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

simona.cerne@ef.uni-lj.si2Faculty of Social Sciences

natasa.kejzar@fdv.uni-lj.si3Faculty of Mathematics and Physicsvladimir.batagelj@fmf.uni-lj.si

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.

!"#$%&'()*$*+,%$'"-).*/001!"#$%&'()'&)*'+,-%.)/001 !"

!"#$%&%'()#*"+,%#'(!"+-.)!"!"#$%&'(&)*$+,$!-(

!"#$%&'()*&+,-./,0/,1..0 2+3#4%,&,(#*5,1..02'46 !"#$%&'(")*+,-*.-*/,,. 0"1)*()*/,,.2&)3 7+89% :#4)9# 7+89% :#4)9#

45) 6"45) 45) 6"45)

; <"'4= >'"%3' ?59' @%9'1 A'4#B C4' A'4 D&'- C4*+4 E"#4' @#3= ?'4'F E&'4 >'3' @%9 G'"'H A+:#I A+:#I' J'4 ?'"'0 C4K"#3 >+3=' J%6' C4'L >'"9+ <"'4M%89' >'*%= N'('O A+:# >'*#3' C(3': D7'P >'"3'4 @'*'8' Q'&%K @#:'

;. !#*#" E&'4' R'8S#" @%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%

$,)/-0"1'(0%+$%+$)(1)(!-2+'(",%'(!-2+'34$-!"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

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

Afg

hani

stan

Eth

iopi

aG

ambi

a, T

heG

uine

aE

ritre

aS

udan

Ang

ola

Nig

eria

Moz

ambi

que

Sie

rra

Leon

eC

omor

osG

uine

a−B

issa

uC

ote

d'Iv

oire

Djib

outi

Bel

ize

Gha

naP

akis

tan

Cen

tral

Afr

ican

Rep

ublic

Equ

ator

ial G

uine

aG

abon

Cam

eroo

nS

eneg

alG

uate

mal

aLa

osH

aiti

Som

alia

Cam

bodi

aT

ajik

ista

nC

ape

Ver

deB

huta

nP

arag

uay

Bol

ivia

Nam

ibia

Nep

alLi

beria

El S

alva

dor

Leso

tho

Pap

ua N

ew G

uine

aV

anua

tuE

ast T

imor

Kiri

bati

Nau

ruB

otsw

ana

Zim

babw

eM

arsh

all I

slan

dsM

icro

nesi

a, F

eder

ated

Sta

tes

ofH

ondu

ras

Sw

azila

ndN

icar

agua

Ken

yaR

wan

daIr

aqS

yria

Jord

anS

amoa

Ton

gaB

enin

Tan

zani

aZ

ambi

aT

ogo

Sol

omon

Isla

nds

Bur

kina

Fas

oM

ali

Sao

Tom

e an

d P

rinci

peY

emen

Uga

nda

Bur

undi

Wes

tern

Sah

ara

Con

go (

Kin

shas

a)M

alaw

iC

ongo

(B

razz

avill

e)M

adag

asca

rM

aurit

ania

Nig

erM

aldi

ves

Cha

dM

ayot

te

Alb

ania

Chi

leT

rinid

ad a

nd T

obag

oA

rgen

tina

Isra

elA

rmen

iaK

azak

hsta

nA

ngui

llaC

hina

Mau

ritiu

sS

ri La

nka

Tha

iland

Bar

bado

sK

orea

, Sou

thT

aiw

anC

uba

Sai

nt H

elen

aK

orea

, Nor

thN

ethe

rland

s A

ntill

esS

aint

Pie

rre

and

Miq

uelo

nA

ntig

ua a

nd B

arbu

daB

rune

iT

urks

and

Cai

cos

Isla

nds

Gre

enla

ndP

alau

Virg

in Is

land

s, B

ritis

hM

acau

S.A

.R.

