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# British Cartogtraphic Society Annual Conference Talk

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### British Cartogtraphic Society Annual Conference Talk

1. 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. 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. 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. 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.
5. 5. Talking With Maps 2010 Red, Green and Blue (RGB) Green Red Blue
6. 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. 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. 8. Talking With Maps 2010 Boundary Data Crown Copyright Ordnance Survey 2010
9. 9. Talking With Maps 2010
10. 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. 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. 12. Talking With Maps 2010 Converting MDS Values to RGB http://www.let.rug.nl/~kleiweg/
13. 13. Talking With Maps 2010 Geographic Distances 3109 by 3109 distance matrix reduced to 3109 by 3 using MDS.
14. 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”.
15. 15. Talking With Maps 2010 Clustering MDS
16. 16. Talking With Maps 2010 Mapping the 41 OAC Variables Produced by Daniel Lewis (UCL)
17. 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. 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. 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. 20. Talking With Maps 2010 Colour Perception RGB CieLab “Perceptual uniformity” Produced with Aidan Slingsby (City Uni.)
21. 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. 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.