Skip to main content
SpringerLink
Log in

Correlation Coordinate Plots: Efficient Layouts for Correlation Tasks

  • Conference paper
  • First Online:
Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 693))

  • 1102 Accesses

Abstract

Correlation is a powerful measure of relationships assisting in estimating trends and making forecasts. It’s use is widespread, being a critical data analysis component of fields including science, engineering, and business. Unfortunately, visualization methods used to identify and estimate correlation are designed to be general, supporting many visualization tasks. Due in large part to their generality, they do not provide the most efficient interface, in terms of speed and accuracy for correlation identifying. To address this shortcoming, we first propose a new correlation task-specific visual design called Correlation Coordinate Plots (CCPs). CCPs transform data into a powerful coordinate system for estimating the direction and strength of correlation. To extend the functionality of this approach to multiple attribute datasets, we propose two approaches. The first design is the Snowflake Visualization, a focus+context layout for exploring all pairwise correlations. The second design enhances the CCP by using principal component analysis to project multiple attributes. We validate CCP by applying it to real-world data sets and test its performance in correlation-specific tasks through an extensive user study that showed improvement in both accuracy and speed of correlation identification.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    CCPs: https://github.com/hoa84/CCPs_SnowflakeViz.

  2. 2.

    http://lib.stat.cmu.edu/datasets/boston.

  3. 3.

    http://lib.stat.cmu.edu/datasets/pollen.data.

  4. 4.

    http://vis.computer.org/vis2004contest/.

References

  1. Anscombe, F.J.: Graphs in statistical analysis. In: American Statistical Association, pp. 17–21 (1973)

    Google Scholar 

  2. Aris, A., Shneiderman, B.: Designing semantic substrates for visual network exploration. InfoVis 6, 281–300 (2007)

    Google Scholar 

  3. Bertini, E., Tatu, A., Keim, D.: Quality metrics in high-dimensional data visualization: an overview and systematization. IEEE Trans. Vis. Comp. Graph. 17(12), 2203–2212 (2011)

    Article  Google Scholar 

  4. Bezerianos, A., Chevalier, F., Dragicevic, P., Elmqvist, N., Fekete, J.D.: Graphdice: a system for exploring multivariate social networks. Comput. Graph. Forum 29(3), 863–872 (2010)

    Article  Google Scholar 

  5. Buering, T., Gerken, J., Reiterer, H.: User interaction with scatterplots on small screens - a comparative evaluation of geometric-semantic zoom and fisheye distortion. IEEE Trans. Vis. Comp. Graph. 12(5), 829–836 (2006)

    Article  Google Scholar 

  6. Chen, Y.A., Almeida, J.S., Richards, A.J., Muller, P., Carroll, R.J., Rohrer, B.: A nonparametric approach to detect nonlinear correlation in gene expression. J. Comput. Stat. Graph. 19(3), 552–568 (2010)

    Article  MathSciNet  Google Scholar 

  7. Dang, T.N., Wilkinson, L.: Transforming scagnostics to reveal hidden features. IEEE Trans. Vis. Comp. Graph. 20(12), 1624–1632 (2014)

    Article  Google Scholar 

  8. Elmqvist, N., Dragicevic, P., Fekete, J.D.: Rolling the dice: multidimensional visual exploration using scatterplot matrix navigation. IEEE Trans. Vis. Comp. Graph. 14(6), 1148–1539 (2008)

    Article  Google Scholar 

  9. Fanea, E., Carpendale, M.S.T., Isenberg, T.: An interactive 3D integration of parallel coordinates and star glyphs. In: InfoVis, pp. 149–156 (2005)

    Google Scholar 

  10. Friendly, M.: Corrgrams: exploratory displays for correlation matrices. Am. Stat. 56(4), 316–324 (2002)

    Article  MathSciNet  Google Scholar 

  11. Geng, Z., Peng, Z., Laramee, R.S., Roberts, J.C., Walker, R.: Angular histograms: frequency-based visualizations for large, high dimensional data. IEEE Trans. Vis. Comput. Graph. 17(12), 2572–2580 (2011)

    Article  Google Scholar 

  12. Harrison, L., Yang, F., Franconeri, S., Chang, R.: Ranking visualizations of correlation using Weber’s law. IEEE Trans. Vis. Comput. Graph. 20(12), 1943–1952 (2014)

    Article  Google Scholar 

  13. Hartigan, J.A.: Printer graphics for clustering. JSCS 4(3), 187–213 (1975)

    MATH  Google Scholar 

  14. Heinrich, J., Stasko, J., Weiskopf, D.: The parallel coordinates matrix. In: EuroVis - Short Papers, pp. 37–41 (2012)

    Google Scholar 

  15. Heinrich, J., Weiskopf, D.: State of the art of parallel coordinates. In: Eurographics STAR, pp. 95–116 (2013)

    Google Scholar 

  16. Holten, D., van Wijk, J.J.: Evaluation of cluster identification performance for different PCP variants. In: EuroVis, vol, 29, no 3 (2010)

    Google Scholar 

  17. Hong, X., Wang, C.X., Thompson, J.S., Allen, B., Malik, W.Q., Ge, X.: On space-frequency correlation of UWB MIMO channels. IEEE Trans. Veh. Tech. 59(9), 4201–4213 (2010)

