Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Clustering of Population Pyramids
Simona Korenjak-Černe1 Nataša Kejžar2
Vladimir Batagelj3
University of Ljubljana, Slovenia
1 Faculty of Economics
simona.cerne@ef.uni-lj.si
2 Faculty of Social Sciences
natasa.kejzar@fdv.uni-lj.si
3 Faculty
of Mathematics and Physics
vladimir.batagelj@fmf.uni-lj.si
COMPSTAT 2008,
Porto, Portugal, August 24-29, 2008
Conclusion
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Outline
1
Introduction
What is population pyramid
Main pyramids’ shapes
Demographic Transition Model
Conclusion
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Outline
Introduction
What is population pyramid
Main pyramids’ shapes
Demographic Transition Model
2 Clustering of the world countries
Data: Population pyramids of the world countries
Analyses: Hierarchical clustering of the world countries
Results
1
Clustering of the 215 world countries from the year 1996
Clustering of the 222 world countries from the year 2001
Clustering of the 222 world countries from the year 2006
Movements among four main clusters for the years 1996, 2001 and
2006
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Outline
Introduction
What is population pyramid
Main pyramids’ shapes
Demographic Transition Model
2 Clustering of the world countries
Data: Population pyramids of the world countries
Analyses: Hierarchical clustering of the world countries
Results
1
Clustering of the 215 world countries from the year 1996
Clustering of the 222 world countries from the year 2001
Clustering of the 222 world countries from the year 2006
Movements among four main clusters for the years 1996, 2001 and
2006
3
Clustering of the 3111 mainland US counties
Data: Population pyramids of the US counties
Analyses: Hierarchical clustering with relational constraint of the
3111 mainland US counties
Results
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Outline
Introduction
What is population pyramid
Main pyramids’ shapes
Demographic Transition Model
2 Clustering of the world countries
Data: Population pyramids of the world countries
Analyses: Hierarchical clustering of the world countries
Results
1
Clustering of the 215 world countries from the year 1996
Clustering of the 222 world countries from the year 2001
Clustering of the 222 world countries from the year 2006
Movements among four main clusters for the years 1996, 2001 and
2006
Clustering of the 3111 mainland US counties
Data: Population pyramids of the US counties
Analyses: Hierarchical clustering with relational constraint of the
3111 mainland US counties
Results
4 Conclusion
3
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Outline
Introduction
What is population pyramid
Main pyramids’ shapes
Demographic Transition Model
2 Clustering of the world countries
Data: Population pyramids of the world countries
Analyses: Hierarchical clustering of the world countries
Results
1
Clustering of the 215 world countries from the year 1996
Clustering of the 222 world countries from the year 2001
Clustering of the 222 world countries from the year 2006
Movements among four main clusters for the years 1996, 2001 and
2006
Clustering of the 3111 mainland US counties
Data: Population pyramids of the US counties
Analyses: Hierarchical clustering with relational constraint of the
3111 mainland US counties
Results
4 Conclusion
5 References
3
References
Introduction
Clustering of the world countries
0
C4K"#3
>+3='
Clustering of the 3111 mainland
US
counties
L
O
P
;.
>'"9+
A+:#
>'"3'4
!#*#"
<"'4M%89'
>'*#3'
@'*'8'
E&'4'
J%6'
Conclusion
>'*%=
C(3':
Q'&%K
R'8S#"
C4'
References
N'('
D7'
@#:'
@%4'
2'3*4*!#,-2%5*6'&'7,37,$#*8)*&#,3)&(%*8)9%$%*:*;%&,3)"&'*3%<'7,%3*=3%>'$)"7,$)?*6'&'7,37,$#*8)*&#,3)&(%
8)9%$%* :* @'3%-,#3),* 8)* A=3)$&%* &#,3)&(%* 8)9%$%* 4* 3'&'.4-5) #6) 47%) 8&4%-'#-) 9) :%&4-(") ;#<,"(4'#&
=%+'.4%->)3'&'.4-5)#6)47%)8&4%-'#-)9)?@A'&'.4-(4'$%)8&4%-&(")?66('-.)B'-%24#-(4%
What is population pyramid
is a very popular presentation of
the age-sex distribution of the
human population of a particular
region
It gives picture of a population’s
age-sex structure, and can also be
used for displaying historical and
future trends.
