MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C51DE6.3A142710" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C51DE6.3A142710 Content-Location: file:///C:/E0F66375/population-liuxu.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Survey on U.S Population - A Clustering View

# 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.

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