Computational Statistics

, Volume 26, Issue 4, pp 613–633 | Cite as

Eulerian tour algorithms for data visualization and the PairViz package

  • C. B. HurleyEmail author
  • R. W. Oldford
Original Paper


PairViz is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. PairViz implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions. We describe these algorithms, their PairViz implementation and discuss their properties and performance. We illustrate their application to two visualization problems, that of assessing rater agreement, and model comparison in regression.


Hamiltonian Eulerian tour Seriation Visualization Parallel coordinates 


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  1. Allison T, Cicchetti D (1976) Sleep in mammals: ecological and constitutional correlates. Science 194: 732–734CrossRefGoogle Scholar
  2. Alspach B, Bermond JC, Sotteau D (1990) Decomposition into cycles I: Hamilton decompositions. In: Hahn G, Sabidussi G, Woodrow RE (eds) Cycles and rays. Kluwer, Boston, pp 9–18Google Scholar
  3. Ankerst M, Berchtold S, Keim DA (1998) Similarity clustering of dimensions for an enhanced visualization of multidimensional data. IEEE Symp Inf Vis 1998: 52–60Google Scholar
  4. Bendix F, Kosara R, Hauser H (2005) Parallel sets: visual analysis of categorical data. IEEE Symp Inf Vis 2005: 1–18Google Scholar
  5. Cleveland WS (1995) Visualizing data. Hobart Press, Summit, NJGoogle Scholar
  6. Csardi G, Nepusz T (2006) The igraph software package for complex network research. InterJournal, Complex Systems 1695Google Scholar
  7. Edmonds J, Johnson EL (1973) Matching, euler tours, and the Chinese postman. Math Program 5: 88–124MathSciNetzbMATHCrossRefGoogle Scholar
  8. Fleiss JL (1971) Measuring nominal scale agreement among many raters. Psychol Bull 76: 378–382CrossRefGoogle Scholar
  9. Friendly M, Kwan E (2003) Effect ordering for data displays. Comput Stat Data Anal 43: 509–539MathSciNetzbMATHCrossRefGoogle Scholar
  10. Gamer M, Lemon J, Fellows I (2009) irr: various coefficients of interrater reliability and agreement. R package version 0.82Google Scholar
  11. Gentleman R, Whalen E, Huber W, Falcon S (2010) graph: a package to handle graph data structures. R package version 1.26.0Google Scholar
  12. Gross, JL, Yellen, J (eds) (2004) Handbook of graph theory. CRC Press, LondonzbMATHGoogle Scholar
  13. Hierholzer C (1873) Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Math Annalen VI:30–32MathSciNetCrossRefGoogle Scholar
  14. Hofmann H (2006) Multivariate categorical data–mosaic plots. In: Unwin A, Theus M, Hofmann H (eds) Graphics of large datasets, visualizing a million. Springer, New York, pp 105–124CrossRefGoogle Scholar
  15. Hurley CB (2004) Clustering visualizations of multidimensional data. J Comput Graphical Stat 13: 788–806MathSciNetCrossRefGoogle Scholar
  16. Hurley CB, Oldford RW (2009) PairViz: visualization using Eulerian tours and Hamiltonian decompositions, R package version 1.1Google Scholar
  17. Hurley CB, Oldford RW (2010) Pairwise display of high dimensional information via Eulerian tours and Hamiltonian decompositions. J Comput Graphical Stat 19(4): 861–886CrossRefGoogle Scholar
  18. Hurley CB, Oldford RW (2011) Graphs as navigational infrastructure for high dimensional data spaces. Comput Stat. doi: 10.1007/s00180-011-0228-6
  19. Lucas DE (1892) Recréations Mathématiques, Vol. II. Gauthier Villars, ParisGoogle Scholar
  20. Theus M (2002) Interactive data visualization using mondrian. J Stat Softw 7(11): 1–9Google Scholar
  21. Unwin A, Volinsky C, Winkler S (2003) Parallel coordinates for exploratory modelling analysis. Comput Stat Data Anal 43: 553–564MathSciNetzbMATHCrossRefGoogle Scholar
  22. Wegman EJ (1990) Hyperdimensional data analysis using parallel coordinates. J Am Stat Assoc 85: 664–675CrossRefGoogle Scholar
  23. Wilkinson L, Anand A, Grossman R (2005) Graph-theoretic scagnostics. IEEE Symp Inf Vis 2005: 157–164Google Scholar
  24. Wills G (2000) A good, simple axis. Stat Comput Stat Graphics Newsl 11: 20–25Google Scholar
  25. Yang J, Peng W, Ward MO, Rundenmeister EA (2003) Interactive hierarchical dimension ordering, spacing and filtering for exploration of high dimensional datasets. IEEE Symp Inf Vis 2003: 105–112Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsNational University of Ireland, MaynoothMaynoothIreland
  2. 2.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

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