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Issue No.12 - Dec. (2011 vol.17)
pp: 2223-2230
Hadley Wickham , Rice University
Heike Hofmann , Iowa State University
We propose a new framework for visualising tables of counts, proportions and probabilities. We call our framework product plots, alluding to the computation of area as a product of height and width, and the statistical concept of generating a joint distribution from the product of conditional and marginal distributions. The framework, with extensions, is sufficient to encompass over 20 visualisations previously described in fields of statistical graphics and infovis, including bar charts, mosaic plots, treemaps, equal area plots and fluctuation diagrams.
Statistics, joint distribution, conditional distribution, treemap, bar chart, mosaic plot.
Hadley Wickham, Heike Hofmann, "Product Plots", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 12, pp. 2223-2230, Dec. 2011, doi:10.1109/TVCG.2011.227
[1] D. R. Cox, “Some remarks on the role in statistics of graphical methods,” Applied Statistics, vol. 27, no. 1, pp. 4–9, 1978.
[2] J. A. Davis and T. W. Smith, “General social surveys, 1972-2008 [machine-readable data file],” 2008. Principal Investigator, James A. Davis, Director and Co-Principal Investigator, Tom W. Smith Co-Principal Investigator, Peter V. Marsden Sponsored by National Science Foundation. –NORC ed.– Chicago: National Opinion Research Center [producer]; Storrs, CT: The Roper Center for Public Opinion Research, University of Connecticut [distributor], 2009.
[3] C. A. Brewer, “, Color use guidelines for mapping and visualization,” in Visualization in Modern Cartography ( A. MacEachren, and D. Taylor eds.), pp. 123–147, Elsevier Science, 1994.
[4] L. Wilkinson, The Grammar of Graphics., Statistics and Computing, Springer, 1999.
[5] L. Wilkinson, A. Anand, and R. Grossman, “Graph-theoretic scagnostics,” in IEEE Symposium on Information Visualization, pp. 157–164, 2005.
[6] J. D. Mackinlay, “Automating the design of graphical presentations of relational information.,” ACM Transactions on Graphics, vol. 5, no. 5, pp. 110–141, 1986.
[7] J. Mackinlay, P. Hanrahan, and C. Stolte, “Show me: Automatic presentation for visual analysis,” IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 6, pp. 1137–1144, 2007.
[8] A. Slingsby, J. Dykes, and J. Wood, “Configuring hierarchical layouts to address research questions,” IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, 2009.
[9] C. Stolte, D. Tang, and P. Hanrahan, “Multiscale visualization using data cubes,” Information Visualization, 2002. INFOVIS 2002. IEEE Symposium on, pp. 7 –14, 2002.
[10] W. Cleveland, The Elements of Graphing Data. Hobart Press, 1985.
[11] R. A. Becker, W. S. Cleveland, and M.-J. Shyu, “The visual design and control of trellis display,” Journal of Computational and Graphical Statistics, vol. 5, no. 2, pp. 123–155, 1996.
[12] D. A. Keim, M. C. Hao, and U. Dayal, “Hierarchical pixel bar charts,” Visualization and Computer Graphics, IEEE Transactions on, vol. 8, no. 3, pp. 255 –269, 2002.
[13] W. S. Cleveland and R. McGill, “Graphical perception: Theory, experimentation and application to the development of graphical methods.,” Journal of the American Statistical Association, vol. 79, no. 387, pp. 531–554, 1984.
[14] W. S. Cleveland and R. McGill, “An experiment in graphical perception,” International Journal of Man-Machine Studies, vol. 25, no. 5, pp. 491 – 500, 1986.
[15] J. Hollands and I. Spence, “Judging proportion with graphs: The summation model,” Applied Cognitive Psychology, vol. 12, no. 2, pp. 173–190, 1998.
[16] D. Simkin and R. Hastie, “An information-processing analysis of graph perception,” Journal of the American Statistical Association, vol. 82, no. 398, pp. 454–465, 1987.
[17] J. Hummel, “Linked bar charts: Analysing categorical data graphically.,” Journal of Computational Statistics, vol. 11, pp. 23–33, 1996.
[18] M. Bruls, K. Huizing, and J. J. van Wijk, “Squarified treemaps,” in IEEE Symposium on Information Visualization, 1999.
[19] H. Hofmann, “Exploring categorical data: Interactive mosaic plots,” Metrika, vol. 51, no. 1, pp. 11–26, 2000.
[20] J. Peltier, “Marimekko replacement – overlapping bars (easy),” 2009. URL .
[21] J. A. Hartigan and B. Kleiner, “Mosaics for contingency tables,” in Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, (Fairfax Station, VA), pp. 268–273, Interface Foundation of North America, Inc., 1981.
[22] M. Friendly, “Mosaic displays for multi-way contingency tables,” Journal of the American Statistical Association, vol. 89, no. 425, pp. 190–200, 1994.
