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The Grammar of Graphics

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Handbook of Computational Statistics

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

The Grammar of Graphics, or GOG, denotes a system with seven orthogonal components. By orthogonal, we mean there are seven graphical component sets whose elements are aspects of the general system and that every combination of aspects in the product of all these sets is meaningful. This sense of the word orthogonality, a term used by computer designers to describe a combinatoric system of components or building blocks, is in some sense similar to the orthogonal factorial analysis of variance (ANOVA), where factors have levels and all possible combinations of levels exist in the ANOVA design. If we interpret each combination of features in a GOG system as a point in a network, then the world described by GOG is represented in a seven-dimensional rectangular lattice.

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References

  • Abiteboul, S., Fischer, P.C., Schek, H.J.: Nested Relations and Complex Objects in Databases. Springer, New York (1989)

    MATH  Google Scholar 

  • Agrawal, R., Gupta, A., Sarawagi, S.: Modeling multidimensional databases. In: Gray, A., Larson, P.-Ã… (eds.) Proceedings of 13th International Conference of Data Engineering (ICDE), IEEE Computer Society, pp. 232–243 (1997)

    Google Scholar 

  • Andrews, D.: Plots of high dimensional data. Biometrics 28, 125–136 (1972)

    Google Scholar 

  • Barnett, V., Lewis, T.: Outliers in Statistical Data. Wiley, New York (1994)

    MATH  Google Scholar 

  • Becker, R.A., Cleveland, W.S., Shyu, M.-J.: The design and control of trellis display. J. Comput. Stat. Graphics 5, 123–155 (1996)

    Google Scholar 

  • Bertin, J.: Smiologie Graphique. Editions Gauthier-Villars, Paris (1967)

    Google Scholar 

  • Date, C.: What is a domain? In: Date, C.: (eds.) Relational Database Writings 1985–1989, pp. 213–313. Addison-Wesley, Reading, MA (1990)

    Google Scholar 

  • Date, C.J., Darwen, H.: Relation-valued attributes. In: Date, C.J., Darwen, H. (eds.) Relational Database: Writings 1989-1991, pp. 75–98. Addison-Wesley, Reading, MA (1992)

    Google Scholar 

  • Feiner, S., Beshers, C.: Worlds within worlds: Metaphors for exploring n-dimensional virtual worlds. In: Proceedings of ACM UIST ’90. pp. 76–83. ACM Press, New York, NY (1990)

    Google Scholar 

  • Fisher, R.: Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh (1925)

    Google Scholar 

  • Fisher, R.: The Design of Experiments. Oliver and Boyd, Edinburgh (1935)

    Google Scholar 

  • Friedman, J.: Exploratory projection pursuit. J. Am. Stat. Assoc. 82, 249–266 (1987)

    Article  MATH  Google Scholar 

  • Glymour, C., Madigan, D., Pregibon, D., Smyth, P.: Statistical inference and data mining. Comm. ACM 39(11), 35–41 (1996)

    Article  Google Scholar 

  • Gyssens, M., Lakshmanan, L.V.S., Subramanian, I.N.: Tables as a paradigm for querying and restructuring (extended abstract). In: Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, pp. 93–103. ACM Press, Montreal, Quebec, Canada (1996)

    Google Scholar 

  • Hand, D.J., Mannila, H., Smyth, P.: Principles of Data Mining: Adaptive Computation and Machine Learning. MIT Press, Cambridge, MA (2001)

    Google Scholar 

  • Hartigan, J., Kleiner, B.: Mosaics for contingency tables. In: Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, pp. 268–273 (1981)

    Google Scholar 

  • Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2001)

    MATH  Google Scholar 

  • Heiberger, R.M.: Computation for the Analysis of Designed Experiments. Wiley, New York (1989)

    MATH  Google Scholar 

  • Inselberg, A.: The plane with parallel coordinates. Visual Comput. 1, 69–91 (1984)

    Article  Google Scholar 

  • Johnson, B., Schneiderman, B.: Treemaps: A space-filling app. roach to the visualization of hierarchical information structures. In: Proceedings of the IEEE Information Visualization ’91, pp. 275–282 (1991)

    Google Scholar 

  • Kutner, M.H., Nachtschiem, C.J., Wasserman, W., Neter, J.: App.lied Linear Statistical Models, Richard D. Irwin, Incorporation, Homewood, IL (1996)

    Google Scholar 

  • Linhart, H., Zucchini, W.: Model Selection. Wiley, New York (1986)

    Book  MATH  Google Scholar 

  • Mackinlay, J.: Automating the design of graphical presentations of relational information. ACM Trans. Graph. (TOG) 5(2), 110–141 (1986)

