XB {fclust}

Xie and Beni index

Description

Produces the Xie and Beni index. The optimal number of clusters k is is such that the index takes the minimum value.

Usage

 XB (Xca, U, H, m)

Arguments

Xca

Matrix or data.frame

U

Membership degree matrix

H

Prototype matrix

m

Parameter of fuzziness (default: 2)

Details

Xca should contain the same dataset used in the clustering algorithm, i.e., if the clustering algorithm is run using standardized data, then XB should be computed using the same standardized data.
m should be the same parameter of fuzziness used in the clustering algorithm.

Value

xb

Value of the Xie and Beni index

Author(s)

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

References

Xie X.L., Beni G. (1991). A validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841-847.

See Also

PC, PE, MPC, SIL, SIL.F, Fclust, Mc

Examples

## McDonald's data
data(Mc)
names(Mc)
## data normalization by dividing the nutrition facts by the Serving Size (column 1)
for (j in 2:(ncol(Mc)-1))
Mc[,j]=Mc[,j]/Mc[,1]
## removing the column Serving Size
Mc=Mc[,-1]
## fuzzy k-means
## (excluded the factor column Type (last column))
clust=FKM(Mc[,1:(ncol(Mc)-1)],k=6,m=1.5,stand=1)
## Xie and Beni index
xb=XB(clust$Xca,clust$U,clust$H,clust$m)