Xie and Beni index
Produces the Xie and Beni index. The optimal number of clusters k is is such that the index takes the minimum value.
XB (Xca, U, H, m)
Xca |
Matrix or data.frame |
U |
Membership degree matrix |
H |
Prototype matrix |
m |
Parameter of fuzziness (default: 2) |
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.
xb |
Value of the Xie and Beni index |
Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini
Xie X.L., Beni G. (1991). A validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841-847.
## 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)
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