# Scatt: Average scattering for clusters - Internal Measure In clv: Cluster Validation Techniques

## Description

Function computes average scattering for clusters.

## Usage

 `1` ```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

`clv.SD` and `clv.SDbw`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# 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) ```

clv documentation built on May 29, 2017, 9:50 a.m.