MARGARIDA 1

23-11-2006 1

Carto-Som – Cartogram creation using self-organizing maps

Roberto HENRIQUES1, Fernando BAÇÃO1 and Victor LOBO1,2

2 Portuguese Naval AcademyAlfeite2810-001 ALMADA

1 Institute of Statistics and Information ManagementNew University of LisbonCampus de Campolide1070-312 LisboaPortugal

23-11-2006 2

SummaryCartograms

definition, objectives and examples

Self-organizing maps

Cartogram creation using the SOM

Tests Portugal 2001 populationUSA 2001 population

Conclusion

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Cartogram: definition

Area cartograms are deliberate exaggerations of a map according to some external geography–related parameter that convey information about regions through their spatial dimensions.

DOUGENIK et al. 1985

www.yorku.ca/anderson/ geog1410_2001/images.htm

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Cartograms: objective

USA 2004 presidential elections

Gastner et al. 2004In red - candidate George W. Bush In blue - candidate John F. Kerry

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±

L e g e n d aL e g e n d a

POP2001POP2001495345 - 2112980

2112981 - 4081550

4081551 - 7203904

7203905 - 12520522

12520523 - 21355648

21355649 - 34516624

±

L e g e n d aL e g e n d a

POP2001POP2001495345 - 2112980

2112981 - 4081550

4081551 - 7203904

7203905 - 12520522

12520523 - 21355648

21355649 - 34516624

Cartogram typesContinuous cartogramsNon-continuous cartograms

Dorling cartograms

http://www.geog.qmw.ac.uk/gbhgis/conference/compare.gif 23-11-2006 6

DOUGENIK, CHRISMAN et al. 1985 HOUSE and KOCMOUD 1998 TOBLER 1973

KEIM et al. 2003 HEILMANN, KEIM et al. 2004 Diffusion Cartogram

Some cartogram algorithms

MARGARIDA 2

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Self-Organizing Map

Kohonen, 1982

Neural network particularly suited for data clustering and data visualization

SOM’s basic idea is to map high-dimensional data into one or two dimensions, maintaining the most relevant features of the data patterns

May be used to extract and illustrate the essential structures in a dataset through a map

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Self-Organizing Map

Define the network size, learning and neighbourhood rates

Randomly initiate the unit’s weightsFor n iterations

For each individual from datasetPresent individual to the networkFind the BMUUpdate the BMU weightsUpdate BMU neighbours’ weight

Update learning and neighbourhood rates

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Carto-SOM methodology

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Carto-SOM variants

1. Standard SOM algorithm without “ocean” data

2. Standard SOM algorithm with median density “ocean” data

3. Standard SOM algorithm with differentiated density “ocean” data

4. Variant of SOM (ocean units are not used in the training process)

Ocean data is assumed as the data generated outside the regions' area

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Variant 1 Standard SOM algorithm without “ocean” data

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Variant 2 Standard SOM algorithm with median density “ocean” data

MARGARIDA 3

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Variant 3 Standard SOM algorithm with median density “ocean” data

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Variant 4 Variant of SOM (ocean units are not used in the training process)

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Carto-SOM using Portugal 2001 population

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Carto-SOM using USA 2001 population

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0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

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Original

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Media

Tests on Portugal cartogram

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original density

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Tests on USA cartogram

MARGARIDA 4

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R2 = 0.86

R2 = 0.8919

0

500000

1000000

1500000

2000000

2500000

0 5 10 15 20 25

x 10^6area

popu

latio

n

Original

t1

t2

t3

t4

t5

t6

Linear (t1)

Linear (t2)

Linear (t3)

Linear (t4)

Linear (t5)

Linear (t6)

R2 = 0.8825

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

40000000

0.000 100.000 200.000 300.000 400.000 500.000 600.000 700.000 800.000 900.000 1000.000

x 10^6Area

Popu

latio

n

Original

t1

t2

t3t4

t5

t6

Linear (t1)

Linear (t3)

Linear (t4)Linear (t5)

Linear (t6)

Linear (t2)

Cartogram density

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Discussion

• Carto-SOM is a general method for constructing density-equalizing projections or cartograms

• Presented tests indicate that the cartograms created are good representations of the study variables.

• Promising directions for further research still remain:• Include in the algorithm methods for computing the final cartogram

shape giving it a more realistic boundary instead of using cells.

• Increase of the number of units used in the SOM training

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Agradecimentos: (Arial/18/bold)

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