Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Clustering of Population Pyramids
Simona Korenjak-Černe1 Nataša Kejžar2Vladimir Batagelj3
University of Ljubljana, Slovenia1Faculty of Economics
[email protected] of Social Sciences
[email protected] of Mathematics and [email protected]
COMPSTAT 2008,Porto, Portugal, August 24-29, 2008
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Outline1 Introduction
What is population pyramidMain pyramids’ shapesDemographic Transition Model
2 Clustering of the world countriesData: Population pyramids of the world countriesAnalyses: Hierarchical clustering of the world countriesResults
Clustering of the 215 world countries from the year 1996Clustering of the 222 world countries from the year 2001Clustering of the 222 world countries from the year 2006Movements among four main clusters for the years 1996, 2001 and2006
3 Clustering of the 3111 mainland US countiesData: Population pyramids of the US countiesAnalyses: Hierarchical clustering with relational constraint of the3111 mainland US countiesResults
4 Conclusion5 References
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Outline1 Introduction
What is population pyramidMain pyramids’ shapesDemographic Transition Model
2 Clustering of the world countriesData: Population pyramids of the world countriesAnalyses: Hierarchical clustering of the world countriesResults
Clustering of the 215 world countries from the year 1996Clustering of the 222 world countries from the year 2001Clustering of the 222 world countries from the year 2006Movements among four main clusters for the years 1996, 2001 and2006
3 Clustering of the 3111 mainland US countiesData: Population pyramids of the US countiesAnalyses: Hierarchical clustering with relational constraint of the3111 mainland US countiesResults
4 Conclusion5 References
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Outline1 Introduction
What is population pyramidMain pyramids’ shapesDemographic Transition Model
2 Clustering of the world countriesData: Population pyramids of the world countriesAnalyses: Hierarchical clustering of the world countriesResults
Clustering of the 215 world countries from the year 1996Clustering of the 222 world countries from the year 2001Clustering of the 222 world countries from the year 2006Movements among four main clusters for the years 1996, 2001 and2006
3 Clustering of the 3111 mainland US countiesData: Population pyramids of the US countiesAnalyses: Hierarchical clustering with relational constraint of the3111 mainland US countiesResults
4 Conclusion5 References
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Outline1 Introduction
What is population pyramidMain pyramids’ shapesDemographic Transition Model
2 Clustering of the world countriesData: Population pyramids of the world countriesAnalyses: Hierarchical clustering of the world countriesResults
Clustering of the 215 world countries from the year 1996Clustering of the 222 world countries from the year 2001Clustering of the 222 world countries from the year 2006Movements among four main clusters for the years 1996, 2001 and2006
3 Clustering of the 3111 mainland US countiesData: Population pyramids of the US countiesAnalyses: Hierarchical clustering with relational constraint of the3111 mainland US countiesResults
4 Conclusion
5 References
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Outline1 Introduction
What is population pyramidMain pyramids’ shapesDemographic Transition Model
2 Clustering of the world countriesData: Population pyramids of the world countriesAnalyses: Hierarchical clustering of the world countriesResults
Clustering of the 215 world countries from the year 1996Clustering of the 222 world countries from the year 2001Clustering of the 222 world countries from the year 2006Movements among four main clusters for the years 1996, 2001 and2006
3 Clustering of the 3111 mainland US countiesData: Population pyramids of the US countiesAnalyses: Hierarchical clustering with relational constraint of the3111 mainland US countiesResults
4 Conclusion5 References
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
What is population pyramidis a very popular presentation ofthe age-sex distribution of thehuman population of a particularregion
It gives picture of a population’sage-sex structure, and can also beused for displaying historical andfuture trends.The shape of the pyramid showsmany demographic, social, andpolitical characteristics of thetime and the region.
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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 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 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 References
Demographic Transition Model
Since the biggest influence on the pyramid’s shape have fertilityand mortality, the explanation of the pyramids’ shapes is oftenrelated to the "Demographic Transition Model" (DTM) thatdescribes the population changes over time (Warren Thompson,1929).
