fs: Fukuyama-Sugeno Index
In zcebeci/fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

View source: R/fs.R

fs	R Documentation

Fukuyama-Sugeno Index

Description

Computes the Fukuyama-Sugeno (Fukuyama & Sugeno, 1989) index for validating the result of a fuzzy and/or possibilistic cluster analysis.

Usage

fs(x, u, v, m, t=NULL, eta, tidx="f")

Arguments

`x`	an object of class ‘ppclust’ containing the clustering results from a fuzzy clustering algorithm in the package ppclust. Alternatively, a numeric data frame or matrix containing the data set.
`u`	a numeric data frame or matrix containing the fuzzy membership values. It should be specified if `x` is not an object of ‘ppclust’.
`v`	a numeric data frame or matrix containing the cluster prototypes. It should be specified if `x` is not an object of ‘ppclust’.
`t`	a numeric data frame or matrix containing the cluster prototypes. It should be specified if `x` is not an object of ‘ppclust’ and the option e or g is assigned to `tidx`.
`m`	a number specifying the fuzzy exponent. It should be specified if `x` is not an object of ‘ppclust’.
`eta`	a number specifying the typicality exponent. It should be specified if `x` is not an object of ‘ppclust’ and `tidx` is either e or g.
`tidx`	a character specifying the type of index. The default is ‘f’ for fuzzy index. The other options are ‘e’ for extended and ‘g’ for generalized index.

Details

In the Fukuyama-Sugeno index by (Fukuyama & Sugeno, 1989), the sum of inter- and intra-cluster differences are used to define the index formula as follows:

I_{FS}=∑\limits_{i=1}^n ∑\limits_{j=1}^k u_{ij}^m \; (d_{ij}^2 - ||\vec{v_j}-\bar{v}||^2)

The first term in the above equation measures the compactness of the clusters while the second term measures the distances of the clusters representatives (Halkidi et al, 2002b). The minimum I_{FS} indicates the optimal clustering.

Value

`fs`	FS index if `tidx` is ‘f’
`fs.e`	extended FS index if `tidx` is ‘e’
`fs.g`	generalized FS index if `tidx` is ‘g’

Author(s)

Zeynel Cebeci

References

Fukuyama, Y. & Sugeno, M. (1989). A new method of choosing the number of cluster for the fuzzy c-means method, Proc. of the 5th Fuzzy Systems Symp., 247-250.

Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2002b). Clustering validity checking methods: part II. ACM Sigmod Record, 31(3):19-27. <doi:10.1145/601858.601862>

Examples

# Load the dataset iris and use the first four feature columns 
data(iris)
x <- iris[,1:4]

# For 3 clusters, run FCM algorithm in the package ppclust 
res.fcm <- ppclust::fcm(x, centers=3)

# Compute the FS index using ppclust object
idx <- fs(res.fcm)
print(idx)
 
# Compute the FS index using X,U and V matrices
idx <- fs(res.fcm$x, res.fcm$u, res.fcm$v, m=2)
print(idx)

zcebeci/fcvalid documentation built on Oct. 4, 2022, 9:01 p.m.