Enabling Automatic Clutter Reduction in Parallel Coordinate Plots

Geoff Ellis
Lancaster University, UK.
http://www.comp.lancs.ac.uk/computing/users/ellisg2/

  

Alan Dix
Lancaster University, UK
http://www.hcibook.com/alan/

Paper at InfoVis2006, 29 Oct - 3 Nov 2006, Balitomore, Maryland, USA.

Abstract

We have previously shown that random sampling is an effective clutter reduction technique and that a sampling lens can facilitate focus+context viewing of particular regions. This demands an efficient method of estimating the overlap or occlusion of large numbers of intersecting lines in order to automatically adjust the sampling rate within the lens. This paper proposes several ways for measuring occlusion in parallel coordinate plots. An empirical study into the accuracy and efficiency of the occlusion measures show that a probabilistic approach combined with a 'binning' technique is very fast and indeed approaches the more expensive 'true' complete measurement.

Keywords: Sampling, random sampling, lens, clutter, occlusion, density reduction, overplotting, information visualisation

References

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  5. Ellis, G.P. and Dix, A. Density control through random sampling : an architectural perspective. Proceedings of Information Visualisation 2002, London, July 2002, IEEE, 82-90
  6. Ellis, G.P., Bertini, E. and Dix, A. The Sampling Lens:Making Sense of Saturated Visualisations. CHI '05 Extended Abstracts on Human Factors in Computing Systems, Portland, USA, 2005, ACM Press, 1351-1354
  7. Ellis G P. and Dix A. the plot, the clutter, the sampling and its lens: occlusion measures for automatic clutter reduction. In proceedings of International Working Conference on Advanced Visual Interfaces (AVI'06), Italy, May 2006, ACM Press, 266-269
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Full reference:
G. Ellis and A. Dix (2006). Enabling Automatic Clutter Reduction in Parallel Coordinate Plots.
IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, Sept.-Oct. 2006, IEEE, pp. 717-724.
http://www.hcibook.com/alan/papers/
InfoVis06-NoClutter/
more:
related work on visualisation at: http://www.hcibook.com/alan/topics/vis/
and about uses of randomness at: http://www.hcibook.com/alan/topics/random/
related papers
G. Ellis and A. Dix (2006).
The plot, the clutter, the sampling and its lens: occlusion measures for automatic clutter reduction. Proceedings of AVI2006. ACM Press. pp. 266-269 abstract and links
G. Ellis, E. Bertini and A. Dix (2005).
The Sampling Lens: making sense of saturated visualisation Proceedings of CHI'2005, Vol. 2, ACM Press. pp. 1351-1354. abstract and links
A. Dix and G. Ellis (2002).
By chance - enhancing interaction with large data sets through statistical sampling. Proceedings of Advanced Visual Interfaces - AVI2002, Trento, Italy, ACM Press. pp.167-176.
abstract, contents and references

Random Algorithm

E( M1 ) = M (1-p)M-1
E( Mn ) = M - E(M1) = M ( 1 - (1-p)M-1)
E( S0 ) = S (1-p)M
E( S1 ) = S * M (p) (1-p)M-1 = M (1-p)M-1
E( Sn ) = S - (E(S0) + E(S1))

overplotted% = 100 * (1 - ((1-p)M + M/S (1-p)M-1)) / (1 - (1-p)M)

Figures (selection)


Figure 2. Lines within the lens at a 10% lens sampling rate


Figure 8. Line overlap proportion


Figure 10. Exp1, 2 and 3 normalised against raster values

http://www.hcibook.com/alan/papers/infovis2006-lens/

Alan Dix 2/6/2006