The shape of the pyramid shows
many demographic, social, and
political characteristics of the
time and the region.
$,)/-0"1'(0%+$%+$)(1)(!-2+'(",%'(!-2+'34$-!"2+-!
'$%145+678+9):)./),+;<<=
!"!#$%&'"()*+),'-./+.%0)%1.)10"#!2)%(3)2.45)67)3.8.9*.0):;;<
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Main pyramids’ shapes
Generally, three main pyramids’ shapes are considered: expansive,
constrictive, and stationary.
EXPANSIVE
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Main pyramids’ shapes
Generally, three main pyramids’ shapes are considered: expansive,
constrictive, and stationary.
EXPANSIVE
CONSTRICTIVE
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Main pyramids’ shapes
Generally, three main pyramids’ shapes are considered: expansive,
constrictive, and stationary.
EXPANSIVE
CONSTRICTIVE
STATIONARY
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Demographic Transition Model
Since the biggest influence on the pyramid’s shape have fertility
and mortality, the explanation of the pyramids’ shapes is often
related to the "Demographic Transition Model" (DTM) that
describes the population changes over time (Warren Thompson,
1929).
High birth rate;
high
death
rate; short life
expectancy
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Demographic Transition Model
Since the biggest influence on the pyramid’s shape have fertility
and mortality, the explanation of the pyramids’ shapes is often
related to the "Demographic Transition Model" (DTM) that
describes the population changes over time (Warren Thompson,
1929).
High birth rate;
high
death
rate; short life
expectancy
High birth rate;
fall in death rate;
slightly longer life
expectancy
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Demographic Transition Model
Since the biggest influence on the pyramid’s shape have fertility
and mortality, the explanation of the pyramids’ shapes is often
related to the "Demographic Transition Model" (DTM) that
describes the population changes over time (Warren Thompson,
1929).
High birth rate;
high
death
rate; short life
expectancy
High birth rate;
fall in death rate;
slightly longer life
expectancy
Declining
birth
rate; low death
rate; longer life
expectancy
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Demographic Transition Model
Since the biggest influence on the pyramid’s shape have fertility
and mortality, the explanation of the pyramids’ shapes is often
related to the "Demographic Transition Model" (DTM) that
describes the population changes over time (Warren Thompson,
1929).
High birth rate;
high
death
rate; short life
expectancy
High birth rate;
fall in death rate;
slightly longer life
expectancy
Declining
birth
rate; low death
rate; longer life
expectancy
Low birth rate;
low death rate;
longer
life
expectancy
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
Data: Population pyramids of the world countries
International Data Base (IDB)
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the world countries
International Data Base (IDB)
34 variables: 17 variables for 5-years age groups for men, and
17 variables for 5-years age groups for women
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the world countries
International Data Base (IDB)
34 variables: 17 variables for 5-years age groups for men, and
17 variables for 5-years age groups for women
Normalized
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the world countries
International Data Base (IDB)
34 variables: 17 variables for 5-years age groups for men, and
17 variables for 5-years age groups for women
Normalized
Euclidean distance between corresponding vectors
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Analyses: Hierarchical clustering of the world countries
Ward’s hierarchical clustering method, implemented in a package
’cluster’ in the statistical environment R.
Observing the shapes of the clusters in the hierarchies in years
from 1996 to 2006
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Analyses: Hierarchical clustering of the world countries
Ward’s hierarchical clustering method, implemented in a package
’cluster’ in the statistical environment R.