Bah

rain

Kuw

ait

Qat

arU

nite

d A

rab

Em

irate

s

Alg

eria

Liby

aE

cuad

orM

oroc

coP

hilip

pine

sJa

mai

caM

ongo

liaV

ietn

amK

yrgy

zsta

nT

urkm

enis

tan

Uzb

ekis

tan

Ban

glad

esh

Iran

Gre

nada

Om

anS

audi

Ara

bia

Aze

rbai

jan

Tuv

alu

Dom

inic

aS

aint

Kitt

s an

d N

evis

Bah

amas

, The

Col

ombi

aN

ew C

aled

onia

Cos

ta R

ica

Fre

nch

Pol

ynes

iaP

anam

aD

omin

ican

Rep

ublic

Per

uIn

dia

Ven

ezue

laE

gypt

Mex

ico

Mal

aysi

aF

ijiS

outh

Afr

ica

Bra

zil

Tur

key

Indo

nesi

aB

urm

aT

unis

iaG

uyan

aS

aint

Luc

iaS

aint

Vin

cent

and

the

Gre

nadi

nes

Sey

chel

les

Sur

inam

eLe

bano

nM

onts

erra

t

And

orra

Hon

g K

ong

S.A

.R.

Sin

gapo

reA

ruba

Cay

man

Isla

nds

Aus

tral

iaC

anad

aU

nite

d S

tate

sB

erm

uda

Liec

hten

stei

nA

ustr

iaG

uern

sey

Italy

San

Mar

ino

Ger

man

yJe

rsey

Luxe

mbo

urg

Sw

itzer

land

Net

herla

nds

Den

mar

kN

orw

ayU

nite

d K

ingd

omIs

le o

f Man

Sw

eden

Mon

aco

Bel

arus

Rus

sia

Geo

rgia

Lith

uani

aE

ston

iaLa

tvia

Ukr

aine

Bos

nia

and

Her

zego

vina

Bel

gium

Fra

nce

Fin

land

Gib

ralta

rC

roat

iaS

love

nia

Bul

garia

Japa

nC

zech

Rep

ublic

Hun

gary

Gre

ece

Por

tuga

lS

pain

Cyp

rus

Icel

and

New

Zea

land

Irel

and

Uru

guay

Far

oe Is

land

sM

aced

onia

Mon

tene

gro

Mol

dova

Mal

taP

olan

dS

lova

kia

Rom

ania

Ser

bia0.

00.

20.

40.

60.

8

Dendrogram of agnes(x = d2, method = "ward")

agnes (*, "ward")d2

Hei

ght

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

Afg

hani

stan

Gam

bia,

The

Gui

nea

Ang

ola

Eth

iopi

aM

adag

asca

rE

ritre

aS

ierr

a Le

one

Mal

dive

sW

est B

ank

Com

oros

Moz

ambi

que

Djib

outi

Libe

riaM

ayot

teS

omal

iaO

man

Ben

inT

anza

nia

Zam

bia

Bur

kina

Fas

oC

ongo

(K

insh

asa)

Bur

undi

Mal

awi

Sao

Tom

e an

d P

rinci

peM

ali

Yem

enC

had

Con

go (

Bra

zzav

ille)

