#+TITLE: Rapport package team
#+AUTHOR: K-means cluster
#+DATE: 2011-04-26 20:25 CET
** Description
K-means clustering with automatically estimated number of clusters
**** Introduction
[[http://en.wikipedia.org/wiki/K-means_clustering][K-means Clustering]]
is a specific and one of the most widespread method of
[[http://en.wikipedia.org/wiki/Cluster_analysis][clustering]]. With
clustering we want to divide our data into groups, which in the objects
are similar to each other. K-means clustering is specified in the way,
here we set the number of groups we want to make. In our case we will
take into account the following variables: /Age/, /Internet usage for
educational purposes (hours per day)/ and /Internet usage in leisure
time (hours per day)/, to find out which observations are the nearest to
each other.
**** References
J. B. MacQueen (1967). /"Some Methods for classification and Analysis of
Multivariate Observations, Proceedings of 5-th Berkeley Symposium on
Mathematical Statistics and Probability"/. 1:281-297
**** Determining the number of clusters
As it was mentioned above, the speciality of the K-means Cluster method
is to set the number of groups we want to produce.
Let's see how to decide which is the ideal number of them!
[[plots/KMeansCluster.tpl-1-hires.png][[[plots/KMeansCluster.tpl-1.png]]]]
We can figure out that, as we see how much the Within groups sum of
squares decreases if we set a higher number of the groups. So the
smaller the difference the smaller the gain we can do with increasing
the number of the clusters (thus in this case the larger decreasing
means the bigger gain).
The ideal number of clusters seems to be /2/.
**** Cluster means
The method of the K-means clustering starts with the step to set k
number of centorids which could be the center of the groups we want to
form. After that there comes several iterations, meanwhile the ideal
centers are being calculated.
The centroids are the observations which are the nearest in average to
all the other observations of their group. But it could be also
interesting which are the typical values of the clusters! One way to
figure out these typical values is to see the group means. The /2/
cluster averages are:
| | age | edu | leisure |
|---------------+-----------+----------+-----------|
| *1.Cluster* | 0.4092 | 1.285 | 0.9275 |
| *2.Cluster* | -0.1251 | -0.393 | -0.2837 |
The size of the above clusters are: /141/ and /461/.
**** Results
On the chart below we can see the produced groups. To distinct which
observation is related to which cluster each of the objects from the
same groups have the same figure and there is a circle which shows the
border of the clusters.
[[plots/KMeansCluster.tpl-2-hires.png][[[plots/KMeansCluster.tpl-2.png]]]]
** Description
K-means clustering with automatically estimated number of clusters
**** Introduction
[[http://en.wikipedia.org/wiki/K-means_clustering][K-means Clustering]]
is a specific and one of the most widespread method of
[[http://en.wikipedia.org/wiki/Cluster_analysis][clustering]]. With
clustering we want to divide our data into groups, which in the objects
are similar to each other. K-means clustering is specified in the way,
here we set the number of groups we want to make. In our case we will
take into account the following variables: /drat/, /cyl/, /wt/ and
/mpg/, to find out which observations are the nearest to each other.
**** References
J. B. MacQueen (1967). /"Some Methods for classification and Analysis of
Multivariate Observations, Proceedings of 5-th Berkeley Symposium on
Mathematical Statistics and Probability"/. 1:281-297
**** Determining the number of clusters
As it was mentioned above, the speciality of the K-means Cluster method
is to set the number of groups we want to produce.
Let's see how to decide which is the ideal number of them!
[[plots/KMeansCluster.tpl-3-hires.png][[[plots/KMeansCluster.tpl-3.png]]]]
We can figure out that, as we see how much the Within groups sum of
squares decreases if we set a higher number of the groups. So the
smaller the difference the smaller the gain we can do with increasing
the number of the clusters (thus in this case the larger decreasing
means the bigger gain).
The ideal number of clusters seems to be /2/.