Observing the shapes of the clusters in the hierarchies in years
from 1996 to 2006
Observing how stable are the main clusters over time
Afghanistan
Ethiopia
Gambia, The
Guinea
Eritrea
Sudan
Angola
Nigeria
Mozambique
Sierra Leone
Comoros
Guinea−Bissau
Cote d'Ivoire
Djibouti
Belize
Ghana
Pakistan
Central African Republic
Equatorial Guinea
Gabon
Cameroon
Senegal
Guatemala
Laos
Haiti
Somalia
Cambodia
Tajikistan
Cape Verde
Bhutan
Paraguay
Bolivia
Namibia
Nepal
Liberia
El Salvador
Lesotho
Papua New Guinea
Vanuatu
East Timor
Kiribati
Nauru
Botswana
Zimbabwe
Marshall Islands
Micronesia, Federated States of
Honduras
Swaziland
Nicaragua
Kenya
Rwanda
Iraq
Syria
Jordan
Samoa
Tonga
Benin
Tanzania
Zambia
Togo
Solomon Islands
Burkina Faso
Mali
Sao Tome and Principe
Yemen
Uganda
Burundi
Western Sahara
Congo (Kinshasa)
Malawi
Congo (Brazzaville)
Madagascar
Mauritania
Niger
Maldives
Chad
Mayotte
Algeria
Libya
Ecuador
Morocco
Philippines
Jamaica
Mongolia
Vietnam
Kyrgyzstan
Turkmenistan
Uzbekistan
Bangladesh
Iran
Grenada
Oman
Saudi Arabia
Azerbaijan
Tuvalu
Dominica
Saint Kitts and Nevis
Bahamas, The
Colombia
New Caledonia
Costa Rica
French Polynesia
Panama
Dominican Republic
Peru
India
Venezuela
Egypt
Mexico
Malaysia
Fiji
South Africa
Brazil
Turkey
Indonesia
Burma
Tunisia
Guyana
Saint Lucia
Saint Vincent and the Grenadines
Seychelles
Suriname
Lebanon
Montserrat
Albania
Chile
Trinidad and Tobago
Argentina
Israel
Armenia
Kazakhstan
Anguilla
China
Mauritius
Sri Lanka
Thailand
Barbados
Korea, South
Taiwan
Cuba
Saint Helena
Korea, North
Netherlands Antilles
Saint Pierre and Miquelon
Antigua and Barbuda
Brunei
Turks and Caicos Islands
Greenland
Palau
Virgin Islands, British
Macau S.A.R.
Bahrain
Kuwait
Qatar
United Arab Emirates
Andorra
Hong Kong S.A.R.
Singapore
Aruba
Cayman Islands
Australia
Canada
United States
Bermuda
Liechtenstein
Austria
Guernsey
Italy
San Marino
Germany
Jersey
Luxembourg
Switzerland
Netherlands
Denmark
Norway
United Kingdom
Isle of Man
Sweden
Monaco
Belarus
Russia
Georgia
Lithuania
Estonia
Latvia
Ukraine
Bosnia and Herzegovina
Belgium
France
Finland
Gibraltar
Croatia
Slovenia
Bulgaria
Japan
Czech Republic
Hungary
Greece
Portugal
Spain
Cyprus
Iceland
New Zealand
Ireland
Uruguay
Faroe Islands
Macedonia
Montenegro
Moldova
Malta
Poland
Slovakia
Romania
Serbia
0.0
0
0
20
20
0.10
0.06
0.02
0.00
0.04
0.08
Male
0.10
0.06
0.02
0.00
0.04
Figure: Clusters of the 215 countries and main pyramids’ shapes for the
year 1996
d2
agnes (*, "ward")
60
60
Female
50
50
Female
70
70
80
80
0.04
40
40
80
80
0.00
30
30
70
70
0.02
20
60
60
Male
0.06
10
50
50
0.10
20
0
40
40
0
10
0.6
20
30
40
50
60
70
80
0.8
Male
Male
0.10
0.06
0.02
0.00
0.04
0.08
10
30
30
0.4
Height
Clustering of the world countries
0
10
10
0.2
Introduction
Dendrogram of agnes(x = d2, method = "ward")
Clustering of the 3111 mainland US counties
Conclusion
Male
0.10
0.06
0.02
0.00
References
Female
0.08
Female
Female
0.08
0.04
0.08
Clustering of the world countries
Male
Conclusion
Female
70
60
50
40
30
20
10
0
10
20
30
40
50
60
70
80
Female
80
Male
Clustering of the 3111 mainland US counties
0
Introduction
0.10
0.06
0.02
0.00
0.04
0.08
0.10
0.06
0.02
0.00
0.04
0.08
Figure: Pyramids’s shapes of the most different sub-clusters
References
Afghanistan
Gambia, The
Guinea
Angola
Ethiopia
Madagascar
Eritrea
Sierra Leone
Maldives
West Bank
Comoros
Mozambique
Djibouti
Liberia
Mayotte
Somalia
Oman
Benin
Tanzania
Zambia
Burkina Faso
Congo (Kinshasa)
Burundi
Malawi
Sao Tome and Principe
Mali
Yemen
Chad
Congo (Brazzaville)
Mauritania
Western Sahara
Niger
Gaza Strip
Uganda
Belize
Honduras
Ghana
Namibia
Nepal
Pakistan
Samoa
Cote d'Ivoire
Iraq
Kenya
Rwanda
Marshall Islands
Cameroon
Senegal
Laos
Nigeria
Guinea−Bissau
Solomon Islands
Sudan
Central African Republic
Equatorial Guinea
Gabon
Guatemala
Haiti
Togo
Swaziland
Albania
Saint Kitts and Nevis
Azerbaijan
Dominica
Tuvalu
Armenia
Kazakhstan
Trinidad and Tobago
Bahamas, The
Colombia
Costa Rica
Indonesia
Panama
New Caledonia
Dominican Republic
India
Egypt
Malaysia
Mexico
Peru
Venezuela
Fiji
South Africa
Brazil
Turkey
French Polynesia
Burma
Tunisia
Guyana
Saint Vincent and the Grenadines
Saint Lucia
Suriname
Seychelles
Lebanon
Montserrat
Kuwait
Saudi Arabia
Algeria
Mongolia
Vietnam
Kyrgyzstan
Uzbekistan
Iran
Bangladesh
Grenada
Jordan
Libya
American Samoa
Bhutan
Paraguay
Kiribati
Papua New Guinea
Bolivia
Lesotho
El Salvador
Philippines
Turkmenistan
Ecuador
Morocco
Vanuatu
Jamaica
Botswana
Nicaragua
Syria
Tajikistan
Zimbabwe
Cambodia
Tonga
Cape Verde
East Timor
Nauru
Micronesia, Federated States of
Anguilla
China
Chile
Mauritius
Sri Lanka
Thailand
Barbados
Korea, South
Taiwan
Virgin Islands, British
Cuba
Saint Helena
Argentina
Israel
Cyprus
Iceland
Ireland
Puerto Rico
Macedonia
New Zealand
Uruguay
Faroe Islands
Korea, North
Netherlands Antilles
Saint Pierre and Miquelon
Virgin Islands
Antigua and Barbuda
Brunei
Guam
Turks and Caicos Islands
Bahrain
Palau
Greenland
Qatar
Northern Mariana Islands
United Arab Emirates
Andorra
Hong Kong S.A.R.
Singapore
Macau S.A.R.
Aruba
Cayman Islands
Bermuda
Liechtenstein
Australia
United States
Canada
Belarus
Russia
Estonia
Latvia
Ukraine
Bosnia and Herzegovina
Georgia
Lithuania
Malta
Serbia
Poland
Slovakia
Romania
Moldova
Montenegro
Austria
Switzerland
Belgium
Luxembourg
Netherlands
Jersey
Germany
Italy
San Marino
Denmark
Sweden
Guernsey
Isle of Man
France
United Kingdom
Norway
Finland
Gibraltar
Monaco
Bulgaria
Czech Republic
Hungary
Croatia
Slovenia
Greece
Spain
Portugal
Japan
0.0
0
0
10
10
20
0.10
0.06
0.02
0.00
0.04
70
60
80
70
0.04
0.08
80
Male
0.10
0.06
0.02
0.00
0.04
Figure: Clusters of the 222 countries and main pyramids’ shapes for the