Mau

ritan

iaW

este

rn S

ahar

aN

iger

Gaz

a S

trip

Uga

nda

Bel

ize

Hon

dura

sG

hana

Nam

ibia

Nep

alP

akis

tan

Sam

oaC

ote

d'Iv

oire

Iraq

Ken

yaR

wan

daM

arsh

all I

slan

dsC

amer

oon

Sen

egal

Laos

Nig

eria

Gui

nea−

Bis

sau

Sol

omon

Isla

nds

Sud

anC

entr

al A

fric

an R

epub

licE

quat

oria

l Gui

nea

Gab

onG

uate

mal

aH

aiti

Tog

oS

waz

iland

Alb

ania

Sai

nt K

itts

and

Nev

isA

zerb

aija

nD

omin

ica

Tuv

alu

Arm

enia

Kaz

akhs

tan

Trin

idad

and

Tob

ago

Bah

amas

, The

Col

ombi

aC

osta

Ric

aIn

done

sia

Pan

ama

New

Cal

edon

iaD

omin

ican

Rep

ublic

Indi

aE

gypt

Mal

aysi

aM

exic

oP

eru

Ven

ezue

la Fiji

Sou

th A

fric

aB

razi

lT

urke

yF

renc

h P

olyn

esia

Bur

ma

Tun

isia

Guy

ana

Sai

nt V

ince

nt a

nd th

e G

rena

dine

sS

aint

Luc

iaS

urin

ame

Sey

chel

les

Leba

non

Mon

tser

rat

Kuw

ait

Sau

di A

rabi

aA

lger

iaM

ongo

liaV

ietn

amK

yrgy

zsta

nU

zbek

ista

nIr

anB

angl

ades

hG

rena

daJo

rdan

Liby

aA

mer

ican

Sam

oaB

huta

nP

arag

uay

Kiri

bati

Pap

ua N

ew G

uine

aB

oliv

iaLe

soth

oE

l Sal

vado

rP

hilip

pine

sT

urkm

enis

tan

Ecu

ador

Mor

occo

Van

uatu

Jam

aica

Bot

swan

aN

icar

agua

Syr

iaT

ajik

ista

nZ

imba

bwe

Cam

bodi

aT

onga

Cap

e V

erde

Eas

t Tim

orN

auru

Mic

rone

sia,

Fed

erat

ed S

tate

s of

And

orra

Hon

g K

ong

S.A

.R.

Sin

gapo

reM

acau

S.A

.R.

Aru

baC

aym

an Is

land

sB

erm

uda

Liec

hten

stei

nA

ustr

alia

Uni

ted

Sta

tes

Can

ada

Bel

arus

Rus

sia

Est

onia

Latv

iaU

krai

neB

osni

a an

d H

erze

govi

naG

eorg

iaLi

thua

nia

Mal

taS

erbi

aP

olan

dS

lova

kia

Rom

ania

Mol

dova

Mon

tene

gro

Aus

tria

Sw

itzer

land

Bel

gium

Luxe

mbo

urg

Net

herla

nds

Jers

eyG

erm

any

Italy

San

Mar

ino

Den

mar

kS

wed

enG

uern

sey

Isle

of M

anF

ranc

eU

nite

d K

ingd

omN

orw

ayF

inla

ndG

ibra

ltar

Mon

aco

Bul

garia

Cze

ch R

epub

licH

unga

ryC

roat

iaS

love

nia

Gre

ece

Spa

inP

ortu

gal

Japa

n

Ang

uilla

Chi

naC

hile

Mau

ritiu

sS

ri La

nka

Tha

iland

Bar

bado

sK

orea

, Sou

thT

aiw

anV

irgin

Isla

nds,

Brit

ish

Cub

aS

aint

Hel

ena

Arg

entin

aIs

rael

Cyp

rus

Icel

and

Irel

and

Pue

rto

Ric

oM

aced

onia

New

Zea

land

Uru

guay

Far

oe Is

land

sK

orea

, Nor

thN

ethe

rland

s A

ntill

esS

aint

Pie

rre

and

Miq

uelo

nV

irgin

Isla

nds

Ant

igua

and

Bar

buda

Bru

nei

Gua

mT

urks

and

Cai

cos

Isla

nds

Bah

rain

Pal

auG

reen

land

Qat

arN

orth

ern

Mar

iana

Isla

nds

Uni

ted

Ara

b E

mira

tes0.

00.

20.

40.

60.

81.

0

Dendrogram of agnes(x = d2, method = "ward")

agnes (*, "ward")d2

Hei

ght

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

Ang

ola

Gam

bia,

The

Mad

agas

car

Gui

nea

Mau

ritan

iaW

este

rn S

ahar

aS

ierr

a Le

one

Djib

outi

Libe

riaC

omor

osM

ozam

biqu

eM

aldi

ves

Wes

t Ban

kM

ayot

teS

omal

iaO

man

Ben

inT

anza

nia

Eth

iopi

aE

ritre

aC

entr

al A

fric

an R

epub

licH

aiti

Tog

oG

uate

mal

aC

amer

oon

Laos

Equ

ator

ial G

uine

aG

abon

Gui

nea−

Bis

sau

Nig

eria

Sen

egal

Cot

e d'

Ivoi

reIr

aqS

olom

on Is

land

sS

udan

Ken

yaR

wan

daB

urki

na F

aso

Bur

undi

Con

go (

Bra

zzav

ille)

