. EDP Sciences (2016)

    Google Scholar 

  24. Wang, W., Wang, H., Dai, G., Wang, H.: Visualization of large hierarchical data by circle packing. In: Proceedings of the CHI, pp. 517–520. ACM (2006)

    Google Scholar 

  25. Wang, Y., Chen, L.: Two-dimensional residual-space-maximized packing. Expert Syst. Appl. 42(7), 3297–3305 (2015)

    Article  Google Scholar 

  26. Wang, Y., Zhang, Q., Lin, F., Seah, H.S.: EngineQV: investigating external cause of engine failures based on geo-temporal association. In: 2019 IEEE Pacific Visualization Symposium (PacificVis), pp. 184–188. IEEE (2019)

    Google Scholar 

  27. Wood, J., Dykes, J.: Spatially ordered treemaps. IEEE Trans. Visual Comput. Graphics 14(6), 1348–1355 (2008)

    Article  Google Scholar 

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Acknowledgment

This work is partially supported by a grant MOE 2017-T1-001-053-04 from Ministry of Education, Singapore.

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Correspondence to Feng Lin .

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Wang, YC., Liu, J., Lin, F., Seah, HS. (2020). Generating Orthogonal Voronoi Treemap for Visualization of Hierarchical Data. In: Magnenat-Thalmann, N., et al. Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science(), vol 12221. Springer, Cham. https://doi.org/10.1007/978-3-030-61864-3_33

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  • DOI: https://doi.org/10.1007/978-3-030-61864-3_33

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-61864-3

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