year 2001
d2
agnes (*, "ward")
80
60
50
0.00
70
50
40
80
Female
0.02
60
40
30
70
Male
0.06
50
30
20
60
0.10
40
20
10
50
Female
0
0
10
10
20
20
30
30
40
40
50
50
0.6
60
60
70
70
80
80
Male
30
10
0
40
0.4
Height
0.8
1.0
Clustering of the world countries
0.08
20
0
30
0.2
Introduction
Clustering of the 3111 mainland US counties
Female
Male
0.10
0.06
0.10 Female
0.06
0.02
0.00
0.04
Conclusion
Male
0.02
0.00
0.04
Male
0.10
0.06
0.02
0.00
References
Dendrogram of agnes(x = d2, method = "ward")
Female
0.08
Female
0.08
0.08
0.04
0.08
Clustering of the world countries
Female
Male
0.06
0.02
0.00
0.04
0.08
Female
70
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
60
50
40
30
20
10
0
0.10
Conclusion
80
Male
80
Female
80
Male
Clustering of the 3111 mainland US counties
0
Introduction
0.10
0.06
0.02
0.00
0.04
0.08
0.10
0.06
0.02
0.00
0.04
0.08
Figure: Pyramids’s shapes of the sub-clusters with the biggest chaining
efect
References
Afghanistan
Angola
Gambia, The
Madagascar
Guinea
Mauritania
Western Sahara
Sierra Leone
Djibouti
Liberia
Comoros
Mozambique
Maldives
West Bank
Mayotte
Somalia
Oman
Benin
Tanzania
Ethiopia
Eritrea
Central African Republic
Haiti
Togo
Guatemala
Cameroon
Laos
Equatorial Guinea
Gabon
Guinea−Bissau
Nigeria
Senegal
Cote d'Ivoire
Iraq
Solomon Islands
Sudan
Kenya
Rwanda
Burkina Faso
Burundi
Congo (Brazzaville)
Congo (Kinshasa)
Gaza Strip
Sao Tome and Principe
Niger
Chad
Mali
Uganda
Malawi
Yemen
Zambia
Bangladesh
Marshall Islands
Belize
Honduras
Ghana
Nepal
Pakistan
Samoa
Bhutan
Paraguay
Kiribati
Papua New Guinea
Bolivia
Jamaica
El Salvador
Philippines
Turkmenistan
Botswana
Lesotho
Namibia
Cambodia
Tonga
Nicaragua
Tajikistan
Syria
Cape Verde
East Timor
Micronesia, Federated States of
Nauru
Swaziland
Zimbabwe
Grenada
Jordan
Libya
Saudi Arabia
Algeria
Mongolia
Iran
Azerbaijan
Vietnam
Brazil
Turkey
French Polynesia
Burma
Guyana
Saint Vincent and the Grenadines
Tunisia
Brunei
Saint Lucia
Suriname
Seychelles
Lebanon
Montserrat
American Samoa
Turks and Caicos Islands
Bahamas, The
Costa Rica
New Caledonia
Guam
Colombia
Indonesia
Panama
Mexico
Peru
Dominican Republic
Malaysia
Venezuela
Egypt
India
Fiji
Ecuador
Morocco
Vanuatu
Kyrgyzstan
Uzbekistan
South Africa
Tuvalu
Northern Mariana Islands
Kuwait
United Arab Emirates
Albania
Saint Kitts and Nevis
Dominica
Argentina
Israel
Anguilla
Virgin Islands, British
Chile
Sri Lanka
Mauritius
Thailand
Armenia
Kazakhstan
Trinidad and Tobago
Antigua and Barbuda
Palau
Bahrain
Greenland
Qatar
Aruba
Bermuda
Cayman Islands
Virgin Islands
Australia
United States
Cyprus
Iceland
Puerto Rico
Macedonia
Faroe Islands
Ireland
New Zealand
Uruguay
Barbados
Korea, South
Taiwan
Saint Helena
China
Cuba
Korea, North
Netherlands Antilles
Saint Pierre and Miquelon
Hong Kong S.A.R.
Singapore
Macau S.A.R.