    Article  Google Scholar 

  18. Huang, T.H., Huang, M.L., Zhang, K.: An interactive scatter plot metrics visualization for decision trend analysis. In: Conference on Machine Learning, Applications, pp. 258–264 (2012)

    Google Scholar 

  19. Inselberg, A.: The plane with parallel coordinates. Vis. Comput. 1(2), 69–91 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  20. Jarrell, S.B.: Basic Statistics. W.C. Brow Comm, Reading (1994)

    Google Scholar 

  21. Johansson, J., Ljung, P., Jern, M., Cooper, M.: Revealing structure in visualizations of dense 2D and 3D parallel coordinates. Inf. Vis. 5(2), 125–136 (2006)

    Article  Google Scholar 

  22. Kay, M., Heer, J.: Beyond Weber’s law a second look at ranking visualizations of correlation. IEEE Trans. Vis. Comput. Graph. 22(1), 469–478 (2016)

    Article  Google Scholar 

  23. Li, J., Martens, J.B., van Wijk, J.J.: Judging correlation from scatterplots and parallel coordinate plots. InfoVis 9, 13–30 (2010)

    Google Scholar 

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

    Article  Google Scholar 

  25. Magnello, E., Vanloon, B.: Introducing Statistics: A Graphic Guide. Icon Books, London (2009)

    Google Scholar 

  26. Sharma, R.K., Wallace, J.W.: Correlation-based sensing for cognitive radio networks bounds and experimental assessment. IEEE Sens. J. 11(3), 657–666 (2011)

    Article  Google Scholar 

  27. Tominski, C., Abello, J., Schumann, H.: Axes-based visualizations with radial layouts. In: ACM symposium on Applied computing, pp. 1242–1247. ACM (2004)

    Google Scholar 

  28. Wang, J., Zheng, N.: A novel fractal image compression scheme with block classification and sorting based on pearsons correlation coefficient. IEEE Trans. Image Process. 22(9), 3690–3702 (2013)

    Article  Google Scholar 

  29. Wattenberg, M.: Visual exploration of multivariate graphs. In: SIGCHI, CHI 2006, pp. 811–819 (2006)

    Google Scholar 

  30. Wilkinson, L., Anand, A., Grossman, R.L.: Graph-theoretic scagnostics. InfoVis. 5, 21 (2005)

    Google Scholar 

  31. Xu, W., Chang, C., Hung, Y.S., Fung, P.C.W.: Asymptotic properties of order statistics correlation coefficient in the normal cases. IEEE Trans. Signal Process. 56(6), 2239–2248 (2008)

    Article  MathSciNet  Google Scholar 

  32. Yu, S., Zhou, W., Jia, W., Guo, S., Xiang, Y., Tang, F.: Discriminating DDoS attacks from flash crowds using flow correlation coefficient. IEEE Trans. PDS 23(6), 1073–1080 (2012)

    Google Scholar 

  33. Zhou, H., Cui, W., Qu, H., Wu, Y., Yuan, X., Zhuo, W.: Splatting lines in parallel coordinates. Comput. Graph. Forum 28(3), 759–766 (2009)

    Article  Google Scholar 

  34. Zhou, H., Yuan, X., Qu, H., Cui, W., Chen, B.: Visual clustering in parallel coordinates. In: Computer Graphics Forum (2008)

    Google Scholar 

Download references

Acknowledgements

We would like to thank our reviewers and colleagues who gave us valuable feedback on our approach. We would also like to thank our funding agents, NSF CIF21 DIBBs (ACI-1443046), NSF Core Program (IIS-1513616), Lawrence Livermore National Laboratory, and Pacific Northwest National Laboratory Analysis in Motion (AIM) Initiative.

Author information

Authors and Affiliations

  1. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA

    Hoa Nguyen

  2. Department of Computer Science and Engineering, University of South Florida, Tampa, USA

    Paul Rosen

Authors
  1. Hoa Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Rosen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hoa Nguyen .

Editor information

Editors and Affiliations

  1. Escola Superior de Tecnologia do IPS, Setúbal, Portugal

    José Braz

  2. MiraLab, University of Geneva, Carouge, Switzerland

    Nadia Magnenat-Thalmann

  3. LISA - ISTIA, University of Angers, Angers, France

    Paul Richard

  4. Department of Computer Science and Electrical Engineering, Jacobs University, Bremen, Germany

    Lars Linsen

  5. University of Groningen, Groningen, The Netherlands

    Alexandru Telea

  6. Università di Catania, Catania, Italy

    Sebastiano Battiato

  7. Research Innovation Center, Canon U.S.A. Inc., San Jose, California, USA

    Francisco Imai

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Nguyen, H., Rosen, P. (2017). Correlation Coordinate Plots: Efficient Layouts for Correlation Tasks. In: Braz, J., et al. Computer Vision, Imaging and Computer Graphics Theory and Applications. VISIGRAPP 2016. Communications in Computer and Information Science, vol 693. Springer, Cham. https://doi.org/10.1007/978-3-319-64870-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-64870-5_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64869-9

  • Online ISBN: 978-3-319-64870-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation