The Community for Technology Leaders
RSS Icon
Issue No.11 - Nov. (2013 vol.19)
pp: 1820-1832
D. Auber , LaBRI, Univ. Bordeaux I, Talence, France
C. Huet , LaBRI, Univ. Bordeaux I, Talence, France
A. Lambert , LaBRI, Univ. Bordeaux I, Talence, France
B. Renoust , LaBRI, Univ. Bordeaux I, Talence, France
A. Sallaberry , LIRMM, Montpellier, France
A. Saulnier , Ina Paris Ile-de-France Centre, Bry-sur-Marne, France
The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.
Data visualization, Layout, Shape, Visualization, Vegetation, Labeling, Fractals,concave polygon labeling, Treemap, tree layout, hierarchical data visualization, Gosper curve
D. Auber, C. Huet, A. Lambert, B. Renoust, A. Sallaberry, A. Saulnier, "GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data", IEEE Transactions on Visualization & Computer Graphics, vol.19, no. 11, pp. 1820-1832, Nov. 2013, doi:10.1109/TVCG.2013.91
[1] E.M. Reingold and J.S. Tilford, "Tidier Drawings of Trees," IEEE Trans. Software Eng., vol. 7, no. 2, pp. 223-228, Mar. 1981.
[2] P. Eades, "Drawing Free Trees," Bull. of the Inst. of Combinatorics and its Applications, vol. 5, pp. 10-36, 1992.
[3] S. Grivet, D. Auber, J.-P. Domenger, and G. Melancon, "Bubble Tree Drawing Algorithm," Proc. Int'l Conf. Computer Vision and Graphics, pp. 633-641, 2004.
[4] B. Johnson and B. Shneiderman, "Tree Maps: A Space-Filling Approach to the Visualization of Hierarchical Information Structures," Proc. IEEE Information Visualization, pp. 284-291, 1991.
[5] J.B. Kruskal and J.M. Landwehr, "Icicle Plots: Better Displays for Hierarchical Clustering," The Am. Statistician, vol. 37, no. 2, pp. 162-168, 1983.
[6] T. Barlow and P. Neville, "A Comparison of 2-D Visualizations of Hierarchies," Proc. IEEE Symp. Information Visualization, pp. 131-138, 2001.
[7] W.M. Murrell, Map on Temperance. Howe's Sheet Anchor Press, 1846.
[8] A. Skupin, "From Metaphor to Method: Cartographic Perspectives on Information Visualization," Proc. IEEE Symp. Information Visualization, pp. 91-98, 2000.
[9] S.I. Fabrikant and A. Skupin, "Cognitively Plausible Information Visualization," Exploring Geovisualization, J. Dykes, A.M. MacEachren, and M.-J. Kraak, eds., pp. 667-682, Elsevier ltd., 2005.
[10] J. Bertin, "Semiology of Graphics: Diagrams, Networks, Maps," 1983.
[11] N. Tractinsky, A. Katz, and D. Ikar, "What Is Beautiful is Usable," Interacting with Computers, vol. 13, no. 2, pp. 127-145, 2000.
[12] Y. Liu, "The Aesthetic and the Ethic Dimensions of Human Factors and Design," Ergonomics, vol. 46, nos. 13/14, pp. 1293-1305, 2003.
[13] A. Sonderegger and J. Sauer, "The Influence of Design Aesthetics in Usability Testing: Effects on User Performance and Perceived Usability," Applied Ergonomics, vol. 41, no. 3, pp. 403-410, 2010.
[14] M. Sarkar and M.H. Brown, "Graphical Fisheye Views," ACM Comm., vol. 37, no. 12, pp. 73-83, 1994.
[15] W. Tobler, "Pseudo-Cartograms," The Am. Cartographer, vol. 13, pp. 43-50, 1986.
[16] D.A. Keim, S.C. North, and C. Panse, "Cartodraw: A Fast Algorithm for Generating Contiguous Cartograms," IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 1, pp. 95-110, Jan./Feb. 2004.
[17] E. Raisz, "The Rectangular Statistical Cartogram," Geographical Rev., vol. 24, no. 2, pp. 292-296, 1934.
[18] M.J. van Kreveld and B. Speckmann, "On Rectangular Cartograms," Computational Geometry, Theory and Applications, vol. 37, no. 3, pp. 175-187, 2007.