**** Cluster means
The method of the K-means clustering starts with the step to set k
number of centorids which could be the center of the groups we want to
form. After that there comes several iterations, meanwhile the ideal
centers are being calculated.
The centroids are the observations which are the nearest in average to
all the other observations of their group. But it could be also
interesting which are the typical values of the clusters! One way to
figure out these typical values is to see the group means. The /2/
cluster averages are:
| | drat | cyl | wt | mpg |
|---------------+-----------+----------+-----------+-----------|
| *1.Cluster* | 0.838 | -1.053 | -0.8794 | 0.946 |
| *2.Cluster* | -0.4904 | 0.6649 | 0.3078 | -0.5118 |
| *3.Cluster* | -1.016 | 1.015 | 2.169 | -1.37 |
The size of the above clusters are: /13/, /16/ and /3/.
**** Results
On the chart below we can see the produced groups. To distinct which
observation is related to which cluster each of the objects from the
same groups have the same figure and there is a circle which shows the
border of the clusters.
[[plots/KMeansCluster.tpl-4-hires.png][[[plots/KMeansCluster.tpl-4.png]]]]
** Description
K-means clustering with automatically estimated number of clusters
**** Introduction
[[http://en.wikipedia.org/wiki/K-means_clustering][K-means Clustering]]
is a specific and one of the most widespread method of
[[http://en.wikipedia.org/wiki/Cluster_analysis][clustering]]. With
clustering we want to divide our data into groups, which in the objects
are similar to each other. K-means clustering is specified in the way,
here we set the number of groups we want to make. In our case we will
take into account the following variables: /drat/, /cyl/, /wt/ and
/mpg/, to find out which observations are the nearest to each other.
**** References
J. B. MacQueen (1967). /"Some Methods for classification and Analysis of
Multivariate Observations, Proceedings of 5-th Berkeley Symposium on
Mathematical Statistics and Probability"/. 1:281-297
**** Determining the number of clusters
As it was mentioned above, the speciality of the K-means Cluster method
is to set the number of groups we want to produce.
As you set, there will be a /7/-means cluster analysis provided.
**** Cluster means
The method of the K-means clustering starts with the step to set k
number of centorids which could be the center of the groups we want to
form. After that there comes several iterations, meanwhile the ideal
centers are being calculated.
The centroids are the observations which are the nearest in average to
all the other observations of their group. But it could be also
interesting which are the typical values of the clusters! One way to
figure out these typical values is to see the group means. The cluster
averages are:
| | drat | cyl | wt | mpg |
|---------------+-----------+-----------+------------+------------|
| *1.Cluster* | -1.265 | -0.105 | 0.1229 | -0.05652 |
| *2.Cluster* | -0.8294 | 1.015 | 0.8644 | -0.837 |
| *3.Cluster* | 0.3898 | -1.225 | -0.04829 | 0.5823 |
| *4.Cluster* | 0.5925 | 0.08166 | -0.1684 | -0.1671 |
| *5.Cluster* | 0.8247 | -1.225 | -1.376 | 1.81 |
| *6.Cluster* | 2.026 | -1.225 | -1.369 | 1.346 |
| *7.Cluster* | 0.5426 | -1.225 | -0.7109 | 0.3002 |
The size of the above clusters are: /2/, /13/, /2/, /6/, /4/, /2/ and
/3/.
**** Results
On the chart below we can see the produced groups. To distinct which
observation is related to which cluster each of the objects from the
same groups have the same figure and there is a circle which shows the
border of the clusters.
[[plots/KMeansCluster.tpl-5-hires.png][[[plots/KMeansCluster.tpl-5.png]]]]
--------------
This report was generated with [[http://www.r-project.org/][R]] (3.0.1)
and [[http://rapport-package.info/][rapport]] (0.51) in /8.181/ sec on
x86\_64-unknown-linux-gnu platform.
[[images/logo.png]]