High birth rate;high deathrate; short lifeexpectancy
High birth rate;fall in death rate;slightly longer lifeexpectancy
Declining birthrate; low deathrate; longer lifeexpectancy
Low birth rate;low death rate;longer lifeexpectancy
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 fertilityand mortality, the explanation of the pyramids’ shapes is oftenrelated to the "Demographic Transition Model" (DTM) thatdescribes the population changes over time (Warren Thompson,1929).
High birth rate;high deathrate; short lifeexpectancy
High birth rate;fall in death rate;slightly longer lifeexpectancy
Declining birthrate; low deathrate; longer lifeexpectancy
Low birth rate;low death rate;longer lifeexpectancy
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 fertilityand mortality, the explanation of the pyramids’ shapes is oftenrelated to the "Demographic Transition Model" (DTM) thatdescribes the population changes over time (Warren Thompson,1929).
High birth rate;high deathrate; short lifeexpectancy
High birth rate;fall in death rate;slightly longer lifeexpectancy
Declining birthrate; low deathrate; longer lifeexpectancy
Low birth rate;low death rate;longer lifeexpectancy
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 fertilityand mortality, the explanation of the pyramids’ shapes is oftenrelated to the "Demographic Transition Model" (DTM) thatdescribes the population changes over time (Warren Thompson,1929).
High birth rate;high deathrate; short lifeexpectancy
High birth rate;fall in death rate;slightly longer lifeexpectancy
Declining birthrate; low deathrate; longer lifeexpectancy
Low birth rate;low death rate;longer lifeexpectancy
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, and17 variables for 5-years age groups for womenNormalizedEuclidean distance between corresponding vectors
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, and17 variables for 5-years age groups for women
NormalizedEuclidean distance between corresponding vectors
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, and17 variables for 5-years age groups for womenNormalized
Euclidean distance between corresponding vectors
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, and17 variables for 5-years age groups for womenNormalizedEuclidean 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 yearsfrom 1996 to 2006
Observing how stable are the main clusters over time
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 yearsfrom 1996 to 2006Observing how stable are the main clusters over time
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
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Figure: Clusters of the 215 countries and main pyramids’ shapes for theyear 1996
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
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Figure: Pyramids’s shapes of the most different sub-clusters
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
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Dendrogram of agnes(x = d2, method = "ward")
agnes (*, "ward")d2
Hei
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010
2030
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0.10 0.06 0.02
Male
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Figure: Clusters of the 222 countries and main pyramids’ shapes for theyear 2001
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
010
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Figure: Pyramids’s shapes of the sub-clusters with the biggest chainingefect
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Afg
hani
stan
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Mad
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0.00 0.04 0.08
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010
2030
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6070
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0.10 0.06 0.02
Male
0.00 0.04 0.08
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Figure: Clusters of the 222 countries and main pyramids’ shapes for theyear 2006
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
1996
010
2030
4050
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80
0.10 0.06 0.02
Male
0.00 0.04 0.08
Female
010
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0.00 0.04 0.08
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0.10 0.06 0.02
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Female
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2006
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A B C DFigure: Pyramids’s shapes of four main clusters of the countries for theyears 1996, 2001 and 2006
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
A B C D
1996 77 47 31 6057 20
1 465 25 1
7 532001 60 72 36 54
6026 40 6
5 318 46
2006 86 45 45 46
Figure: Movements presented with the number of countries among fourmain clusters for the years 1996, 2001 and 2006
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, and18 variables for 5-years age groups for womenNormalizedEuclidean distance between corresponding vectors
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 200036 variables: 18 variables for 5-years age groups for men, and18 variables for 5-years age groups for women
NormalizedEuclidean distance between corresponding vectors
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 200036 variables: 18 variables for 5-years age groups for men, and18 variables for 5-years age groups for womenNormalized
Euclidean distance between corresponding vectors
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 200036 variables: 18 variables for 5-years age groups for men, and18 variables for 5-years age groups for womenNormalizedEuclidean distance between corresponding vectors
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Analyses: Hierarchical clustering with relational constraintof the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented inPajek (Batagelj and Mrvar), the program for analysis andvisualization of large networks.