Andorra
Jersey
Austria
Switzerland
Guernsey
Germany
Italy
San Marino
Japan
Monaco
Belgium
United Kingdom
France
Isle of Man
Denmark
Norway
Finland
Gibraltar
Sweden
Bosnia and Herzegovina
Canada
Luxembourg
Netherlands
Liechtenstein
Belarus
Russia
Ukraine
Georgia
Estonia
Latvia
Lithuania
Moldova
Montenegro
Poland
Slovakia
Bulgaria
Czech Republic
Hungary
Croatia
Slovenia
Malta
Serbia
Romania
Greece
Spain
Portugal
0.0
0
0.10
0.06
0.02
0.00
0.04
0.08
0.10
0.06
0.02
0.00
0.04
50
60
70
80
Male
40
0
0.04
80
0.00
70
80
70
60
80
0.02
60
50
70
0.06
50
40
60
50
40
0.10
40
30
30
Female
30
20
20
Male
30
20
10
10
10
20
0
30
10
40
20
50
30
0.6
60
40
70
50
80
60
70
80
0.8
Male
20
10
0
0
0.4
Height
1.0
Clustering of the world countries
10
0
0.2
Introduction
Dendrogram of agnes(x = d2, method = "ward")
Clustering of the 3111 mainland US counties
Female
Male
0.10
0.10
0.06
0.02
0.00
0.04
Conclusion
Male
0.06
0.02
0.00
0.04
0.10
0.06
References
Female
Female
0.08
Female
0.08
Male
Female
0.08
0.08
0.02
0.00
Figure: Clusters of the 222 countries and main pyramids’ shapes for the
d2
year 2006
agnes (*, "ward")
0.04
0.08
0.02
0.00
0.04
0.08
80
70
50
40
30
20
10
70
50
40
0.08
0.02
0.00
0.04
0.08
80
Female
40
50
60
70
80
60
50
B
0.08
0.06
Male
40
0.04
0.10
Female
30
0.00
Female
30
0.04
20
0.02
0.08
20
0.00
10
0.06
0.04
10
0.02
70
80
70
50
40
30
0.10
0.00
0
0.06
Male
20
0.08
0.10
Female
10
A
0.04
0.02
60
70
50
0.08
0.06
Male
40
0.04
0.10
Female
30
0.00
0
0.00
0.08
20
0.02
60
70
60
50
40
30
20
0.02
0.04
10
0.06
Male
10
0.06
0.00
0
0.10
Female
0
0.10
0.02
60
70
50
40
30
20
10
0.08
80
Male
0.04
0.06
Male
0
0.00
0
Female
60
70
60
50
40
30
20
0.02
0.10
80
Male
10
0.06
60
70
50
40
30
20
10
0
0.06
80
Female
0
0.10
2006
0.10
30
0.08
80
Male
0.04
20
0.00
Female
10
0.02
Conclusion
Male
80
0.06
Female
60
70
50
40
30
20
10
0
0.10
2001
Male
60
70
60
50
40
30
20
0
10
1996
Female
80
Male
80
Female
80
Male
Clustering of the 3111 mainland US counties
0
Clustering of the world countries
0
Introduction
0.10
0.06
0.02
0.00
0.04
C
0.08
0.10
0.06
0.02
0.00
0.04
0.08
D
Figure: Pyramids’s shapes of four main clusters of the countries for the
years 1996, 2001 and 2006
References
Introduction
Clustering of the world countries
A
1996
2001
B
C
D
77
57 20
47
31
5 25 1
60
1
46
7
53
60
60
26
2006
Clustering of the 3111 mainland US counties
86
72
36
5 31
40
6
45
References
54
8
45
Conclusion
46
46
Figure: Movements presented with the number of countries among four
main clusters for the years 1996, 2001 and 2006
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Data: Population pyramids of the US counties
3111 mainland US counties in the year 2000
Conclusion
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the US counties
3111 mainland US counties in the year 2000
36 variables: 18 variables for 5-years age groups for men, and
18 variables for 5-years age groups for women
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the US counties
3111 mainland US counties in the year 2000
36 variables: 18 variables for 5-years age groups for men, and
18 variables for 5-years age groups for women
Normalized
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Data: Population pyramids of the US counties
3111 mainland US counties in the year 2000
36 variables: 18 variables for 5-years age groups for men, and
18 variables for 5-years age groups for women
Normalized
Euclidean distance between corresponding vectors
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Analyses: Hierarchical clustering with relational constraint
of the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented in
Pajek (Batagelj and Mrvar), the program for analysis and
visualization of large networks.
The relational constraint is based on neighboring counties
(Ferligoj, Batagelj, 1983).
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Analyses: Hierarchical clustering with relational constraint
of the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented in
Pajek (Batagelj and Mrvar), the program for analysis and
visualization of large networks.
The relational constraint is based on neighboring counties
(Ferligoj, Batagelj, 1983).