[19] M. Rooke, T. Grossman, and G. Fitzmaurice, "AppMap: Exploring User Interface Visualizations," Proc. Graphics Interface Conf., pp. 111-118, 2011.
[20] T. Kohonen, Self-Organizing Maps. Springer-Verlag, 1995.
[21] A. Skupin, "A Cartographic Approach to Visualizing Conf. Abstracts," IEEE Computer Graphics and Applications, vol. 22, no. 1, pp. 50-58, Jan./Feb. 2002.
[22] Y. Hu, E.R. Gansner, and S.G. Kobourov, "Visualizing Graphs and Clusters as Maps," IEEE Computer Graphics and Applications, vol. 30, no. 6, pp. 54-66, Nov./Dec. 2010.
[23] J.A. Wise, J.J. Thomas, K. Pennock, D. Lantrip, M. Pottier, A. Schur, and V. Crow, "Visualizing the Non-Visual: Spatial Analysis and Interaction with Information from Text Documents," Proc. IEEE Symp. Information Visualization, pp. 51-58. 1995.
[24] R. van Liere and W.C. de Leeuw, "GraphSplatting: Visualizing Graphs as Continuous Fields," IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 2, pp. 206-212, Apr. 2003.
[25] I.Y. Liao, M. Petrou, and R. Zhao, "A Fractal-Based Relaxation Algorithm for Shape from Terrain Image," Computer Vision Image Understanding, vol. 109, no. 3, pp. 227-243, 2008.
[26] D.A. Keim, H.-P. Kriegel, and M. Ankerst, "Recursive Pattern: A Technique for Visualizing Very Large Amounts of Data," Proc. IEEE Sixth Visualization Conf., pp. 279-286, 1995.
[27] M. Wattenberg, "A Note on Space-Filling Visualizations and Space-Filling Curves," Proc. IEEE Symp. Information Visualization, p. 24, 2005.
[28] C. Muelder and K.-L. Ma, "Rapid Graph Layout Using Space Filling Curves," IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 14, pp. 1301-1308, Nov. 2008.
[29] A. Sallaberry, C. Muelder, and K.-L. Ma, "Clustering, Visualizing, and Navigating for Large Dynamic Graphs," Proc. Symp. Graph Drawing, vol. 7704, pp. 487-498, 2013.
[30] M. Graham and J.B. Kennedy, "A Survey of Multiple Tree Visualisation," Information Visualization, vol. 9, no. 4, pp. 235-252, 2010.
[31] K. Andrews and H. Heidegger, "Information Slices: Visualising and Exploring Large Hierarchies Using Cascading, Semi-Circular Discs," Proc. IEEE Symp. Information Visualization, pp. 9-12, 1998.
[32] J.T. Stasko and E. Zhang, "Focus+Context Display and Navigation Techniques for Enhancing Radial, Space-Filling Hierarchy Visualizations," Proc. IEEE Symp. Information Visualization, pp. 57-65, 2000.
[33] M. Bruls, K. Huizing, and J.J. van Wijk, "Squarified Treemaps," Proc. Joint Eurographics/IEEE TVCG Symp. Visualization, pp. 33-42, 2000.
[34] B.B. Bederson, B. Shneiderman, and M. Wattenberg, "Ordered and Quantum Treemaps: Making Effective Use of 2D Space to Display Hierarchies," ACM Trans. Graphics, vol. 21, no. 4, pp. 833-854, 2002.
[35] R. Vliegen, J.J. van Wijk, and E.-J. van der Linden, "Visualizing Business Data with Generalized Treemaps," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 789-796, Sept./Oct. 2006.
[36] S. Tak and A. Cockburn, "Enhanced Spatial Stability with Hilbert and Moore Treemaps," IEEE Trans. Visualization and Computer Graphics, vol. 19, no. 1, pp. 141-148, Jan. 2013.
[37] M. Balzer, O. Deussen, and C. Lewerentz, "Voronoi Treemaps for the Visualization of Software Metrics," Proc. ACM Symp. Software Visualization, pp. 165-172, 2005.
[38] M. Balzer and O. Deussen, "Voronoi Treemaps," Proc. IEEE Symp. Information Visualization, p. 7, 2005.
