SIL.F {fclust}

Fuzzy silhouette index

Description

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

Usage

 SIL.F (Xca, U, alpha, distance)

Arguments

Xca

Matrix or data.frame

U

Membership degree matrix

alpha

Weighting coefficient (default: 1)

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.F should be computed using the same standardized data.
Set distance=TRUE if Xca is a distance/dissimilarity matrix.

Value

sil.f

Value of the fuzzy silhouette index

Author(s)

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

References

Campello R.J.G.B., Hruschka E.R., 2006. A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Sets and Systems, 157, 2858-2875.

See Also

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