Con

go (

Kin

shas

a)G

aza

Str

ipS

ao T

ome

and

Prin

cipe

Nig

erC

had

Mal

iU

gand

aM

alaw

iY

emen

Zam

bia

Ban

glad

esh

Mar

shal

l Isl

ands

Bel

ize

Hon

dura

sG

hana

Nep

alP

akis

tan

Sam

oaB

huta

nP

arag

uay

Kiri

bati

Pap

ua N

ew G

uine

aB

oliv

iaJa

mai

caE

l Sal

vado

rP

hilip

pine

sT

urkm

enis

tan

Bot

swan

aLe

soth

oN

amib

iaC

ambo

dia

Ton

gaN

icar

agua

Taj

ikis

tan

Syr

iaC

ape

Ver

deE

ast T

imor

Mic

rone

sia,

Fed

erat

ed S

tate

s of

Nau

ruS

waz

iland

Zim

babw

eG

rena

daJo

rdan

Liby

aS

audi

Ara

bia

Alg

eria

Mon

golia

Iran

Aze

rbai

jan

Vie

tnam

Bra

zil

Tur

key

Fre

nch

Pol

ynes

iaB

urm

aG

uyan

aS

aint

Vin

cent

and

the

Gre

nadi

nes

Tun

isia

Bru

nei

Sai

nt L

ucia

Sur

inam

eS

eych

elle

sLe

bano

nM

onts

erra

tA

mer

ican

Sam

oaT

urks

and

Cai

cos

Isla

nds

Bah

amas

, The

Cos

ta R

ica

New

Cal

edon

iaG

uam

Col

ombi

aIn

done

sia

Pan

ama

Mex

ico

Per

uD

omin

ican

Rep

ublic

Mal

aysi

aV

enez

uela

Egy

ptIn

dia

Fiji

Ecu

ador

Mor

occo

Van

uatu

Kyr

gyzs

tan

Uzb

ekis

tan

Sou

th A

fric

aT

uval

uN

orth

ern

Mar

iana

Isla

nds

Kuw

ait

Uni

ted

Ara

b E

mira

tes

Alb

ania

Sai

nt K

itts

and

Nev

isD

omin

ica

Arg

entin

aIs

rael

Ang

uilla

Virg

in Is

land

s, B

ritis

hC

hile

Sri

Lank

aM

aurit

ius

Tha

iland

Arm

enia

Kaz

akhs

tan

Trin

idad

and

Tob

ago

Ant

igua

and

Bar

buda

Pal

auB

ahra

inG

reen

land

Qat

arA

ruba

Ber

mud

aC

aym

an Is

land

sV

irgin

Isla

nds

Aus

tral

iaU

nite

d S

tate

sC

ypru

sIc

elan

dP

uert

o R

ico

Mac

edon

iaF

aroe

Isla

nds

Irel

and

New

Zea

land

Uru

guay

Bar

bado

sK

orea

, Sou

thT

aiw

anS

aint

Hel

ena

Chi

naC

uba

Kor

ea, N

orth

Net

herla

nds

Ant

illes

Sai

nt P

ierr

e an

d M

ique

lon

Hon

g K

ong

S.A

.R.

Sin

gapo

reM

acau

S.A

.R.

And

orra

Jers

eyA

ustr

iaS

witz

erla

ndG

uern

sey

Ger

man

yIta

lyS

an M

arin

oJa

pan

Mon

aco

Bel

gium

Uni

ted

Kin

gdom

Fra

nce

Isle

of M

anD

enm

ark

Nor

way

Fin

land

Gib

ralta

rS

wed

enB

osni

a an

d H

erze

govi

naC

anad

aLu

xem

bour

gN

ethe

rland

sLi

echt

enst

ein

Bel

arus

Rus

sia

Ukr

aine

Geo

rgia

Est

onia

Latv

iaLi

thua

nia

Mol

dova

Mon

tene

gro

Pol

and

Slo

vaki

aB

ulga

riaC

zech

Rep

ublic

Hun

gary

Cro

atia

Slo

veni

aM

alta

Ser

bia

Rom

ania

Gre

ece

Spa

inP

ortu

gal0.

00.

20.

40.

60.

81.

0

Dendrogram of agnes(x = d2, method = "ward")

agnes (*, "ward")d2

Hei

ght

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

20010

1020

3040

5060

7080

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

2006

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

010

2030

4050

6070

80

0.10 0.06 0.02

Male

0.00 0.04 0.08

Female

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

5565

7585

0.10 0.08 0.06 0.04 0.02 0.00

Male

0.00 0.02 0.04 0.06 0.08 0.10

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

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 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.