The document discusses techniques for enhancing parallel coordinate visualizations using curves. It describes how curving lines can help follow objects across axis intersections and resolve clutter. The techniques are best for tracking outliers or small, selected subsets. Spreading techniques are also described to differentiate objects that share values, though they work best on categorical data and with focus+context. Future work is proposed to investigate when curves are most useful and test user understanding further.

1. Using Curves to Enhance Parallel
Coordinate Visualisations
• Martin Graham & Jessie Kennedy
• Napier University, Edinburgh

2. Overview
• Background
• Using Curves
• Spreading and Focus+Context
• Conclusions
• Future Work

3. Background
• Parallel Coordinates visualise multi-
dimensional data across a set of parallel
axes – 1 axis per data dimension
(Inselberg & Dimsdale, 1990)
• Objects represented as poly-lines across the axes,
intersecting the axes at the appropriate value
X Y Z R
1 1 1 1 (X, Y, Z, R)
2 2 2 2
(1.5, 2, 3, 3.2)
3 3 3 3
4 4 4 4
5 5 5 5

4. Background
• Various refinements made to the basic
technique by IV researchers
• General Interactivity
• Selecting, filtering, re-arranging axes
• Angular Brushing – Hauser et al
• Pick out polylines with segments of certain Ѳ –
helps identify trends between attributes
• Hierarchical clustering - Fua et al
• Stats-based distortions – G. & N. Andrienko

5. Background
• Exploring Parallel Coordinates as a
technique to visualise and filter individual
and company CV data
• Quantitative data - salary
• Categorical data
• Ordinal – qualification i.e. Masters > Bachelors
• Nominal – sector i.e. Legal, IT, Engineering

6. Background
Q. How do we follow lines after crossing points?

7. Using Curves
Visual properties of curves can aid us

8. Using Curves
Can act in conjunction with colouring and brushing

9. Using Curves
• Curved paths tend to resolve individually
• Gives better picture of dataset population
• Bad for screen clutter with many curves

10. Using Curves
• We can use curves because in our data
sets the lines act as connectors only
• In Inselberg’s original work, the intersections
of polylines between axes carried information
about the higher order object they formed
• But with heterogeneous dimensions, the
positions of inter-axial line crossings don’t
mean anything

11. Spreading & focus+context
• Curves can help differentiate objects that
share an attribute value, especially if they
are dissimilar in other values
• But for categorical data especially, paths can
form a number of dense knots
• Can we use screen space more effectively to
spread these paths out over a distance?

12. Spreading & focus+context
Spreading out points on categorical axes

13. Spreading & focus+context
Can also be applied to traditional poly-line representations

14. Spreading & focus+context
• Bounding boxes around categories keep
objects visually grouped
• A curve’s position of intersection in the
bounding box is decided by averaging its
vertical coordinates in adjacent axes
• Impact can be increased if selected
values are expanded – i.e. focus+context

15. Initial User Testing
• Simple observation of six representative
users using system
• Users could track curves across axes for
small sets, especially outliers
• Users questioned need to draw all objects
as curves
• Users mostly liked parallel coordinates as
a whole

16. Conclusions
• Developed techniques that enable objects
to be followed through ‘crossing-points’ in
parallel coordinate visualisations
• Techniques work best when
• …tracking outliers – often the interesting objects
• …used on small sets of user selected objects
• …used in conjunction with brushing techniques
that use colour

17. Future work
• Investigate situations when it is best to
use curved representations
• Curved paths for brushed and/or selected
items only to reduce screen clutter?
• Further investigation of focus+context
effect
• Link the focus effect across axes so selected
items get more space on every axis, not just
in the axis of selection

18. Future work
• General issues
• Implementing undo functions for selections
• What if one individual fits multiple values on
an axis?
• Further User Testing

19. Acknowledgements
• OPAL – EU Project IST-2001-33288
• http://www.dcs.napier.ac.uk/~marting