# Dis: Total separation between clusters - Internal Measure In clv: Cluster Validation Techniques

## Description

Function computes total separation between clusters.

## Usage

 `1` ```clv.Dis(cluster.center) ```

## Arguments

 `cluster.center` `numeric matrix` or `data.frame` where columns correspond to variables and rows cluster centers.

## Details

The definition of total separation between clusters is given by equation:

`Dis` = (Dmax/Dmin) * sum{forall i in 1:|C|} 1 /( sum{forall j in 1:|C|} ||vi - vj|| )

where:

 |C| - number of clusters, vi, vj - centers of clusters i and j, Dmax - defined as: max{||vi - vj||: vi,vj - centers of clusters }, Dmin - defined as: min{||vi - vj||: vi,vj - centers of clusters }, ||x|| - means: sqrt(x*x').

This value is a part of `clv.SD` and `clv.SDbw`.

## Value

As result `Dis` value is returned.

## 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 12``` ```# 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 Dis index scatt <- clv.Scatt(iris.data, v.pred) dis <- clv.Dis(scatt\$cluster.center) ```

### Example output

```Loading required package: cluster