clv.Dens_bw: Inter-cluster density - Internal Measure

Description

Function computes inter-cluster density.

Usage

clv.DensBw(data, clust, scatt.obj, dist="euclidean")

Arguments

data

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.

scatt.obj

object returned by clv.Scatt function.

dist

chosen metric: "euclidean" (default value), "manhattan", "correlation"

Value

As result Dens_bw value is returned.

Details

The definition of inter-cluster density is given by equation:

Dens_bw = 1/(|C|*(|C|-1)) * sum{forall i in 1:|C|} sum{forall j in 1:|C| and j != i} density(u(i,j))/max{density(v(i)), density(v(j))}

where:

|C|

- number of clusters,

v(i), v(j)

- centers of clusters i and j,

u(i,j)

- middle point of the line segment defined by the clusters' centers v(i), v(j),

Let define function f(x,u):

f(x,u) = 0

if dist(x,u) > stdev (stdev is defined in clv.Scatt)

Function f is used in definition of density(u):

density(u) = sum{forall i in 1:n(i,j)} f(xi,u)

where n(i,j) is the number of objects which belongs to clusters i and j and xi is such object.

This value is used by clv.SDbw.

Examples

Run this code

# 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 Dens_bw index
scatt <- clv.Scatt(iris.data, v.pred)
dens.bw <- clv.DensBw(iris.data, v.pred, scatt)