Post on 20-Aug-2020
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
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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
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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
0.0006
0.0007
0.0008
0.0009
Aveiro Beja
Braga
Bragan
ça
Castel
o Branc
o
Coimbra
Évora
Faro
Guarda
Leiria
Lisbo
a
Portale
grePort
o
Santar
ém
Setúba
l
Viana d
o Caste
lo
Vila R
eal
Viseu
Portuguese region
Pop
ulat
ion
dens
ity
Original
t1
t2
t3
t4
t5
t6
Media
Tests on Portugal cartogram
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0,00000
0,00005
0,00010
0,00015
0,00020
0,00025
0,00030
0,00035
0,00040
0,00045
0,00050
Flor
ida
Loui
sian
a
Geo
rgia
Mis
siss
ippi
Alab
ama
Sout
h C
arol
ina
Arka
nsas
Texa
s
Nor
th C
arol
ina
Tenn
esse
e
New
Mex
ico
Okl
ahom
a
Ariz
ona
Kent
ucky
Virg
inia
Mar
ylan
d
Kans
as
Mis
sour
i
Wes
t Virg
inia
Col
orad
o
New
Jer
sey
Indi
ana
Ohi
o
Nev
ada
Cal
iforn
ia
Uta
h
Rho
de Is
land
Con
nect
icut
Penn
sylv
ania
Illino
is
Mas
sach
uset
ts
Neb
rask
a
Iow
a
Wyo
min
g
New
Yor
k
Verm
ont
New
Ham
pshi
re
Mic
higa
n
Sout
h D
akot
a
Ore
gon
Wis
cons
in
Mic
higa
n
Mai
ne
Was
hing
ton
Idah
o
Mon
tana
Nor
th D
akot
a
Min
neso
ta
States
original density
t1
t2
t3
t4
t5
t6
Average
Pop
ulat
ion
dens
ity
Tests on USA cartogram
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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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