The relational constraint is based on neighboring counties(Ferligoj, Batagelj, 1983).
The maximal method to calculate new dissimilarity betweenclustersThe tolerant strategy to determine the relation between thenew cluster and other clusters (Batagelj, Ferligoj, Mrvar,2008).
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Analyses: Hierarchical clustering with relational constraintof the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented inPajek (Batagelj and Mrvar), the program for analysis andvisualization of large networks.
The relational constraint is based on neighboring counties(Ferligoj, Batagelj, 1983).The maximal method to calculate new dissimilarity betweenclusters
The tolerant strategy to determine the relation between thenew cluster and other clusters (Batagelj, Ferligoj, Mrvar,2008).
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Analyses: Hierarchical clustering with relational constraintof the 3111 mainland US counties
Hierarchical clustering with relational constraints implemented inPajek (Batagelj and Mrvar), the program for analysis andvisualization of large networks.
The relational constraint is based on neighboring counties(Ferligoj, Batagelj, 1983).The maximal method to calculate new dissimilarity betweenclustersThe tolerant strategy to determine the relation between thenew cluster and other clusters (Batagelj, Ferligoj, Mrvar,2008).
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Pajek
Figure: Clustering of US counties in the year 2000 with relationalconstraints
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
Comments
We identified 9 clusters:4 larger groups2 groups with older population3 groups of mostly student population54 outliers (in cyan color)
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
05
1525
3545
5565
7585
0.10 0.08 0.06 0.04 0.02 0.00
Male
0.00 0.04 0.08 0.12
Female
05
1525
3545
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7585
0.10 0.08 0.06 0.04 0.02 0.00
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Female
05
1525
3545
5565
7585
0.14 0.10 0.06 0.02
Male
0.00 0.05 0.10 0.15
Female
Figure: Pyramids’ shapes of three clusters with two counties
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
05
1525
3545
5565
7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04
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05
1525
3545
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7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04
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Figure: Pyramids’ shapes of two largest clusters
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
05
1525
3545
5565
7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04
Female
05
1525
3545
5565
7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04
Female
Figure: Pyramids’ shapes of clusters with older population
Introduction Clustering of the world countries Clustering of the 3111 mainland US counties Conclusion References
05
1525
3545
5565
7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04 0.05
Female
05
1525
3545
5565
7585
0.04 0.03 0.02 0.01 0.00
Male
0.00 0.01 0.02 0.03 0.04
Female
Figure: Pyramids’ shapes of the two remaining clusters
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 thehuman life, noticeable changes in shapes can be seen.
2 Most of the main four clusters are quite stable throughobserved years.
3 The results confirm strong influences of local characteristics(for example universities) on the pyramids’ shapes of smallerpopulations.
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 thehuman life, noticeable changes in shapes can be seen.
2 Most of the main four clusters are quite stable throughobserved years.
3 The results confirm strong influences of local characteristics(for example universities) on the pyramids’ shapes of smallerpopulations.
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 thehuman life, noticeable changes in shapes can be seen.
2 Most of the main four clusters are quite stable throughobserved years.
3 The results confirm strong influences of local characteristics(for example universities) on the pyramids’ shapes of smallerpopulations.
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 IntelligentPattern Recognition, Matrixreasonong, Equicom, Inc.
Batagelj V., Ferligoj A. and Mrvar A. (2008): Hierarchical clustering in large networks. Presented at SunbeltXXVIII, 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. RFoundation for Statistical Computing, Vienna, Austria.
http://www.R-project.org.
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