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British Cartogtraphic Society Annual Conference Talk
1. Talking
With Maps
2010
A Method of Representing Large,
Multidimensional Datasets in a
Single Map.
James Cheshire
UCL Department of Geography and Centre for Advanced Spatial Analysis.
james.cheshire@ucl.ac.uk
spatialanalysis.co.uk
@spatialanalysis
2. Talking
With Maps
2010 Outline
•Context.
•Mixing red, green and blue (RGB)
values for maps.
•Reducing the number of variables
(dimensions) using MDS.
•Applications in geodemographics.
•Future Work.
3. Talking
With Maps
2010 Context
•Interested in large demographic
datasets (such as the electoral roll
and census).
•My research requires extensive use of
distance matrices. Can be up to
10500 x 10500.
•How best to map this data?
4. Talking
With Maps
2010 Context
•Clustering.
•Reducing the number of variables
through:
• Principle components analysis.
• Multidimensional scaling (also known as
principle coordinates analysis).
•Colour selection.
• Many transitions are not discrete.
• RGB offers three continuous axes.
6. Talking
With Maps
2010 Red, Green and Blue (RGB)
The three coordinates in RGB space
can be produced by re-scaling the
values of three variables to between 0 en.wikipedia.org/wiki/RGB_color_model
and 255.
7. Talking
With Maps
2010 For Example: Election Results
Labour= Red.
Other (incl. Lib Dems.)= Green.
Conservative= Blue.
20% Lab + 30% Other + 50% Cons
51+76 + 128 = Final Colour
60% Lab + 10% Other + 30% Cons
153+25 + 77 = Final Colour
Wards with similar voting behaviour should
be given a similar colour.
8. Talking
With Maps
2010
Boundary Data Crown Copyright Ordnance Survey 2010
10. Talking
With Maps
2010 Multidimensional Scaling (MDS)
•We will treat it here as a “black box”
method of reducing the dimensionality
of a dataset to a set of coordinates in
n-dimensional space.
• n is usually 2 or 3.
• MDS places the points in euclidean
space.
11. Talking
With Maps MDS of the Distances between 20 European Cities
2010
There are 20 cities. Thus creating a 20 x 20
distance matrix. MDS simplifies this
matrix into 20 XY coordinate pairs.
12. Talking
With Maps
2010 Converting MDS Values to RGB
http://www.let.rug.nl/~kleiweg/
13. Talking
With Maps
2010 Geographic Distances
3109 by 3109 distance matrix
reduced to 3109 by 3 using MDS.
14. Talking
With Maps
2010 Surnames
In this case a 10500 Geographic distance
by 10500 matrix has substituted for a
been reduced to measure of “surname
10500 by 3. distance”.
16. Talking
With Maps
2010 Mapping the 41 OAC Variables
Produced by Daniel Lewis (UCL)
17. Talking
With Maps
2010 Implementation
•MDS can be undertaken with many
statistics packages: R, STATA, SAS,
SPSS (i think).
•Maps produced in ArcGIS 9.x using
custom VBA script.
• Enabled RGB values to be stored in
attribute table.
18. Talking
With Maps
2010 Strengths
•Offers a continuous colour transition
linked to the data.
•Most effective with spatially
autocorrelated variables.
•Good with small spatial units.
•Although the methods behind them
may be a little complex, the maps
themselves are intuitive.
19. Talking
With Maps
2010 Outliers
Both maps have to
occupy the same area
in RGB space. For the
above map much of
this space is empty
thanks to the
Hawaiian Islands.
20. Talking
With Maps
2010 Colour Perception
RGB CieLab
“Perceptual
uniformity”
Produced with Aidan
Slingsby (City Uni.)
21. Talking
With Maps
2010 Summary
•Combing MDS with the RGB colour
model offers a useful tool to visualise
large, multivariate datasets.
•It isn’t perfect.
•But a good alternative to other
approaches, especially in the context
of geodemographics.
22. Talking
With Maps
2010 Thanks to:
Scott Tansley (ESRI (UK)).
Aidan Slingsby (City University).
Daniel Lewis (UCL).
Paul Longley (UCL).
Pablo Mateos (UCL).
My PhD is co-funded by the ESRC
and ESRI (UK).
Slides and high-res. maps available from
spatialanalysis.co.uk,
or email me: james.cheshire@ucl.ac.uk.
