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Structure revealing techniques based on parallel coordinates plot

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Abstract

Parallel coordinates plot (PCP) is an excellent tool for multivariate visualization and analysis, but it may fail to reveal inherent structures for complex and large datasets. Therefore, polyline clustering and coordinate sorting are inevitable for the accurate data exploration and analysis. In this paper, we propose a suite of novel clustering and dimension sorting techniques in PCP, to reveal and highlight hidden trend and correlation information of polylines. Spectrum theory is first introduced to specifically design clustering and sorting techniques for a clear view of clusters in PCP. We also provide an efficient correlation based sorting technique to optimize the ordering of coordinates to reveal correlated relations, and show how our view-range metrics, generated based on the aggregation constraints, can be used to make a clear view for easy data perception and analysis. Experimental results generated using our framework visually represent meaningful structures to guide the user, and improve the efficiency of the analysis, especially for the complex and noisy data.

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References

  1. Artero, A.O., De Oliveira, M., Levkowitz, H.: Uncovering clusters in crowded parallel coordinates visualizations. In: IEEE Symposium on Information Visualization, pp. 81–88 (2004)

    Chapter  Google Scholar 

  2. Bach, F., Jordan, M.: Learning spectral clustering. Adv. Neural Inf. Process. Syst. 16, 305–312 (2004)

    Google Scholar 

  3. Chung, F.: Spectral graph theory. In: Conference Board of the Mathematical Sciences, pp. 88–95 (1997)

    Google Scholar 

  4. Dasgupta, A., Kosara, R.: Pargnostics: screen-space metrics for parallel coordinates. IEEE Trans. Vis. Comput. Graph. 16(6), 1017–1026 (2010)

    Article  Google Scholar 

  5. Donath, W.E., Hoffman, A.J.: Lower bounds for the partitioning of graphs. IBM J. Res. Dev. 17, 420–425 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dubes, R.C., Jain, A.K.: Algorithms for Clustering Data. Prentice Hall, New York (1988)

    MATH  Google Scholar 

  7. Fiedler, M.: Algebraic connectivity of graphs. Czechoslov. Math. J., 298–305 (1973)

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

  9. Friendly, M., Kwan, E.: Effect ordering for data displays. Comput. Stat. Data Anal. 37, 47–53 (2002)

    Google Scholar 

  10. Fua, Y., Ware, M.O., Rundensteiner, E.A.: Hierarchical parallel coordinates for exploration of large datasets. IEEE Vis., 43–50 (1999)

  11. Fua, Y., Ware, M.O., Rundensteiner, E.A.: Structure-based brushes: a mechanism for navigating hierarchically organized data and information spaces. IEEE Trans. Vis. Comput. Graph. 6(2), 150–159 (2000)

    Article  Google Scholar 

  12. Hagen, L., Kahng, A.: New spectral methods for ratio cut partitioning and clustering. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 11(9), 1074–1085 (1992)

    Article  Google Scholar 

  13. Hauser, H., Ledermann, F., Doleisch, H.: Angular brushing of extended parallel coordinates. In: IEEE Symposium on Information Visualization, pp. 127–131 (2002)

    Google Scholar 

  14. Inselberg, A.: Parallel Coordinates: Visual Multidimensional Geometry and Its Applications. Springer, New York (2009)

    MATH  Google Scholar 

  15. Inselberg, A., Dimsdale, B.: Parallel coordinates: a tool for visualizing multidimensional geometry. IEEE Vis., 361–378 (1990)

  16. Johansson, J., Ljung, P., Jern, M., Cooper, M.: Revealing structure within clustered parallel coordinates displays. In: IEEE Symposium on Information Visualization, pp. 125–132 (2005)

    Chapter  Google Scholar 

  17. Johansson, J., Ljung, P., Cooper, M.: Depth cues and density in temporal parallel coordinates. Comput. Graph. Forum, 35–42 (2007)

  18. Keim, D.: Designing pixel-oriented visualization techniques: theory and applications. IEEE Trans. Vis. Comput. Graph. 6, 59–78 (2000)

    Article  Google Scholar 

  19. Mcdonnell, K.T., Mueller, K.: Illustrative parallel coordinates. Comput. Graph. Forum, 1031–1038 (2008)

  20. Meila, M.: Comparing clusterings by the variation of information. In: Proceedings of the 16th Annual Conference on Computational Learning Theory, pp. 173–187 (2003)

    Google Scholar 

  21. Novotny, M.: Visually effective information visualization of large data. In: Central European Seminar on Computer Graphics (2004)

    Google Scholar 

  22. Novotny, M., Hauser, H.: Outlier-preserving focus+ context visualization in parallel coordinates. IEEE Trans. Vis. Comput. Graph. 12(5), 893–900 (2006)

    Article  Google Scholar 

  23. Peng, W., Ward, M.O., Rundensteiner, E.A.: Clutter reduction in multi-dimensional data visualization using dimension reordering. In: IEEE Symposium on Information Visualization, pp. 89–96 (2004)

    Chapter  Google Scholar 

  24. Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)

    Article  Google Scholar 

  25. The homepage of xmdvtool–multivariate data visualization tool. www.davis.wpi.edu/~xmdv/index.html (2012)

  26. Wegman, E.J., Luo, Q.: High dimensional clustering using parallel coordinates and the grand tour. Comput. Sci. Stat. 28, 352–360 (1997)

    Google Scholar 

  27. Zhou, H., Yuan, X., Qu, H., Cui, W., Chen, B.: Visual clustering in parallel coordinates. Comput. Graph. Forum 27(3), 1047–1054 (2008)

    Article  Google Scholar 

Download references

Acknowledgements

This paper has been supported by NSF grants IIS0916235, CCF0702699, and CNS0959979.

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Correspondence to Xin Zhao.

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Zhao, X., Kaufman, A. Structure revealing techniques based on parallel coordinates plot. Vis Comput 28, 541–551 (2012). https://doi.org/10.1007/s00371-012-0713-0

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