R: Average scattering for clusters - Internal Measure

clv.Scatt {clv} | R Documentation

## Average scattering for clusters - Internal Measure

### Description

Function computes average scattering for clusters.

### Usage

    clv.Scatt(data, clust, dist="euclidean")

### Arguments

`data` | `numeric matrix` or `data.frame` where columns correspond to variables and rows to observations
`clust` | integer `vector` with information about cluster id the object is assigned to. If vector is not integer type, it will be coerced with warning.
`dist` | choosen metric: "euclidean" (default value), "manhattan", "correlation"

### Details

Let scatter for set X assigned as sigma(X) be defined as vector of variances computed for particular dimensions. Average scattering for clusters is defined as:

`Scatt` = (1/|C|) * sum{forall i in 1:|C|} ||sigma(Ci)||/||sigma(X)||

where:

|C| | - number of clusters,
i | - cluster id,
Ci | - cluster with id 'i',
X | - set with all objects,
||x|| | - sqrt(x*x').

Standard deviation is defined as:

`stdev` = (1/|C|) * sqrt( sum{forall i in 1:|C|} ||sigma(Ci)|| )

### Value

As result `list` with three values is returned.

`Scatt` | - average scattering for clusters value,
`stdev` | - standard deviation value,
`cluster.center` | - numeric `matrix` where columns correspond to variables and rows to cluster centers.

### Author(s)

Lukasz Nieweglowski

### References

M. Haldiki, Y. Batistakis, M. Vazirgiannis On Clustering Validation Techniques, http://citeseer.ist.psu.edu/513619.html

### See Also

`clv.SD` and `clv.SDbw`

### Examples

    # load and prepare data
    library(clv)
    data(iris)
    iris.data <- iris[,1:4]

    # cluster data
    agnes.mod <- agnes(iris.data) # create cluster tree
    v.pred <- as.integer(cutree(agnes.mod,5)) # "cut" the tree

    # compute Scatt index
    scatt <- clv.Scatt(iris.data, v.pred)

[Package clv version 0.3-2.2 Index]