    Google Scholar 

  • Makinouchi, A.: A consideration on normal form of not-necessarily-normalized relation in the relational model. In: Proceedings of the Third International Conference on Very Large Data Bases. pp. 447–453 (1977)

    Google Scholar 

  • Mendelssohn, R.C.: The bureau of labor statistic’s table producing language (TPL). In: Proceedings of the 1974 annual conference, Bureau of Labor Statistics, pp. 116–122. Washington, DC (1974)

    Google Scholar 

  • Mihalisin, T., Timlin, J., Schwegler, J.: Visualizing multivariate functions, data, and distributions. IEEE Computer Graphics and Applications. 11(13), 28–35 (1991)

    Article  Google Scholar 

  • Mosteller, F., Parunak, A.: Identifying extreme cells in a sizable contingency table: Probabilistic and exploratory app. roaches. In: Hoaglin, D.C., Mosteller, F., Tukey, J.W. (eds.) Exploring Data Tables, Trends, and Shapes, pp. 189–224. Wiley, New York (1985)

    Google Scholar 

  • Nelder, J.A.: The analysis of randomised experiments with orthogonal block structure (Parts I and II). Proc. Roy. Soc. Lond. Series A 283, 147–178 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  • Norton, A., Rubin, M., Wilkinson, L.: Streaming graphics. Stat. Comput. Graph. Newsletter 12(1), 11–14 (2001)

    Google Scholar 

  • Pedersen, D., Riis, K., Pedersen, T.B.: A powerful and SQL-compatible data model and query language for OLAP. In: Proceedings of the thirteenth Australasian conference on Database technologies, Australian Computer Society, Incorporation, pp. 121–130. Melbourne, Victoria, Australia (2002)

    Google Scholar 

  • Ramsay, J., Silverman, B.: Functional Data Analysis. Springer, New York (1997)

    MATH  Google Scholar 

  • Roth, S.F., Kolojejchick, J., Mattis, J., Chuah, M.C., Goldstein, J., Juarez, O.: SAGE tools: a knowledge-based environment for designing and perusing data visualizations. In: Proceedings of the CHI ’94 conference companion on Human factors in computing systems, pp. 27–28. ACM Press, Boston, Massachusetts, USA (1994)

    Google Scholar 

  • Sarawagi, S., Agrawal, R., Megiddo, N.: Discovery-driven exploration of OLAP data cubes. In: Proceedings of the Sixth International Conference on Extending Database Technology (EDBT) (1998)

    Google Scholar 

  • Shoshani, A.: OLAP and statistical databases: similarities and differences. In: Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, pp. 185–196. ACM Press, Tucson, Arizona, USA (1997)

    Google Scholar 

  • Simkin, D., Hastie, R.: An information processing analysis of graph perception. J. Am. Stat. Assoc. 82, 454–465 (1987)

    Article  Google Scholar 

  • Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)

    Article  MATH  Google Scholar 

  • Stolte, C., Tang, D., Hanrahan, P.: Polaris: A system for query, analysis, and visualization of multidimensional relational databases. IEEE Trans. Visual. Comput. Graph. 8 1, 52–65 (2002)

    Article  Google Scholar 

  • Taylor, B.N.: The international system of units (SI). In: Special Publication 330, pp. 171–182. NIST, Washington, DC (1997)

    Google Scholar 

  • Tukey, J.W.: Exploratory Data Analysis. Addison-Wesley Publishing Company, Reading, MA (1977)

    MATH  Google Scholar 

  • Wegman, E.J.: Hyperdimensional data analysis using parallel coordinates. J. Am. Stat. Assoc. 85, 664–675 (1985)

    Article  Google Scholar 

  • Wilkinson, G.N., Rogers, C.E.: Symbolic description of factorial models for analysis of variance. J. Roy. Stat. Soc. Series C 22, 392–399 (1973)

    Google Scholar 

  • Wilkinson, L.: A graph algebra. In: Computing Science and Statistics: Proceedings of the 28th Symposium on the Interface, pp. 341–351 (1996)

    Google Scholar 

  • Wilkinson, L.: The Grammar of Graphics. Springer, New York (1999)

    MATH  Google Scholar 

  • Wilkinson, L., Rope, D., Carr, D., Rubin, M.: The language of graphics. J. Comput. Graph. Stat. 9, 530–543 (2000)

    MathSciNet  Google Scholar 

  • Wills, G.: Using the java 2 platform for advanced information visualization. Unpublished paper presented at the Annual Java One conference (2002)

    Google Scholar 

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Wilkinson, L. (2012). The Grammar of Graphics. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21551-3_13

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