[23] H. Hofmann, “Constructing and reading mosaicplots,” Computational Statistics and Data Analysis, vol. 43, no. 4, pp. 565–580, 2003.
[24] H. Hofmann, “Generalized odds ratios for visual modeling,” Journal of Computational and Graphical Statistics, vol. 10, no. 4, pp. 628–640, 2001.
[25] B. Shneiderman, “Tree visualization with tree-maps: 2-d spacefilling approach,” ACM Trans. Graph., vol. 11, no. 1, pp. 92–99, 1992.
[26] R. Vliegen, J. J. van Wikj, and E.-J. van der Linden, “Visualizing business data with generalized treemaps,” IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 789– 796, 2006.
[27] N. Kong, J. Heer, and M. Agrawala, “Perceptual Guidelines for Creating Rectangular Treemaps,” Visualization and Computer Graphics, IEEE Transactions on, vol. 16, no. 6, pp. 990–998, 2010.
[28] A. Unwin and H. Hofmann, “New interactive graphics tools for exploratory analysis of spatial data,” in Innovations in GIS 5, pp. 46–55, London: Taylor Francis, 1998.
[29] A. R. Unwin, C. Volinsky, and S. Winkler, “Parallel coordinates for exploratory modelling analysis,” Computational Statistics & Data Analysis, vol. 43, no. 4, pp. 553–564, 2003.
[30] A. R. Unwin, M. Theus, and H. Hofmann, Graphics of Large Datasets. Springer, 2006.
[31] L. Denby and C. Mallows, “Variations on the histogram,” Journal of Computational and Graphical Statistics, vol. 18, no. 1, pp. 21–31, 2009.
[32] H. Hofmann and M. Theus, “Interactive graphics for visualizing conditional distributions,” Unpublished manuscript, 2005.
[33] J. LeBlanc, M. Ward, and N. Wittels, “Exploring n-dimensional databases,” in Proceedings of Visualization '90, pp. 230–237, 1990.
[34] A. R. Unwin, G. Hawkins, H. Hofmann, and B. Siegl, “Interactive graphics for data sets with missing values - MANET,” Journal of Computational and Graphical Statistics, vol. 5, no. 2, pp. 113–122, 1996.
[35] H. Wainer, “The suspended rootogram and other visual displays: An empirical validation,” The American Statistician, vol. 28, no. 4, pp. 143–145, 1974.
[36] J. W. Tukey, Exploratory Data Analysis. Addison–Wesley, preliminary ed., 1971.
[37] H. Lü and J. Fogarty, “Cascaded treemaps: examining the visibility and stability of structure in treemaps,” in Proceedings of Graphics Interface 2008, pp. 259–266, Canadian Information Processing Society, 2008.
[38] G. Draper, Y. Livnat, and R. Riesenfeld, “A survey of radial methods for information visualization,” IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 5, pp. 759 –776, 2009.
[39] L. Lalanne, Appendice Sur La Representation Graphique Des Tableaux Météorologiques Et Des Lois Naturelles En Général. Cours Complet de Météorologie, 1843.
[40] M. Friendly, “A fourfold display for 2 by 2 by k table,” Tech. Rep. 217, Psychology Department, York University, 1995.
[41] F. Nightingale, Notes on matters affecting the health, efficiency and hospital administration of the British Army. London: Private publication, 1857.
[42] K. Andrews and H. Heidegger, “Information slices: Visualising and exploring large hierarchies using cascading, semi-circular discs,” >in Proc. IEEE InfoVis, 1998.
[43] S. Diehl, F. Beck, and M. Burch, “Uncovering Strengths and Weaknesses of Radial Visualizations—an Empirical Approach,” Visualization and Computer Graphics, IEEE Transactions on, vol. 16, no. 6, pp. 935–942, 2010.
[44] X. Lou, S. Liu, and T. Wang, “Fanlens: Dynamic hierarchical exploration of tabular data,” in Infovis 2007 (poster), 2007.
[45] J. Stasko and E. Zhang, “Focus+context display and navigation techniques for enhancing radial, space-filling hierarchy visualizations,” in Proc. IEEE InfoVis, 2000.
[46] K. Wetzel, “pebbles - using circular treemaps to visualize disk usage,” 2008. URL http://lip.sourceforge.netctreemap.html.
[47] M. Wattenberg, “A note on space-filling visualizations and space-filling curves,” in Proc. IEEE InfoVis, 2005.
[48] M. Balzer and O. Deussen, “Voronoi treemaps,” in Proc. IEEE InfoVis, 2005.
[49] R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2010. ISBN 3-900051-07-0.
[50] H. Wickham, ggplot2: Elegant graphics for data analysis. useR, Springer, July 2009.
[51] D. W. Scott, “Averaged shifted histograms: Effective nonpara-metric density estimators in several dimensions,” The Annals of Statistics, vol. 13, pp. 1024–1040, 1985.
[52] D. W. Scott, Multivariate density estimation. Wiley Online Library, 1992.
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