SIL {fclust}

Silhouette index

Description

Produces the silhouette index. The optimal number of clusters k is is such that the index takes the maximum value.

Usage

 SIL (Xca, U, distance)

Arguments

Xca

Matrix or data.frame

U

Membership degree matrix

distance

If distance=TRUE, Xca is assumed to contain distances/dissimilarities (default: FALSE)

Details

Xca should contain the same dataset used in the clustering algorithm, i.e., if the clustering algorithm is run using standardized data, then SIL should be computed using the same standardized data.
Set distance=TRUE if Xca is a distance/dissimilarity matrix.

Value

sil.obj

Vector containing the silhouette indexes for all the objects

sil

Value of the silhouette index (mean of sil.obj)

Author(s)

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

References

Kaufman L., Rousseeuw P.J., 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

See Also

PC, PE, MPC, SIL.F, XB, 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)
## silhouette index
sil=SIL(clust$Xca,clust$U)