Survey on=
U.S. po=
pulation
1980~2002
--a Clustering View
Data we have:
Total residential population=
Population by age: <1, 1-4, 5-14=
, 15-24,
25-34, 35-44, 45-54,55-64,65-74,75-84,>85
Fertility Rate
Death Rate
Live Birth
Every one of these is a vector of 23
dimensions (1980~2002). LINK
A bad representation:

Although this
looks fancy, little information can be extracted from this 3D image. <=
/o:p>
Trivial Plot using MATLAB:

&nb=
sp; =
&nb=
sp; =
&nb=
sp; Total Population of =
U.S.
=
This plot
just indicates that =
U.S.
population is growing over years, roughly linear. Can we explore more?=
Find relationship between data using HCE:
Cluster of the
Populations at Different Ages from 1985~2002 to Find the Correlated Ages
What can be inferred from this clus=
tering?
1.
Live birth is mostly rela=
ted to
the population with age <1. This makes sense since live birth makes the
greatest contribution to the life under 1 year old.
2.
The old age has the highe=
st
similarity to the total population. This indicates the problem of population
getting old. In fact the old are the most stable population.
3.
25~34, the most shaky
population, the behavior is different from the whole population, thus they =
are
not clustered together with populations with other ages. The reason might be
the immigrant, people at age 25~34 are eager to come to U.S. to pursue their “U.S. dr=
eam”.
Transpose the data matrix and testify:
&n=
bsp;
=

&nb=
sp; Relationship between “> 85=
8221;
to total population =
&nb=
sp; =
Relationship
between “35~44” to total population
Although it’s surprising, tot=
al
population has linear relationship with population older than 85.Total
population has nearly linear relationship with population 35~44.
More Plot:
=

Relationship
between “25~34” to total population  =
; &n=
bsp; Relationship
between “15~24” to total population
25-34: as the total population grow=
s up,
population of 25~34 increase first and then decrease
15-24: as the total population grow=
s up,
population of 15~24 decrease first and then increase
The inflexion is around 1988~1993. =
What
happened? USSA Decomposition? First Iraq Wa=
r?
Bill Clinton was elected President?
An explanation: The U.S. population=
has a periodic
feature. The population of 15~24 grow to be 25~34 while the whole
population while the whole population grow. When 25~34 reach the peak their
fertilization results in the peak of 15~24 after 15 years. The younger
population follows more vivid periodic changing.
Another interesting observation:

Clusters of Population Structure at
Different Years
The inflexion =
happens
to cluster the profile of population into 2 clusters: before 1992 and after
1992. What’s the main difference between pre-1992 and post-1992 U.S.
population structure? Youngest and oldest population tends grow and keep to=
be
a large number after 1992, 25~34 starts to decrease after 1992.


Tendency of Population “1~4”,
“5~14”, “25~34”
Conclusion on how to use HCE to explore data
relationships:
1.
Once you want to figure o=
ut he
relationship between variables, put them into HCE and find out the nearest
neighbors, they might be tightly correlated, like the population >85 and
total population of =
U.S.
2.
After finding correlated
variables, scatter plot them, they may have linear or quadratic relationshi=
p.
3.
Transposing the 2D data a=
nd do
cluster again may lead to further discovery.
------=_NextPart_01C51DE6.3A142710
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