On National Teacher Day, meet the 2024-25 Kenan Fellows
Enhancing Parallel Coordinates with Curves
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
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?
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