[39] A. Sud, D. Fisher, and H.-P. Lee, "Fast Dynamic Voronoi Treemaps," Proc. Int'l Symp. Voronoi Diagrams in Science and Eng., pp. 85-94, 2010.
[40] B.B. Bederson, "Photomesa: A Zoomable Image Browser Using Quantum Treemaps and Bubblemaps," Proc. ACM Symp. User Interface Software and Technology, pp. 71-80, 2001.
[41] R. Wettel and M. Lanza, "Visualizing Software Systems as Cities," Proc. IEEE Fourth Int'l Workshop Visualizing Software for Understanding and Analysis, pp. 92-99, 2007.
[42] H.-J. Schulz, S. Hadlak, and H. Schumann, "Point-Based Tree Representation: A New Approach for Large Hierarchies," Proc. IEEE Pacific Visualization Symp., pp. 81-88, 2009.
[43] K. Buchin, D. Eppstein, M. Löffler, M. Nöllenburg, and R.I. Silveira, "Adjacency-Preserving Spatial Treemaps," Proc. 12th Int'l Symp. Algorithms and Data Structures, pp. 159-170, 2011.
[44] J. Wood and J. Dykes, "Spatially Ordered Treemaps," IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 1348-1355, Nov./Dec. 2008.
[45] B.B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freedman and Co., 1983.
[46] T. Itoh, C. Muelder, K.-L. Ma, and J. Sese, "A Hybrid Space-Filling and Force-Directed Layout Method for Visualizing Multiple-Category Graphs," Proc. IEEE Pacific Visualization Symp., pp. 121-128, 2009.
[47] H.J. Haverkort and F. van Walderveen, "Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves," Computational Geometry, Theory and Applications, vol. 43, no. 2, pp. 131-147, 2010.
[48] B. Mandelbrot, Fractals: Form, Chance, and Dimension. W.H. Freeman, 1977.
[49] W.T. Tutte, "How to Draw a Graph," Proc. London Math. Soc., vol. 13, pp. 743-768, 1963.
[50] G. Neyer, "Map Labeling with Application to Graph Drawing," Drawing Graphs: Methods and Models, M. Kaufmann and D. Wagner, eds., vol. 2025, pp. 247-273, Springer, 2001.
[51] K. Börner, Atlas of Science: Visualizing What We Know. MIT Press, 2010.
[52] F.Y.L. Chin, J. Snoeyink, and C.A. Wang, "Finding the Medial Axis of a Simple Polygon in Linear Time," Discrete and Computational Geometry, vol. 21, no. 3, pp. 405-420, 1999.
[53] R. Uehara and Y. Uno, "Efficient Algorithms for the Longest Path Problem," Proc. 15th Int'l Symp. Algorithms and Computation, pp. 871-883, 2004.
[54] S. Bateman, R.L. Mandryk, C. Gutwin, A. Genest, D. McDine, and C.A. Brooks, "Useful Junk?: The Effects of Visual Embellishment on Comprehension and Memorability of Charts," Proc. 28th Int'l Conf. Human Factors in Computing Systems, pp. 2573-2582, 2010.
[55] P. Luzzardi, C. Freitas, R. Cava, G. Duarte, and M. Vasconcelos, "An Extended Set of Ergonomic Criteria for Information Visualization Techniques," Proc. Seventh IASTED Int'l Conf. Computer Graphics And Imaging, pp. 236-241, 2004.
[56] I. EIC, Ergonomic Requirements for Office Work with Visual Display Terminals, 1998.
[57] C. Plaisant, "The Challenge of Information Visualization Evaluation," Proc. Working Conf. Advanced Visual Interfaces, pp. 109-116, 2004.
[58] Y. Wang, S. Teoh, and K.-L. Ma, "Evaluating the Effectiveness of Tree Visualization Systems for Knowledge Discovery," Proc. Eurographics/IEEE-VGTC Symp. Visualization, pp. 67-74, 2006.
[59] J.J. van Wijk and W.A.A. Nuij, "Smooth and Efficient Zooming and Panning," Proc. IEEE Symp. Information Visualization, pp. 15-23, 2003.
[60] J. Yang, W. Peng, M.O. Ward, and E.A. Rundensteiner, "Interactive Hierarchical Dimension Ordering, Spacing and Filtering for Exploration of High Dimensional Data Sets," Proc. IEEE Symp. Information Visualization, pp. 105-112, 2003.
153 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool