Dens_bw: Inter-cluster density - Internal Measure

In clv: Cluster Validation Techniques

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"

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),
density(x)	- see below.

Let define function f(x,u):

f(x,u) = 0	if dist(x,u) > stdev (stdev is defined in clv.Scatt)
f(x,u) = 1	otherwise

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.

Value

As result Dens_bw value is returned.

Author(s)

Lukasz Nieweglowski

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

clv documentation built on Sept. 28, 2023, 9:06 a.m.