The maximal method to calculate new dissimilarity between
clusters
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Analyses: Hierarchical clustering with relational constraint
of the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented in
Pajek (Batagelj and Mrvar), the program for analysis and
visualization of large networks.
The relational constraint is based on neighboring counties
(Ferligoj, Batagelj, 1983).
The maximal method to calculate new dissimilarity between
clusters
The tolerant strategy to determine the relation between the
new cluster and other clusters (Batagelj, Ferligoj, Mrvar,
2008).
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Pajek
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Comments
We identified 9 clusters:
4 larger groups
2 groups with older population
3 groups of mostly student population
54 outliers (in cyan color)
Conclusion
References
Clustering of the world countries
Clustering of the 3111 mainland US counties
Female
0.04
0.08
0.12
Female
75
0
5
15
25
35
45
55
65
75
0
5
15
25
35
45
55
65
75
65
55
45
35
25
15
5
0.10 0.08 0.06 0.04 0.02 0.00 0.00
Male
Conclusion
85
Male
85
Female
85
Male
0
Introduction
0.10
0.08
0.06
0.04
0.02
0.00 0.00 0.02 0.04 0.06 0.08 0.10
0.14
0.10
0.06
0.02
0.00
0.05
0.10
0.15
Figure: Pyramids’ shapes of three clusters with two counties
References
Clustering of the world countries
Clustering of the 3111 mainland US counties
Male
Female
75
65
55
45
35
25
15
5
0
5
15
25
35
45
55
65
75
85
Female
85
Male
0
Introduction
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
Figure: Pyramids’ shapes of two largest clusters
Conclusion
References
Clustering of the world countries
Clustering of the 3111 mainland US counties
Male
Conclusion
Female
75
65
55
45
35
25
15
5
0
5
15
25
35
45
55
65
75
85
Female
85
Male
0
Introduction
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
Figure: Pyramids’ shapes of clusters with older population
References
Clustering of the world countries
Clustering of the 3111 mainland US counties
Male
Conclusion
Female
75
65
55
45
35
25
15
5
0
5
15
25
35
45
55
65
75
85
Female
85
Male
0
Introduction
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
0.05
0.04
0.03
0.02
0.01
0.00 0.00
0.01
0.02
0.03
0.04
Figure: Pyramids’ shapes of the two remaining clusters
References
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Conclusion
1
Although the observation period of 10 years was short for the
human life, noticeable changes in shapes can be seen.
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Conclusion
1
Although the observation period of 10 years was short for the
human life, noticeable changes in shapes can be seen.
2
Most of the main four clusters are quite stable through
observed years.
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
Conclusion
1
Although the observation period of 10 years was short for the
human life, noticeable changes in shapes can be seen.
2
Most of the main four clusters are quite stable through
observed years.
3
The results confirm strong influences of local characteristics
(for example universities) on the pyramids’ shapes of smaller
populations.
Introduction
Clustering of the world countries
Clustering of the 3111 mainland US counties
Conclusion
References
References
Andreev, L. and Andreev, M. (2004) Analysis of Population Pyramids by a New Method for Intelligent
Pattern Recognition, Matrixreasonong, Equicom, Inc.
Batagelj V., Ferligoj A. and Mrvar A. (2008): Hierarchical clustering in large networks. Presented at Sunbelt
XXVIII, 22-27. January 2008, St. Pete Beach, Florida, USA.
Ferligoj A. and Batagelj V. (1983): Some types of clustering with relational constraints. Psychometrika,
48(4), p. 541-552.
Kaufman, L. and Rousseeuw, P.J. (1990) Finding Groups in Data: An Introduction to Cluster Analysis,
Wiley, New York.
Pressat, R. (1978) Statistical Demography (Translated and adapted by Damien A. Courtney), Methuen,
University Press, Cambridge.
International Data Base.
http://www.census.gov/ipc/www/idbnew.html
Mrvar, A. and Batagelj, V. (1996-2008) The Pajek program – home page.
http://pajek.imfm.si/
R Development Core Team (2008) R: A Language and Environment for Statistical Computing. R
Foundation for Statistical Computing, Vienna, Austria.
http://www.R-project.org.