e1071 (version 1.5-20)

fclustIndex: Fuzzy Cluster Indexes (Validity/Performance Measures)

Description

Calculates the values of several fuzzy validity measures. The values of the indexes can be independently used in order to evaluate and compare clustering partitions or even to determine the number of clusters existing in a data set.

Usage

fclustIndex(y, x, index = "all")

Arguments

y

An object of a fuzzy clustering result of class "fclust"

x

Data matrix

index

The validity measures used: "gath.geva", "xie.beni", "fukuyama.sugeno", "partition.coefficient", "partition.entropy", "proportion.exponent", "separation.index"

Value

• Returns a vector with the validity measures values.

Details

The validity measures and a short description of them follows, where $N$ is the number of data points, $u_{ij}$ the values of the membership matrix, $v_j$ the centers of the clusters and $k$ te number of clusters. [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

References

James C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, 1981, NY. L. X. Xie and G. Beni, Validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 3, n. 8, p. 841-847, 1991. I. Gath and A. B. Geva, Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, n. 7, p. 773-781, 1989. Y. Fukuyama and M. Sugeno, A new method of choosing the number of clusters for the fuzzy $c$-means method, Proc. 5th Fuzzy Syst. Symp., p. 247-250, 1989 (in japanese).

See Also

cmeans

Examples

# a 2-dimensional example
x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=1,sd=0.3),ncol=2))
cl<-cmeans(x,2,20,verbose=TRUE,method="cmeans")
resultindexes <- fclustIndex(cl,x, index="all")
resultindexes